Observations: How to make them quickly and use them effectively

In competitive programming, the success of a programmer hinges crucially on their ability to observe and analyze problems. This observational phase is a critical yet often undervalued aspect of problem-solving, forming the bedrock upon which efficient solutions are built. It involves not just a superficial understanding of the problem statement, but a deeper analysis of its nuances and underlying patterns. Effective observation can mean the difference between identifying the most suitable algorithms and approaches, or missing out on key insights that could lead to optimal solutions.

Furthermore, the skill of observation extends to recognizing potential pitfalls, understanding constraints, and predicting the behavior of different approaches. This comprehensive strategy not only aids in tailoring solutions more precisely but also in anticipating challenges. For aspiring competitive programmers, refining observational skills is thus as vital as enhancing coding abilities, as it significantly influences the journey from problem understanding to solution implementation. Today, I’ll discuss some tips that can help speed up your observation phase. 

Time Complexity and Constraints

The key to unlocking the most efficient solutions lies in a keen understanding and analysis of the problem's constraints. Constraints are not just arbitrary numbers; they are critical clues pointing towards the nature of the expected solution. The first and most important tip I can offer is to pay close attention to these constraints. They reveal much about the problem, guiding you towards specific approaches and techniques.

It's essential to remember that problem setters design these constraints deliberately. They typically provide just enough time for an optimally efficient solution, with few exceptions. For example, older USACO problems sometimes presented the same problems in higher divisions as in lower ones but with increased limits. In such cases, the time allowed may be more generous than necessary. However, in most scenarios, it’s crucial to work within the strict confines of these constraints.

Here’s a detailed strategy to fully harness the power of problem constraints:

• Document Every Constraint: Start by systematically noting down every constraint applied to each variable. This includes constraints on the number of elements, the range of values these elements can take, and any specific limitations like the values of coordinates. Understanding these constraints helps in framing a precise and efficient approach to the problem.

• Focus on Small Limits: Small limits often hold significant implications. For instance, if you encounter a problem where N = 10^5 and K = 10, it's a strong hint towards a solution with O(NK) or O(NK^2) complexity. Small limits like these are an invitation to creatively nest loops and explore solutions that might otherwise be deemed too complex or inefficient.

• Don’t Overlook Large Limits: Conversely, large limits also carry their own messages. A limit as high as 10^18, for example, suggests that logarithmic approaches might be necessary. Such large numbers typically require strategies that reduce the computational load, such as utilizing logarithms to manage these limits effectively. For example, in the problem Searching For Soulmates, (spoilers) it’s easy to assume that an O(1) solution is necessary, since the constraints are so large, however, this is not necessarily the case. 

Let’s dive into some specific limits and what they could imply:

• N = 1e5, 2e5, 5e5, etc: This range of limits, while offering minimal direct guidance, still tells us something important. It essentially rules out any solution that would involve nested iterations through N due to time constraints. This nudges us towards considering algorithms that operate linearly or include some logarithmic components. If these are coupled with smaller limits, it opens up possibilities to nest loops with N and the smaller limits, prompting thoughts towards such combined approaches. Here, the concept of amortization, which involves spreading out computational costs, becomes extremely relevant; also think about scenarios where loops of N can be nested, but through smart amortization, the overall complexity remains O(N).

• N = 5,000 - 7,500: This is a distinct and telling limit. It essentially warns against attempting algorithms with O(N^2 log N) complexity, as they are likely to cause timeouts. Instead, the focus should shift to O(N^2) algorithms. Here, the aim is to find solutions that involve iterating through N twice in nested loops, without incorporating additional logarithmic factors.

• N = 1,000 - 2,000: In this range, while logarithmic factors such as sorting or binary search are possible, they aren't always necessary. Your algorithmic considerations can include but aren't limited to, methods that incorporate log N factors.

• N = 500: Like the 5,000 - 7,500 range, this limit also suggests an O(N^3) approach. Solutions here should ideally be tailored to fit precisely within this complexity range.

• N = 200: At this level, you are likely looking at either O(N^3) or O(N^3 log N) algorithms. This is a nuanced distinction but an important one in terms of the complexity you can afford in your solution.

• N = 20: This specific limit often indicates the use of bit manipulation, with bitmasking being a prevalent technique. For higher levels like gold and above, this usually translates into bitmask dynamic programming. For lower levels like silver and bronze, it often means iterating over all subsets.

• N = 10: Though not as common, this constraint typically implies solutions involving permutations of elements.

In sum, a nuanced understanding and interpretation of constraints in competitive programming is not just beneficial; it's essential. These constraints guide you towards the most appropriate and efficient algorithms and techniques for a given problem. By tailoring your approach based on these constraints, you can develop solutions that are not only effective but also elegantly aligned with the problem's requirements.

Forced/Optimal Actions in Problem-Solving

An invaluable strategy is to focus on identifying 'forced' actions within a problem. These are actions or steps that you are compelled to take, given the constraints and nature of the problem. They represent truths or necessities that are unchangeable within the context of the problem. By recognizing these forced actions, you establish a robust foundation for further observations and analysis. This approach not only simplifies complex problems but also streamlines the path to finding a solution.

To better grasp this concept, let's delve into an illustrative example. Imagine a scenario where you have an array of positive integers, and your goal is to reduce every element in the array to zero. The only operation available to you is to decrement two adjacent elements by one, and you can repeat this operation as many times as necessary.

At first glance, the problem might seem daunting, with multiple potential starting points for operations. However, upon closer examination, you realize there are 'forced' operations. Consider the leftmost integer in the array, let's say it's 'x'. You are inevitably required to apply the operation to the first two integers 'x' times to reduce the leftmost integer to zero. This is a forced action – one without which the leftmost element can never become zero. Recognizing this forced operation is pivotal. It leads to the realization that all subsequent operations are similarly 'forced', aimed at continually reducing the leftmost non-zero element to zero. By identifying this pattern of forced actions, you effectively outline the entire solution methodology for the problem.

Optimal Actions: A Variant of Forced Actions

Another angle to consider is identifying actions that are 'optimal', which is a common variation in problem-solving. These are actions that, while not strictly forced by the problem's constraints, represent the most efficient path to a solution.

Let’s again take the example of the "Searching For Soulmates" problem. The following content will spoil the problem, so if you have not solved it yet and desire to do so on your own, I recommend skipping past this next part.

Focus on the division operation. It becomes evident that it is always optimal to add at most once before each division. Adding more than once is less efficient as it could be replaced with a more optimal sequence: adding less and dividing earlier. For instance, a sequence like "+ + /" is more effectively executed as “/ +”.

In essence, you are 'forced' to add either 0 or 1 times before a division because it is never optimal to add more. This insight significantly narrows down the range of possible action sequences, guiding you closer to the correct solution. Recognizing these optimal actions is about understanding the inherent efficiency of certain steps within the problem's framework.

In conclusion, focusing on forced and optimal actions in problem-solving is a powerful strategy in competitive programming. It simplifies complex problems by highlighting necessary or highly efficient steps. This approach not only aids in establishing a clear direction for solving problems but also enhances the overall efficiency and effectiveness of the solution. By mastering the art of identifying these actions, you can significantly improve your problem-solving skills and performance in competitive programming.

The Vital Role of Best/Worst Case Analysis in Competitive Programming

A critical and often game-changing approach is the analysis of best and worst-case scenarios for any given problem. This method is particularly effective in problems where the objective is to derive the best possible outcome. In fact, there are a lot of problems (even in USACO) where the best or worst case solution is actually the answer to the entire problem! Delving into the best and worst cases not only provides a starting point for your problem-solving journey but also offers a framework within which you can examine how the actual solution may deviate from these extremes.

Take, for instance, this problem from Codeforces. You are presented with two lists, A and B. The challenge is to insert elements from B into A, in any order and position, to minimize the Longest Increasing Subsequence (LIS) of the combined sequence. The LIS is the largest sequence of indices in an array where each element is larger than the preceding one.

First, like described, think about the worst case and best case. Here, the worst case isn’t very relevant. However, the best case answer for this problem is that the shortest LIS of any combined sequence is equal to the LIS of A, or in other words, the answer is at least equal to the length of the LIS of A. This is because, since A is always a subsequence of the combined sequence, thus making any increasing subsequence in A available as an increasing subsequence of the final sequence as well. 

It turns out that you can always achieve the best case by inserting the elements of B into A in a certain order, and the first step to noticing this is thinking about the best case in the first place. For more details on the problem or how the solution works, feel free to check out the problem and the editorial itself. 

Furthermore, it's crucial to note that the best/worst-case scenario analysis doesn't just apply to the final solution but can also relate to the resources or steps required in solving the problem. This is exemplified in the “Closest Cow Wins” USACO Silver problem. Once again, if you wish to solve the problem by yourself, I’d advise you to skip this next part, as I will give major spoilers. 

Now, the question you should ask yourself is, what is the worst case on the number of cows Farmer John must use to get ALL patches of grass? Is it always equal to placing one cow on each patch of grass? Can we do better? 

It turns out that we need at most 2M cows, as we can place 2 cows to surround each of Farmer Nhoj’s cows, which is the main observation for the problem. This highlights how analyzing the worst-case scenario in terms of resources needed can lead to crucial breakthroughs.

In summary, the analysis of best and worst-case scenarios is not just beneficial but often essential. This technique simplifies complex challenges and is key to identifying the most efficient and effective solutions. By examining these scenarios, programmers can gain a deeper insight into the intricacies of a problem, thus guiding them towards a more targeted and successful problem-solving strategy. 

Observation Starting Points

When you begin to tackle a problem, there are several critical questions and considerations that can guide your thought process. These starting points can help you unravel the problem more efficiently.

Correctness and Solution Strategy:

• Greedy Algorithm Feasibility: Start by asking whether a greedy algorithm is applicable. What aspects of the problem make it suitable for a greedy approach? Prioritize understanding what to choose or optimize at each step. If a greedy solution isn't feasible, identify the scenarios where it fails. This understanding can guide you towards constructing a more robust solution that accounts for these failures.

• Forced and Optimal Actions: Consider if there are any forced actions or clearly optimal paths that make other options irrelevant. Identify if there are must-do steps, such as addressing a specific edge case or a particular sequence of actions that seems unavoidable.

• Dynamic Programming (For Advanced Levels): For higher difficulty levels, contemplate whether dynamic programming (DP) is suitable. Assess if the time and memory complexity are manageable for maintaining all necessary states. Determine what states are crucial for the DP solution.

• Sorting and Order of Elements: Evaluate whether sorting the elements could simplify the problem. Sometimes, the order of elements plays a crucial role, and sorting can bring clarity or make the problem more approachable.

• Graph Construction and Data Structures: Think about the possibility of constructing a graph or other data structures using the problem's elements. Organizing the components into a different structure can often provide new insights and simplify the problem.

Time Complexity and Optimization:

• Naive Solution Analysis: Identify the most naive solution first. This step provides a baseline from which you can work to optimize. Question immediately if there are apparent ways to enhance this basic solution.

• Amortization Opportunities: Look for situations where amortization might be applicable. There may be processes that seem time-consuming at first glance but are actually feasible when their cost is spread out over the course of the algorithm.

• Eliminating Time-Intensive Approaches: Recognize solutions that will definitely not run within the time constraints. Decide whether these approaches can be completely ruled out or if they can be optimized to fit within the time limits.

• Interpreting Constraints for Time Complexity: Analyze the problem's constraints to determine the viable complexity of your solution. Look for small limits or combinations of limits that suggest a certain range of complexity, typically around 1e7 to 1e8 operations.

By addressing these points when starting a problem, you can form a structured approach to making observations. This process not only aids in understanding the problem better but also in devising an efficient strategy for solving it. Keep in mind that the key to successful problem-solving in competitive programming often lies in these initial observations and the strategy that stems from them.

How to use observations effectively

Once you've made key observations in a problem, the next crucial step is leveraging these observations to guide you towards the correct solution. Observations are powerful tools, but their true value is realized only when you know how to effectively use them.

Simplifying the Problem with Observations

The primary benefit of making astute observations is their ability to strip down a problem to its essence, removing extraneous details. This process of simplification is often the turning point in problem-solving. Take, for instance, a complex-looking problem from Codeforces. At first glance, the problem might appear daunting due to its length and intricate details. However, with the pivotal observation that the optimal choice is a weight exactly equal to Polycarp’s strength, the problem transforms. It becomes a much simpler task: to find the athlete with the maximum endurance and sufficient strength. By using observations to pare down the problem, you can discard irrelevant information and focus on the crux of the challenge. Tackling this simplified version is usually far less daunting and leads to the solution more efficiently. So, after making crucial observations, consider whether the problem can be reduced to something simpler and more manageable.

Reducing the Range of Possibilities

Observations, particularly those related to forced or optimal actions, can drastically narrow down the range of possible solutions. This reduction allows for a more rapid and focused exploration of potential solutions. Refer back to the earlier example of the “Searching for Soulmates” problem. The observation made in this problem significantly reduced the possible sequences of operations, facilitating a quicker discovery of the optimal sequence. In general, once you have observations that limit the possibilities, repeat this analytical process on the reduced set of possibilities. Investigate whether there's more to deduce, further refining your approach.

Continuous Observation: The Never-Ending Cycle

Observations in problem-solving are not a one-off task but a continuous, iterative process. Many problems, particularly ad-hoc and constructive types, are almost entirely based on making a series of observations. To solve these, one must continuously observe, analyze, and deduce, building on each observation to get closer to the solution. Consider whether your initial observation can be applied to other aspects of the problem, or if it can be generalized to encompass broader scenarios. Treat each observation as a stepping stone, and view the simplified version of the problem as a new challenge. This continuous cycle of observation and analysis is crucial. It's through this iterative process that you edge closer to the right answer, regardless of the problem’s complexity.

Conclusion

Observations act as a beacon, guiding programmers through the often murky waters of competitive problem-solving. They help in simplifying problems, reducing the range of possibilities, and continuously steering thoughts towards the most effective solution. As we have discussed, whether it's deducing the implications of time complexity and constraints, exploiting the best and worst-case scenarios, or using observations to iteratively refine the problem-solving approach, each aspect underscores the same principle: keen observation is the key to unlocking the full potential of your problem-solving skills.

In conclusion, for those journeying through the competitive programming landscape, the message is clear: cultivate and refine your observational skills. Embrace the practice of looking beyond the obvious, questioning the given, and exploring the implications of every detail. As you do so, you’ll find that your ability to dissect and conquer complex problems grows stronger, making you not just a better programmer, but a masterful problem solver.

A Comprehensive Guide on Using Codeforces To Practice For USACO

Codeforces is probably the single best resource for preparing for USACO outside of, of course, USACO itself. So, today, I’ll dive into how to most effectively use this resource. 

Overview

Contests and Rating System

Codeforces is centered around its contests, which are hosted on average about once or twice a week. There are 4 divisions of Codeforces contests: Divisions 1 through 4. These divisions are based on its rating system, which is an ELO rating system very similar to Chess’ FIDE ratings. 

The different titles for ratings are: 

• Newbie: 0-1200

• Pupil: 1200-1399

• Specialist: 1400-1599

• Expert: 1600-1899

• Candidate Master: 1900-2099

• Master: 2100-2299

• International Master: 2300-2399

• Grandmaster: 2400-2599

• International Grandmaster: 2600-2999

• Legendary Grandmaster: 3000+

Here are the different titles as shown on Benjamin Qi’s rating graph.

Division 4 contests are for those rated below 1400. Division 3 contests are for those rated below 1600. Division 2 contests are for those rated below 1900/2100, and division 1 contests are for those rated above 1900. 

The reason that division 2 contests have different cutoffs is because there are 2 different types of division 2 contests. The first type is a standalone division 2 contest, where there is no division 1 contest counterpart. Since there is no division 1 contest to go with this, people rated from 1900-2099 are allowed to compete. The second type consists of both a division 1 and a division 2 contest at the same time, with some of the same problems. Here, since there is a division 1 contest, people rated 1900+ must participate in division 1, while only people below 1900 can participate in division 2. 

Lastly, there is one other type of contest, which is a “global” contest, where every single person no matter the rating participates in the same contest. In these contests, to accommodate both the lower rated and higher rated participants, there are usually many problems (8-10) with a large range of difficulties.  

Within each contest, there can be anywhere from 5-10 problems. The first problem is A, the second is B, etc. In this blog, if I refer to Div2A, that means the first problem of a contest in division 2. 

When it comes to correspondence to USACO divisions, Codeforces is, overall, a bit of a different style from USACO and Olympiad problems in general, thus, there isn’t a strict 1 to 1 from Codeforces problems to USACO problems. However, if I had to give an estimate, USACO Bronze problems are around Div2B-C, Silver problems are around Div2D-E, Gold problems are around Div1B-C, and Platinum problems are around Div1C+. 

As for the rating system, I’d estimate that Bronze competitors should be a Codeforces rating of around 1000-1200, Silver competitors should be a rating of around 1200-1500, Gold Competitors should be a rating of around 1500-1800, and Platinum competitors should be 1800+. Again, Codeforces problems are a bit of a different style from USACO problems, so there are many competitors that are better at USACO but worse at Codeforces, and vice versa. So, take these estimates with a grain of salt. 

Problemset

Codeforces also has a problemset, which, like USACO, consists entirely of problems from past contests. Within this library of past contests, Codeforces has over 9000 problems! 

Each problem has a rating difficulty between 800 and 3500. In general, a contestant with a rating of “x” should be able to solve “x” rated problems at least 50% of the time in contests. 

How do the problem difficulties match up to USACO divisions? Again, Codeforces style problems are a bit different from USACO’s style, but here are a few general guidelines. 

• Beginner: 800-1000

• Bronze: 1100-1500

• Silver: 1600-2100

• Gold: 2100-2400

• Platinum: 2400+

Keep in mind that Codeforces problems are meant to be solved at a much faster pace than USACO. You tend to have 2 hours for 5-6 problems rather than 4 hours for 3 problems, which makes USACO problems for a division harder than the corresponding Codeforces problems that a contestant of that division would be able to solve. 

Problems also have tags, such as: “binary search”, “data structures”, “dfs and similar”, “graphs”, etc. Much like the USACO Guide, you can use these tags for targeted practice. 

Here is an example of a problem on the Problemset page. Under the problem name are tags such as “dp”, “greedy”, “math”, etc, and to the right, there is a number indicating difficulty.

Improving With Codeforces

Participate in Contests

Codeforces contests are an amazing way to practice contest skills, measure your progress, and keep up motivation. Division 2 contests are hosted really often, about once a week! The other 3 divisions are much less frequently hosted. Luckily, when it comes to USACO, mastering division 2 contests and being able to solve all problems in contests consistently can definitely push you to Platinum, and maybe even camp. I’d recommend competing in every single Codeforces contest that you are able to.

To check for upcoming contests, you can either go to the contests tab, or check the Codeforces calender.

Practicing Contest Skills.

Codeforces contests provide a diverse range of problems that demand creativity, a thorough understanding of algorithms, and a mastery of data structures. The real-time, high-pressure environment is perfect for cultivating your problem-solving abilities. During these timed challenges, you'll learn to quickly comprehend problem statements, devise efficient solutions, and code them accurately under time constraints. This kind of practice is essential in competitive programming, where precision and speed can make all the difference.

Furthermore, live contests enforce a level of rigor and discipline that is often not present in regular practice sessions. This aspect is crucial in preparing for high-stakes competitions like USACO.

In a typical practice environment, it's common to seek external assistance or hints when you're stuck on a problem or can't debug an error. However, in a contest setting, such luxuries are absent. If you encounter a bug in your code, the onus is on you to identify and rectify it, without the option to peek at the failing test case or seek external help. This scenario forces you to engage deeply with your code, enhancing your debugging skills and attention to detail.

Imagine spending over 1 hour trying to spot a bug in your code during a contest. This is not just a test of your technical skills, but also of your patience and perseverance. It teaches you to systematically comb through your code, develop hypotheses about potential errors, and test these hypotheses rigorously. This kind of persistence is a valuable trait in any programmer and is particularly crucial in competitive programming, where understanding and fixing your own mistakes is often the difference between success and failure.

Speed

While USACO emphasizes solving fewer, more complex problems within a generous time limit, Codeforces adopts a different approach. With typically 5-6 problems to solve in a 2-hour window, the initial problems, which are relatively simpler, test your speed and implementation skills. Although these "easier" problems might not stretch your algorithmic thinking to its limits, they are excellent for improving your coding speed and efficiency. This is crucial because in contests like USACO, quickly dispatching the simpler problems frees up valuable time for the more challenging ones, potentially impacting your overall score.

Measuring Progress

Throughout the months of April-December, USACO hosts no competitions. This also means that most competitors are improving the most during these months, and coming back stronger than ever in the December contest. However, since it is such a long period of time, it is easy to lose track of your progress during these months, and be in a spot where you aren’t sure whether you are ready for the upcoming USACO season. Codeforces contests and its rating system can help with this. 

By participating in many division 2 contests, you can get an effective measurement of your progress. For example, if you just made it to the silver division in the US Open contest in March, and you reached 1800 in rating on Codeforces, you can be pretty confident that you’ll be able to make Gold in December. 

Of course, still keep a few problems from USACO around to measure your true progress. But since USACO and Codeforces are both competitive programming, improving in Codeforces translates to improvement in USACO, and doing contests consistently can be a great measurement of your progress. 

Motivation

As highlighted in one of my other blogs about motivation, contests can significantly boost your drive to improve. The dynamic and competitive atmosphere of a live contest makes the experience more engaging compared to routine practice. Time seems to fly during these events, with two hours feeling like mere moments. The adrenaline rush and the pressure to perform can often push you to delve deeper into problem-solving, making it an effective and enjoyable form of practice.

Effectively use the Problem Set

Understanding the Problem Set Interface

Before diving into the practice methods, it's crucial to understand how to navigate the Codeforces problem set. On the problem set page, you'll notice filters on the right side, allowing you to sort problems by difficulty and tags. These filters are your gateway to customizing your practice routine.

Method 1: Blind Practice

Blind practice is about solving problems without prior hints or knowledge of the underlying concepts they test. It mimics the unpredictability of actual competitions, where you don't know what type of problem you'll encounter.

• Selecting the Difficulty: Start by using the difficulty filter. If you’re unsure about your starting level, refer to the guidelines correlating your division to a Codeforces difficulty rating. Attempt a few problems at this level. If they seem too easy or too hard, adjust the difficulty rating accordingly until you find a challenging yet solvable range.

• Avoiding Hints: For a true blind practice experience, disable the visibility of tags for unsolved problems. This option, found on the right side of the problem set page, helps avoid unintentional hints and encourages you to develop problem-solving skills from scratch.

Method 2: Targeted Practice

Targeted practice focuses on honing specific skills or concepts. It's ideal for working on your weak areas or mastering new algorithms and data structures.

• Filtering by Tags: Identify the areas you want to improve or learn. Use the tag filter to select problems related to that concept, be it dynamic programming, graph theory, or any other category.

• Balancing Difficulty: Even with tag-specific problems, maintain a balance in difficulty. If you are at the silver level, for instance, tackling a 3500-rated graph problem might be counterproductive. Choose problems that push your limits but remain within a realistic scope of solving.

For example, if you are a silver competitor wanting to practice binary search, you might filter 1800 difficulty binary search problems as shown.

A Structured Approach to Division Mastery

For those newly promoted to a division or aspiring to climb higher, here's a structured approach to use the Codeforces problem set effectively:

• Learning Phase: Begin with acquiring the necessary knowledge base. This includes algorithms, data structures, and techniques pertinent to your division level. Utilize resources like textbooks, online courses, and tutorials to build a solid foundation. The USACO guide is a great resource for learning all things necessary for a particular division.

• Blind Practice Phase: Once you're comfortable with the theoretical aspects, shift to blind practice. This phase helps you apply your knowledge in diverse situations, enhancing your adaptability and problem-solving speed.

• Targeted Practice Phase: As you approach mastery of your current division, identify areas that still pose challenges. Use targeted practice to focus on these topics, refining your skills and eliminating weaknesses.

Do Virtual Contests

Doing contests are such effective ways to improve both your problem-solving skills and your contest skills that even virtual contests are an amazing way to practice. These simulations of real contests not only boost your problem-solving and contest skills but also play a vital role in maintaining your motivation.

The Mechanics of Virtual Contests

Virtual contests on Codeforces are designed to mimic the experience of participating in a live contest. To embark on a virtual contest:

• Accessing Virtual Contests: Navigate to the contests page on Codeforces. Under each contest title, you'll find two options: 'Enter' and 'Virtual Participation'.

• Initiating a Virtual Contest: Choose 'Virtual Participation' and select a time to start. Once you begin, Codeforces replicates the conditions of a live contest. You won't have access to test cases or the ability to view other competitors' solutions during the contest.

This is what the virtual participating page will look like. Pick a time where you will be ready to start the virtual contest (most likely within the next 10 minutes), and click “virtual participation”.

Choosing the Right Virtual Contest

When it comes to selecting which virtual contest to tackle, here are some guidelines:

• Starting with Educational Rounds: For beginners and those looking to solidify their foundational knowledge, the 'Educational' rounds on Codeforces are an excellent choice. These rounds focus on fundamental algorithms and problem-solving skills, offering a comprehensive practice experience. With over 150 educational rounds available, they provide a vast resource for consistent learning and practice.

• Progressing to Division Contests: Once you've navigated through the educational rounds, or if you're looking for more diverse challenges, consider participating in Division 1 or Division 2 contests. Your choice should align with your current Codeforces rating and your USACO division. Generally, Division 2 contests are suitable for most competitors, but if you are in the USACO Platinum division, venturing into Division 1 contests can offer the advanced challenges you might be seeking.

Benefits of Virtual Contests

• Flexibility: Unlike scheduled live contests, virtual contests offer the flexibility to practice under real contest conditions at a time that suits you.

• Real-Contest Environment: By simulating the constraints and pressures of a live contest, virtual contests provide an authentic experience that sharpens your ability to perform under similar conditions in actual competitions.

• Skill Enhancement: Regular participation in virtual contests helps in improving your problem-solving speed, accuracy, and efficiency, essential traits for any competitive programmer.

• Motivation and Progress Tracking: Keeping up with regular virtual contests can be motivating, especially as you see your skills improving. They serve as a benchmark for your progress and a reminder of your growing capabilities.

Additional Codeforces Features

Gym: A Hub for Diverse Contests

The 'Gym' section on Codeforces is a treasure trove of unofficial contests. It's a space where users can engage with a wide array of competitions, ranging from renowned global challenges like the ICPC and Google Code Jam to local contests organized by educational institutions. This feature not only allows you to participate in these contests but also offers the unique opportunity to contribute by setting problems and organizing your own contests. The Gym is an excellent resource for those seeking to experience different formats and problem sets beyond the standard Codeforces contests.

Custom Invocation

Custom invocation on Codeforces is an integrated tool that functions as a versatile code runner. Accessible from the 'Problemset' tab through the 'Custom Test' option, it supports a range of programming languages. This tool is invaluable in several scenarios:

• Handling Undefined Behavior: In languages like C++, certain actions (like division by zero or integer overflow) can lead to undefined behavior, resulting in discrepancies between local and Codeforces results. The custom invocation allows you to test how Codeforces interprets your code, ensuring that your solutions are consistent with the platform's behavior.

• Alternative to Local IDEs: There are instances where your local integrated development environment (IDE) may encounter issues, such as difficulties in running code with large arrays in C++. In such cases, Codeforces' custom invocation offers a reliable alternative for running and debugging your code.

Codeforces’ built-in IDE

Blogs: A Window into the Codeforces Community

Blogs are a central feature of the Codeforces ecosystem, with the homepage showcasing a mix of contest announcements and user-generated content. These blogs serve multiple purposes:

• Learning from the Community: While personal journey blogs offer motivational insights, the true educational value lies in the detailed guides and discussions about specific algorithms. Many users post comprehensive tutorials and explanations, making these blogs a valuable learning resource.

• Engagement and Interaction: Codeforces blogs are more than just informational; they're interactive. You can share your experiences, ask questions, and engage in discussions, often receiving feedback and insights from fellow competitive programmers. This interaction fosters a sense of community and collaborative learning.

However, it’s important to approach these blogs with a mindful strategy. While they are rich in content, spending excessive time on them can divert attention from actual problem-solving practice. Use these blogs judiciously, focusing on content that directly contributes to your skill development.

Conclusion

Codeforces emerges as an essential resource for competitive programming enthusiasts, especially for those preparing for challenges like the USACO. With its diverse contests, ranging across various divisions and a rating system akin to an ELO rating, the platform offers a rigorous yet nurturing environment for sharpening coding skills. Its extensive problem set, featuring over 9000 problems with varying difficulties, facilitates both broad-based and targeted practice. Unique features like the Gym for a variety of contest experiences, custom invocation tools for code testing, and interactive blogs for community engagement further enrich the learning experience. Whether it’s maintaining momentum during the USACO off-season or enhancing problem-solving speed and accuracy, Codeforces provides invaluable tools and opportunities for growth.

Participating in both live and virtual contests on Codeforces is not just about solving problems; it’s about developing critical skills such as precision, speed, and resilience under pressure. These contests, along with the platform's comprehensive features, offer a realistic and challenging environment for progress tracking and skill enhancement. The platform serves as more than just a practice arena; it’s a community that fosters learning and improvement, catering to programmers at all levels. By fully leveraging Codeforces, from its problem sets to its community-driven features, competitive programmers can significantly boost their capabilities, preparing them for the rigors and demands of competitions like USACO.

How do USACO and Competitive Programming Fit Into Your Journey?

In the fast-paced world of technology and innovation, competitive programming stands as a beacon for students aiming to carve out a remarkable niche in their academic and professional journeys. Particularly in the context of the United States of America Computing Olympiad (USACO), it offers a unique blend of challenges and opportunities. As a multifaceted arena, competitive programming extends beyond just a test of coding skills; it's a gateway to enhancing one's educational and career prospects. This blog aims to delve into how USACO and competitive programming can be pivotal in shaping your journey, starting from the bustling halls of high school to the competitive corridors of the job market.

Embarking on this exploration, we will first examine how competitive programming can be a significant advantage in college admissions. It's not just about the algorithms and data structures; it's about demonstrating to colleges your ability to think critically and solve complex problems. For high school students juggling academics, extracurricular activities, and perhaps even part-time jobs, fitting competitive programming into an already packed schedule might seem daunting. However, we will provide insights and strategies to integrate this valuable pursuit seamlessly into your daily life. Additionally, we will highlight the tangible benefits that competitive programming offers in your job search, underscoring how it can be a game-changer in securing your dream job. Lastly, we will touch upon the overarching theme of how competitive programming inherently enhances problem-solving skills, an attribute that transcends the confines of coding and becomes a lifelong asset. Join us as we unravel these facets, illustrating how competitive programming is not just an activity, but a journey that shapes your intellectual and professional identity.

Middle/Early High School

Middle and high school years are a time of exploration and discovery, where students begin to shape their interests and talents. It's during this phase that the world of competitive programming can offer a stimulating and enriching experience. If you're a middle schooler or in the early years of high school, this is the perfect time to dive into the exciting realm of competitive programming. As you enjoy your childhood, which indeed should be full of fun and learning, integrating competitive programming into your activities can set a strong foundation for your future endeavors.

Competitive programming is not just another extracurricular; it's a journey into the world of logic, creativity, and problem-solving. Unlike traditional STEM subjects, which often have straightforward, objective answers, computer science and competitive programming offer a canvas for creativity. Here, you're not just learning to code; you're learning to think in innovative ways, to approach problems from different angles, and to find solutions that are as unique as they are effective. This aspect of competitive programming makes it not only intellectually stimulating but also incredibly fun. It challenges the mind while allowing for a personal touch in every solution you devise.

Moreover, the scope for growth in competitive programming is boundless. With various levels and divisions in competitions like USACO, you can continuously measure and challenge your progress. But the journey doesn't end at reaching the top in national ranks. The international arena is vast, with thousands of like-minded peers to compete against and learn from. This endless horizon of improvement sets competitive programming apart from more finite academic achievements like SAT scores or school grades. It's a field where the learning never stops, and the sky's the limit.

Starting early in competitive programming or USACO is an investment in your future. It's not just about coding; it's about developing a mindset that values continuous learning, problem-solving, and creative thinking. These are skills that will serve you well, no matter what path you choose in life. The benefits of competitive programming are manifold, affecting both your short-term academic achievements and your long-term career prospects.

If this is your first encounter with competitive programming, let this blog be the nudge you need to get started. And don't worry if you're unsure where to begin. We have resources and guides, including a blog on how to start your journey in competitive programming. Take the first step into this fascinating world, and you might just find a passion that shapes your future in ways you never imagined. So, grab your computer, fire up your curiosity, and embark on an adventure that promises to be as rewarding as it is challenging. Happy coding!

High School

As you navigate through the later years of high school, the focus inevitably shifts towards college applications. This period is crucial for building a strong profile that showcases your talents and interests. Competitive programming, especially through platforms like the United States of America Computing Olympiad (USACO), emerges as an exceptional activity to include in your college applications. Let's delve deeper into why competitive programming can be a significant asset in your college admissions journey.

Firstly, USACO offers a clear framework for demonstrating measurable progress in programming. With its tiered system of Bronze, Silver, Gold, and Platinum divisions, each level represents a step up in complexity and skill. Achieving the higher divisions, particularly Gold and Platinum, stands as a testament to your dedication and expertise in programming. Colleges and universities, well-versed in the rigors of USACO, understand the significance of these achievements. When admissions officers see "USACO Platinum" on your application, it speaks volumes about your proficiency in programming and your ability to tackle complex problems. This recognition is invaluable in an increasingly competitive academic landscape.

The limitless potential for growth and recognition in USACO sets it apart from other standardized measures like the SAT. In competitive programming, there's no upper limit to what you can achieve. Reaching the Platinum division is just the beginning. The journey can lead you to become a USACO finalist, an invitation to the prestigious USACO Camp, reserved for the top contenders in the Platinum division. This achievement alone can significantly bolster your college application. But the opportunities don't stop there. If you excel further, becoming a repeat finalist or even qualifying for the International Olympiad in Informatics (IOI) team, you could be in contention for an IOI medal. Such accolades are often viewed by top colleges as indicators of exceptional talent and potential, making them near-guarantees for admission to prestigious institutions.

Additionally, the skills honed through competitive programming have a broad application. Many students who excel in USACO also find success in other Olympiad competitions, such as the USA Mathematical Olympiad (USAMO) or the USA Physics Olympiad (USAPHO). This crossover success is due to the universal problem-solving skills developed through competitive programming. However, it’s important to recognize that while the fundamental skills of problem-solving are transferable, each discipline has its unique aspects. Excelling in competitive programming provides a strong foundation, but mastering other subjects requires dedicated effort and understanding of their specific nuances.

Participation in USACO and competitive programming presents a multifaceted opportunity for aspiring college students. It not only showcases your technical skills but also your commitment to learning and excellence. The measurable progression, the absence of an upper limit in achievements, and the transferable problem-solving skills make competitive programming a powerful component of your college application. Engaging in this challenging yet rewarding field could be a pivotal step in securing admission to a prestigious college and setting the stage for a successful academic and professional career.

Fitting USACO and Competitive Programming Into A Busy High School Schedule

Now that we have established USACO’s potential as a boost to your college applications, how can we fit it into your schedule? Integrating USACO and competitive programming into a busy high school schedule can be a daunting task, but with the right approach, it's entirely feasible. As we've highlighted, the benefits of excelling in USACO for college applications are significant. However, balancing this with academics, extracurriculars, and personal life requires strategic planning and smart time management. Let's expand on how you can effectively incorporate USACO into your bustling high school life.

Prioritizing USACO

Achieving high ranks in USACO, such as reaching the Platinum division or getting selected for USACO Camp, can significantly elevate your college application. These accomplishments often carry more weight than standard achievements like club leadership positions or high school ranks, which are more common and less distinctive. Therefore, it's advisable to prioritize competitive programming, especially if your goal is to optimize your college applications. That said, it's important to maintain a balance. If you have a deep passion for other activities, don't sideline them entirely. The key is to find a healthy equilibrium where you can pursue competitive programming without sacrificing other interests that are important to you.

Practicing Optimally

Effective practice is crucial, given the limited time you might have for competitive programming. It's essential to recognize that quality trumps quantity. Practicing while exhausted, such as immediately after a long day at school, might not be as fruitful. Instead, identify times when you are most alert and focused. This could be early in the morning, during a quiet evening, or even during weekends. Allocate more routine, less mentally taxing tasks – like certain homework assignments or organizational tasks – for times when you're feeling less energized. This strategic distribution of tasks ensures that your competitive programming practice is both efficient and effective.

Integrating Problem-Solving into Daily Life

One effective technique used by top competitors is to integrate problem-solving into their daily routines. This doesn't mean spending every waking hour coding. Instead, it's about keeping your mind actively engaged with programming problems throughout the day. For instance, you can start your day by reviewing a few problems. As you go through your school day, during breaks or less intensive classes, mull over these problems. This constant engagement helps in developing solutions subconsciously. By the time you sit down to code, you'll have a clearer idea of how to approach the problem, making your practice sessions more productive.

Creating a Structured Schedule

Having a structured schedule can make a world of difference. Dedicate specific time blocks each week solely to USACO practice. Treat these blocks like any other important commitment – no distractions, no excuses. Consistency is key here. Even if it's just an hour or two each week, regular practice can lead to significant improvements over time.

Leveraging Resources Efficiently

Lastly, make use of available resources to maximize your learning. This includes online forums, coding platforms, and educational materials specifically designed for USACO. Joining a community of fellow competitors can also be beneficial, as it allows for the exchange of ideas, strategies, and motivation.

In conclusion, fitting USACO into a busy high school schedule is all about strategic prioritization, effective time management, and consistent practice. By integrating problem-solving into your daily life, practicing optimally, and utilizing resources wisely, you can make significant strides in competitive programming while balancing your academic and personal commitments. Remember, the journey through USACO is not just about excelling in competitions; it's about developing critical thinking skills, resilience, and a problem-solving mindset that will benefit you in all areas of life.

Post-High School Benefits of Competitive Programming

Competitive programming, particularly experiences gained through platforms like USACO, extends its benefits far beyond high school and into college and professional life. It's a misconception to think that the skills developed through these competitions become redundant post-college. On the contrary, they often serve as a robust foundation for future successes, especially in technology and related fields. Let's explore how the skills honed through competitive programming can be advantageous in college and beyond.

Interviewing Skills

One of the most immediate benefits of competitive programming in a post-high school scenario is its relevance to job interviews, particularly in fields like software engineering. In our technology-driven world, the demand for software engineers is constantly growing. The nature of job interviews in this sector often leans heavily on algorithmic and problem-solving skills. Competitive programmers, especially those who have excelled in USACO, tend to find these algorithm-based interview questions more approachable and sometimes even trivial. While software engineering interviews can encompass a broader range of topics, the edge provided by a background in competitive programming is undeniable.

Additionally, competitive programming skills are increasingly valued in the finance industry, especially in roles like quantitative developers, traders, and researchers. These positions often require strong algorithmic thinking and problem-solving abilities, skills that are rigorously developed through competitive programming.

ICPC: The Collegiate Arena

The International Collegiate Programming Contest (ICPC) is a natural progression for competitive programmers entering college. Often compared to USACO or IOI, ICPC presents a unique challenge: it's a team-based competition. Competing in teams of three, participants tackle problems collaboratively, representing their colleges against teams from across the globe. The dynamics of team competition add a new layer of complexity and learning opportunity, enhancing not just your coding skills but also your ability to work effectively with others.

Becoming an ICPC world champion is a coveted achievement in the competitive programming community, a testament to one's coding prowess and teamwork skills. Participation in ICPC not only continues the competitive programming journey but also enhances your college experience, offering opportunities for networking, collaboration, and significant personal and professional growth.

Continuous Learning and Challenges

Competitive programming in college isn't just about maintaining skills; it's about continuous learning and tackling new challenges. The problems encountered in collegiate-level competitions are often more complex and require deeper understanding and creativity. This continuous engagement with challenging problems ensures that your problem-solving skills remain sharp and evolve.

In summary, the journey through competitive programming offers long-term benefits that extend well into your college years and professional life. The skills developed through these competitions are highly applicable and sought after in various fields, particularly in technology and finance. Moreover, platforms like ICPC provide a continuation of this journey in college, offering new challenges and opportunities for growth. Far from becoming redundant, the skills and experiences from competitive programming become foundational elements of your academic and professional success. Whether it's acing job interviews, excelling in team competitions, or continuously pushing the boundaries of your problem-solving abilities, competitive programming sets you up for a lifetime of learning and achievement

The Overall Benefits of Problem-Solving Skills

The problem-solving skills honed through competitive programming are indeed far-reaching, extending well beyond the realms of coding and academia. These skills are adaptable and can be applied in a myriad of situations in both personal and professional life. Let’s delve deeper into how these skills, cultivated in the competitive programming environment, can be beneficial across various domains.

Transferring Skills to Other Academic Disciplines

Competitive programming primarily revolves around breaking down complex problems into manageable parts and finding efficient solutions. This approach is not exclusive to programming; it's a universal skill applicable to a wide range of academic subjects. For instance, in mathematics and physics, problem-solving involves understanding concepts, applying them creatively, and thinking logically - skills that are directly transferable from competitive programming. Once you've mastered these problem-solving techniques, your ability to grasp and excel in other subjects that demand similar skills significantly improves. It's not just about learning the content; it's about applying a problem-solving mindset that can transform the way you approach any academic challenge.

Application in Diverse Professional Scenarios

In the workplace, regardless of your field, the ability to problem-solve is invaluable. Whether you’re conducting research, involved in strategic planning, or making investment decisions, the ability to analyze situations, think critically, and devise effective solutions is crucial. For example, in research, identifying the right approach to a problem, anticipating potential issues, and finding solutions can be the difference between success and failure. In the world of investing, being able to quickly assess risks, understand market trends, and make informed decisions is essential – skills that are all enhanced by a strong foundation in problem-solving.

Everyday Life Decisions

Beyond academics and professional life, problem-solving skills are also beneficial in everyday decision-making. Simple choices, like whether to order food or cook at home, can be approached with the same logical framework used in competitive programming. By assessing the situation, considering various factors, and weighing the pros and cons, you can make more informed and rational decisions in your daily life. This ability to think critically and solve problems can lead to better choices and, consequently, a more organized and efficient lifestyle.

Developing a Problem-Solving Mindset

At the core of these benefits is the development of a problem-solving mindset. This mindset is about more than just finding answers; it’s about being curious, persistent, and creative. It involves looking at problems from different perspectives, thinking outside the box, and being resilient in the face of challenges. These attributes are beneficial not just in specific tasks or subjects but in how you approach life in general.

The problem-solving skills developed through competitive programming are multifaceted and versatile. They enhance your abilities in other academic disciplines, equip you with valuable tools for a wide range of professional scenarios, and even aid in making everyday decisions more effectively. Above all, they foster a problem-solving mindset that can lead to personal growth, success, and a more fulfilling life. Whether in a coding competition, a classroom, the workplace, or the myriad decisions of daily life, these skills are a powerful asset, shaping not just what you do, but how you think and approach the world around you.

Conclusion

As we conclude this exploration into the world of USACO and competitive programming, it’s clear that these arenas are much more than platforms for technical skill development. They are incubators for a mindset that is analytical, creative, and relentlessly problem-solving. From middle school hallways to college campuses, and eventually into the diverse paths of professional life, the journey through competitive programming equips individuals with a toolkit of skills that are universally applicable and highly valued.

The journey through USACO and competitive programming is an investment in a future where technology and innovation continue to shape our world. By cultivating a robust set of problem-solving skills, you prepare not just for a career in software engineering or a related field, but for a lifetime of thoughtful decision-making, effective collaboration, and continuous learning. These skills transcend the immediate challenges of programming competitions and become integral to how you approach challenges, big and small, in everyday life.

As you step forward, remember that competitive programming is more than a line on your resume; it is a testament to your ability to think, adapt, and excel. Whether you're a student just starting out or a professional reflecting on your educational journey, the lessons learned through competitive programming are invaluable. They teach resilience, foster creativity, and instill a problem-solving spirit that will guide you through the myriad challenges and opportunities life presents. So, embrace these experiences, cherish the skills you develop, and look forward to a future enriched by the invaluable lessons learned through competitive programming.

How USACO Camper, Grace Cai, went from USACO Bronze to USACO Camp to MIT

Here is the full Q&A, where I talk with Grace about her journey through competitive programming: How USACO Camper, Grace Cai, went from USACO Bronze to USACO Camp to MIT

Hello, everyone! I'm Riya, and today we have the pleasure of hosting a remarkable guest, Grace Cai. Grace, a former USACO camper, will be sharing her inspiring journey from USACO Bronze to USACO Camp to MIT. We'll delve into her experiences and strategies, and hopefully provide some invaluable insights for aspiring programmers.

Early Challenges and the Path to Silver: 

Grace's journey into the world of competitive programming began in ninth grade when she attended a STEM-focused high school, Montgomery Blair High School in Maryland. Introduced to USACO through her school's computer club, she was immediately intrigued by the world of algorithms and logical problem-solving.

In her initial encounters with USACO, Grace admits to facing challenges, particularly as she was coding in Python. Although she swiftly progressed from Bronze to Silver, the transition was not without its struggles. Concepts like BFS and DFS remained elusive, and she realized she needed a more structured approach.

Serious Learning and Algorithm Mastery: 

It was at the end of her ninth-grade year that Grace embarked on a serious journey into algorithms. She attended a specialized camp designed to prepare students for USACO, dedicating two weeks to intensive algorithmic coding. Here, she honed her skills in areas like shortest path algorithms and MST (Minimum Spanning Tree), laying the foundation for her future success.

As she delved deeper into algorithms, Grace began exploring USACO Platinum topics. Networking with her peers, who were already in the Platinum division, proved instrumental in her learning process. She also scoured the USACO website and utilized Codeforces, specifically the Division 2D and 2E problems in the problem set, to enhance her problem-solving abilities.

Furthermore, Grace highly recommends participating in Codeforces contests. The platform's categorization of problems by tags and its emphasis on logic and solid coding skills made it a valuable resource. Codeforces contests also provide the unique challenge of not displaying individual test cases, requiring participants to ensure the robustness of their solutions.

Problem-solving Approach: 

Grace's approach to competitive programming stands out for its meticulous and analytical strategy. Her methodical approach revolves around maintaining a problem log, where she records her solutions, improvements, and personal reflections for every problem she attempts. This practice has proven invaluable in her journey, offering several key advantages:

• Identifying Areas for Growth: By documenting her solutions and reflecting on her thought processes, Grace gains a deeper understanding of her strengths and weaknesses. She can pinpoint specific areas where improvement is needed, allowing her to tailor her practice to address these gaps effectively.

• Tracking Progress: The problem log serves as a progress tracker over time. Grace can revisit her previous attempts, comparing her past and current solutions to gauge her advancement. This historical perspective motivates her to strive for continuous improvement and provides a clear sense of accomplishment as she witnesses her growth.

• Effective Learning from Mistakes: Grace doesn't shy away from recording mistakes or suboptimal solutions in her log. Instead, she views them as valuable learning opportunities. Analyzing her errors and understanding what went wrong empowers her to avoid making similar mistakes in future challenges.

• Strategic Topic Selection: Grace's approach to problem selection is equally calculated. She concentrates on recent problems that align with the specific topics she aims to master. Rather than randomly picking problems, she strategically targets those that present new challenges or delve into unfamiliar concepts. This approach ensures her learning remains purposeful and relevant to her competitive programming goals.

In essence, Grace's structured and analytical approach is a blueprint for success in competitive programming, offering a clear path to improvement and excellence.

Optimizing Study Hours: 

Grace's study hours during her intense summer learning varied between 8 to 14 hours per day. She dedicated herself to putting in the long hours every day, as solving more problems and getting in more repetitions can drastically improve problem solving skills.

However, in her tenth-grade year, Grace realized that quality work mattered more than quantity. She emphasized the importance of analyzing her solutions, learning from her mistakes, and pushing herself to tackle difficult problems. This shift in focus significantly contributed to her rapid improvement.

Hard Work Paying off

Grace's determination and meticulous preparation paid off during the December contest of her tenth-grade year. Not only did she manage to get a perfect score on silver, but she also achieved a high score on the Gold division, allowing her to advance directly to Platinum in one contest! This remarkable achievement demonstrated the results of her dedication and analytical approach.

However, her hard work extended past just the confines of Gold. Within her first contest in Platinum, Grace was able to score a 556 after solving one full problem, and achieving partial credit on the others. This was a big achievement for her, as she was already reaching camp level scores despite only being in silver just one year prior. However, this was just the beginning, as she would go on to increase her scores dramatically over the next few contests. 

Practicing for Platinum

Between her first and second contest in Platinum, Grace’s score increased almost 200, which is half of a problem! Between these contests, Grace practiced largely the same kind of problems as before - division 2 Codeforces and Platinum problems- but with one big change: topic lists. 

Grace met many fellow competitors who were also studying for USACO, and received many resources from them, the most effective being a list of topics, along with different problems that one could use to reference and practice those topics. The problems came from various sources, including Codeforces, Peking University Online Judge, ACM, spoj, and of course, USACO. She was able to utilize this resource to learn many new algorithms that she had never heard of before and get lots of practice with the algorithms she was already knowledgeable in. Plus, she made many new friends!

However, Platinum’s curriculum was simply too large to cover; topics that had never shown up before could come up in the next contest. Thus, despite coming across unfamiliar topics in contests, Grace decided to not get hung up on them, and instead prioritize topics that are most likely to show up, and become an expert in those areas. This maximizes the value of her practice, as a topic that may show up once every 3 years is never worth practicing as much as Dynamic Programming. Luckily, the topic lists that Grace received had a priority within them, and Grace was able to focus on more important topics within her practice. 

Qualifying for Camp

Throughout the year of 2017, Grace went on to set more and more impressive scores. In January, Grace achieved a 556, and in the February contest, Grace scored a 744, which was two full problem solves along with partial credit on the last problem. These scores were more than sufficient for camp, and in 2017, Grace was selected as a USACO finalist. 

Motivation

Sitting down and coding for 8-14 hours in one day is understandably a chore to many, and people often get burnt out when practicing this much every day. For Grace however, doing competitive programming is more of a hobby, and she always found her practice sessions exciting and peaceful, as it allowed her to express logic in a nice way. In fact, Grace emphasizes that having a natural interest in programming is incredibly important. Often, people do USACO purely for the sake of college applications, and while this is a valid motivation, if you don’t have the natural interest in it, you won’t be able to put in the long hours when you need to. 

Of course, even with a passion for problem solving, thinking about hard concepts for hours on end is incredibly tiring. Thus, when faced with fatigue, Grace would take a five minute break, and then force herself to come back to it to avoid procrastination and distraction. 

Another technique Grace used to gain motivation was to get herself into a routine. Every day after school, Grace would immediately open up a problem and start thinking about it. Then only at night would Grace do her homework. This made it so that it was as natural as brushing her teeth for Grace to practice every day. In fact, competitive programming worked as more of a de-stressing activity for Grace from things like school and homework. Even if the problem was hard, focusing on one thing without a care for anything else at the moment was really relaxing.  

Debugging

Like many, Grace initially had lots of trouble with debugging. When she was competing in the Facebook Hacker Cup in 9th grade, she started using C++ for the first time, and began learning the standard library. As she was learning how to use C++’s map for the first time, Grace ran into a bug that took her around eight hours to fix! In the end, the reality with programming in general is that you will run into really simple bugs that can take many hours to find, however, there are many ways you can improve at debugging and avoiding bugs in the first place. 

As Grace improved and rose in the divisions, she was able to greatly improve her debugging skills. The first skill Grace emphasizes is knowing where to find the bugs. For example, you are very unlikely to have bugs when reading in input, so you can mostly skip past that when debugging. In general, identifying places where bugs are most likely to reside can drastically decrease your debugging time.  

Another thing Grace emphasizes is readability. Oftentimes, less experienced programmers introduce lots of redundancy and unnecessary complexity into their code, such as unnecessary break statements, or implementations that technically work but are very unconventional. Having a clean implementation that is nicely structured can greatly speed up the debugging process, and also helps avoid bugs. To help improve code cleanliness, Grace suggests thinking about the problem more clearly and planning out implementation before jumping right into the code.  

Many programmers, especially those using C++, will also have a long template, including a list of “#define”s. While these are not inherently bad and can definitely speed up implementation if one is really familiar with them, they can clutter your code up, and make it harder to understand the code when reviewing it during debugging. Grace initially had a long list of macros, but eventually got rid of all of them except for a few that were most commonly used, such as “f0r” to represent a for loop starting at 0. However, macros that are useful for debugging are those that can help with printing. For example, a macro that can print out everything in a list in one statement can speed up debugging, as you are able to print your data and reevaluate more quickly.  

Grace’s Advice and Journey’s end

Grace emphasizes the importance of enjoying yourself when doing USACO. If you don’t enjoy problem solving, then the long journey to achieving milestones in USACO will be painful, especially the grind to Camp. Furthermore, high school is the best time to do competitive programming, since it builds a strong problem-solving and programming foundation, and when you’re in college, there are many other opportunities within computer science to explore. 

After becoming a finalist in 10th grade, Grace went on to do a lot of impressive computer science research so that she could explore other areas in computer science. However, she still really enjoyed competitive programming and looks back fondly upon it as an exciting experience.

Q&A

If I’m a junior, and I’m shooting for USACO camp, what strategy should I use in Platinum Contests?

In the recent contests, USACO added a concrete list of subtasks for each problem, making contest strategy more important than ever. 

For a contest strategy, Grace recommends identifying and solving the easiest problem first, getting full credit if possible. This is because having a problem solved can greatly boost your confidence in solving the other two problems, which is essential for the mental game in contests. However, at first, it can be difficult to even identify which problem is the easiest and which ones are the harder problems, so how do you do it? Grace emphasizes the importance of thoroughly reading ALL of the problems and subtasks as soon as you begin, as it can give you great insights into the difficulties and potential solutions for all the problems. 

Furthermore, Grace suggests dedicating the first hour of the contest to reading the problems and then brainstorming solutions without actually coding anything up. This approach ensures that contestants don’t waste time on coding up easy subtasks, and instead spend the time trying to figure out the whole problem, which can save implementation time. However, it is also important to acknowledge the power of subtasks; if you are unable to find the full solution for a problem in a fixed time period, you should pivot to subtasks instead, as getting 40% on a problem and 60% on another puts you in the same spot as one full solve. In the end, finding a good balance between subtasks and the full solution is crucial. 

How do I continuously make progress on a problem in a contest even after I’m stuck?

Oftentimes, the situation arises that a contestant gets a lot of ideas about a problem in the first ten minutes thinking about it, and afterwards, makes little to no progress. For this common issue, Grace suggests two solutions. 

First, if you have been stuck on a problem for a good amount of time, switch problems. Thinking about another problem and then coming back can generate a lot of subconscious thoughts about the problem. Furthermore, your mind is more refreshed on the problem after switching and coming back, so you can potentially see perspectives that you hadn’t seen before, and solve the problem using these new insights.  

Second, think about different ideas and ways to approach the problem. It’s really easy for a competitor to get stuck in a loop where they keep trying to solve the problem using the idea they came up with first, thinking that the idea has led to part of a solution and that it must lead to the full solution as well. However, this is not optimal, as ideas that work for part of a problem can be a dead end for the rest. Thus, rethinking the problem and trying out different approaches can really help with getting unstuck. For generating different ideas for a problem, Grace recommends drawing out small test cases and breaking the problem down into subtasks, and exploring all the possible ways to solve them. 

Lastly, Grace emphasizes the importance of persistence. Even if you’re stuck for thirty minutes or an hour, with enough thinking, the right idea can always pop into your head. 

What are the best (free) resources for studying for USACO?

The best resources, and the ones that Grace used, are online problem libraries, in websites such as Codeforces, spoj, poj, etc. Furthermore, make sure to use these resources effectively by reading the solutions thoroughly and understanding why the solution works for problems that you were unable to solve. 

If you are worse at math, is it better to focus on math problems?  

Grace thinks that while math skills can be beneficial, they are not as critical as problem-solving abilities for USACO success. Many aspects of USACO require a distinct skill set, and a strong focus on problem-solving is paramount.

What is more effective, doing blind practice, or topic-based practice? 

Grace considers topic-based practice valuable for mastering specific problem-solving strategies. However, she also emphasized the importance of attempting random problems to assess adaptability and versatility in applying problem-solving skills. Thus, Grace recommends starting with topic-based practice to gain valuable algorithmic skills, and then transitioning to random practice to develop problem-solving skills. 

Conclusion

In conclusion, Grace Cai's insights and experiences provide invaluable guidance for USACO participants at all levels of proficiency. Her journey from the bronze division to platinum underscores the significance of dedication and continuous learning in the realm of competitive programming. Additionally, Grace invites those interested in art to visit her art Instagram account under the username "introoging", where she showcases her creative works. In parting, she encouraged all aspiring USACO students not to be discouraged by divisions or competition levels, emphasizing that hard work and perseverance can lead to rapid progress in competitive programming.

How to Gain and Maintain Motivation When Practicing for USACO

Oftentimes, the hardest part about getting better at USACO and competitive programming in general is motivation. Today, I will discuss ways to be more motivated when practicing. 

The importance of motivation

Motivation, despite being intangible, is the most important force in competitive programming, or anything in life for that matter. In fact, it is the main barrier that separates the better coders from the worse. While algorithmic knowledge is very important, the main distinguishing factor between being able to solve a problem and being stuck is problem-solving skills, and problem-solving skills can only be developed through repeated practice.

However, it is much easier said than done. Burnout is very real, and can hit you at any moment. Even if you have become disciplined enough to practice for 10 hours every day for a whole year, the very next day you could want to quit. Thus, being motivated, and maintaining motivation is the most important thing to being successful as a competitive programmer. 

Competitive Programming Sites Outside of USACO

The first way to improve your overall motivation is to compete on competitive programming websites aside from USACO. As you already know, there is a long gap between March and December, where there are zero USACO contests. This dry spell during the summer and the first semester of your school year can kill your motivation, as it will feel like you are practicing for nothing, with no tangible results to measure your progress or to show for. 

The way you can remedy this is by competing on other competitive programming sites, such as Codeforces, LeetCode, CodeChef, AtCoder, etc. Within these four sites, there are almost 4 contests a week that you can work with. Furthermore, each one has its own rating system that can assist you in measuring your progress. If you compete on these sites regularly, you can not only measure your progress, but you can also experience the excitement of seeing yourself grow; seeing your rating graph steadily increase gives me a sense of accomplishment like nothing else. 

Contests are also much more interesting than normal practice. When doing a contest, time will fly by, and two hours will feel like nothing. Also, if you are competing under time pressure, you’ll tend to automatically work harder towards solving a problem. It still counts as practice as well, since you are doing problems and coding them up to completion. 

Perhaps the greatest benefit of contests is developing your contest skills and speed. All programming sites outside of USACO tend to emphasize speed, as they must cater to programmers of all levels, so the problems can greatly vary. Thus, solving the easier problems faster becomes more and more important. As you practice solving easier problems faster, you’ll be able to translate those skills into solving harder and harder problems faster as well. Furthermore, you’ll be able to simulate the pressure that you face in a USACO contest, and become more comfortable and confident when faced with that pressure when the season rolls around. 

Virtual contests

Taking the fact that contests are more interesting to the extreme, you can do virtual contests. Under the right conditions, taking a virtual contest can put the same time pressure on you as actual contests, pushing you to practice harder and solve more problems. By doing virtual contests, you can grind through 5 problems without even knowing it, passively increasing both your problem-solving and contest skills even more than before.

The site that I would recommend most to do virtual contests in is Codeforces. It has an incredible built-in virtual contest feature, and there have been so many contests on Codeforces that you’ll never run out of contests to do a virtual one on. Furthermore, they have contests for all divisions; if you are bronze, I’d recommend doing division 3 contests. For those in silver and gold, I’d recommend doing division 2 contests, and for those in platinum, I’d recommend doing division 1. 

To participate in a virtual contest on Codeforces, click on the “Virtual Participation”, choose a time, and get started!

What about if you are unable to take virtual contests seriously, knowing in the back of your mind that they will never matter as much as a normal contest? I cannot deny that virtual contests will never have the feel of a real contest, but there are many ways you can simulate the real thing. First, try doing virtual contests with friends, and competing against them. This can motivate all of you to improve. Furthermore, there is a Discord bot that allows you to do “rated” virtual contests. The bot is called the TLE bot, which you can read about here. You can either set this bot up on your own server, or you can join the AC server to use it (the invite link is in the same link). With this bot, you have a virtual rating that changes every time you do a virtual contest, and you can use that as motivation to grind out virtual contests. 

An example of how to use the TLE bot’s virtual rating system.

The best part about virtual contests is that you can do them on your own time, and whenever you want! Codeforces contests or contests from the other sites can be at awkward times sometimes, so it is understandable if you can’t make it to all of them. As such, virtual contests are perhaps the best replacement. 

Think of virtual contests and normal contests as stepping stones for USACO. Use virtual contests to constantly improve problem-solving and contest skills between the live Codeforces contests, and use the live Codeforces contests to improve between the USACO seasons.

To start, I’d recommend doing virtual contests of the Codeforces Educational contests. They provide the most learning value, and are very fun and concise!  

Doing harder problems

As you may have heard many times, the sweet spot for the difficulty of problems you should practice is just above your skill level. You should be doing problems that you are unable to solve 50% of the time, and when you do solve them, it should have taken more than an hour. When you finish such a problem after a long, hard battle, the sense of accomplishment it brings is unlike anything else. For starters, after you finish a live contest or virtual contest, always try to upsolve (solving the contest problems after the contest) the problem right after the last one that you were able to solve. 

On the right side of Codeforces’ Problemset tab, you can filter problems for difficulty. A common strategy is to find a difficulty that is just above your skill level, and once you master it, move up in difficulty.

However, if you choose problems that you can solve 50% of the time, the half of the time when you can’t solve it, it will kill your motivation a bit. To remedy this, utilize editorials/solutions. If you find yourself losing motivation fast after not being able to solve a problem, simply go to the editorial. Make sure you take note of why you weren’t able to make the correct observation to solve the problem, so that doing problems where you need to look at the solution isn’t a waste of time. Even after you look at the solution, try to code it up yourself. If you find yourself having to look at the solution too often, simply move down in difficulty for problems you are practicing. 

Skip Tedious Tasks if you Must

Imagine this: you’ve been looking at a Codeforces problem for two hours, and after a long fight, you finally give up and look at the editorial. You realize that you missed one simple observation that would’ve pushed the solution you had in mind to completion. Now, as me and many others have advised, you should implement this anyway. However, for this particular problem, you know the implementation is incredibly long and unnecessarily tedious, and you can’t think of any reasons implementing this would help you in any way. 

Skip it! Even though it will never not be helpful to implement a solution that you’ve looked at, skip it if the implementation is too tedious. As long as you realize and take note of why you were unable to think of the observation or solution yourself, there is no need to spend an excessive amount of time on implementing the solution. It is better that you lose out on a bit of learning but still have the motivation to practice than procrastinate practicing simply because the next step in your practice is really tedious. 

It doesn’t have to be after you’ve looked at a solution. Even if you are able to think of the right solution to a problem, and have confirmed that the solution is right, you can rarely skip the implementation phase if you know it is long and will demotivate you greatly. 

Of course, skip implementations in moderation. These tedious problems WILL come up in a USACO contest, and you cannot skip them then. Thus, practice these implementations most of the time, but if you are feeling particularly demotivated by the dread of having to implement a really annoying solution, you can skip it once in a while. 

Friendly Competition

Friendly competition with peers can be one of the biggest motivators. I’ll share with you a story about none other than Riya, and her journey through the ranks of the USACO. This story underscores the pivotal role that friendly competition plays in not only enhancing one's coding skills but also in staying motivated. In her transformation from a Bronze-level coder to reaching the prestigious Platinum tier, Riya harnessed the spirit of a fierce rivalry to fuel her ambition and resilience. Let's explore how adopting a similar mindset could be beneficial for anyone in the competitive programming landscape. To watch the full video about her story, check out the video here.

Embracing Friendly Rivalry

Riya's initial encounter with friendly competition came when she observed a peer—whom we'll call Jane—progressing to the Silver division of USACO. Despite Riya's initial placement in Bronze, she recognized that she had just as much potential as Jane. This realization ignited Riya's competitive spirit. Jane's achievement wasn't a source of envy but a beacon of possibility for Riya. She intensified her study regimen and soon matched Jane's accomplishment by ascending to Silver.

The Impact of Belief

The story took a twist when, at one point, Riya found herself complacent, resulting in her stalling in the Silver division while Jane advanced to Gold. Seeing Jane conquer challenges encouraged Riya to revisit problems she had previously deemed too daunting. It wasn't about a placebo effect; it was a shift in mindset. The act of believing one can solve a problem often makes the crucial difference between giving up and persisting through difficulties.

From Gold to Platinum

Motivated by this newfound perspective, Riya not only progressed to Gold but continued her upward trajectory to Platinum. Her journey exemplified that a year of consistent effort and learning from silent, friendly competition can yield remarkable results. It was not only the adoption of better study techniques but also the motivational push provided by Jane's successes that spurred Riya on.

Broadening the Competitive Network

Upon reaching Platinum, Riya began to cultivate a wider circle of competitors. She engaged with fellow USACO participants, particularly her classmates, and used their progress as her own benchmarks. This friendly rivalry encouraged everyone involved to strive for greater heights, illustrating that collective success often stems from individual contributions.

Lessons from Teaching

Riya's experiences at the USACO camp, where she mentored students, further validated the value of friendly competition. She observed her students using each other's achievements as motivation, thus confirming that such competition is instrumental in overcoming more challenging problems.

Harnessing the Competitive Edge: Strategies for Success

The Power of Positivity

It is essential to keep the 'friendly' aspect in competition. The goal is not to outshine others but to use their progress as constructive motivation for self-improvement.

Expanding the Circle

Relying on a single person for motivation can be limiting. Riya advocates for having a network of competitors to ensure consistent inspiration and drive.

Community Engagement

Finding a supportive community can be invaluable. Platforms like the USACO forums or competitive programming Discords can connect you with motivated individuals.

Observing and Emulating

Monitoring and emulating the practice routines of active problem solvers on platforms like Codeforces can provide insight into effective study habits.

Collaborative Growth

Riya recommends finding a coding buddy, as mutual assistance in problem-solving can accelerate learning and progress.

Structured Learning Environments

Joining a class or group specific to your USACO division can provide a structured and competitive learning environment.

Takeaway

Friendly competition has the potential to make the solitary journey of programming feel like a shared adventure, full of camaraderie and mutual achievement. Riya's story is a testament to the fact that seeing others excel should inspire, not intimidate. This approach to competition not only spurs personal growth but also contributes to a healthier, more collaborative coding culture.

As Riya's experiences illustrate, leveraging friendly competition is a strategy that extends beyond mere rivalry. It's about embracing a mindset where others' successes catalyze our own efforts to excel. For those inspired by Riya's journey, remember that the essence of competition lies not in surpassing others but in continuously surpassing our own past performances.

Take Breaks

As with any activity, to avoid burnout, take breaks! Breaks can mean multiple things. After you’ve done a virtual contest, take a break! After you’ve practiced hard from Monday to Saturday, take Sunday off! After you have advanced a division as a result of hard work from the past few months, take a week off! These breaks can serve as a great reset for your mental state, and can bring you back better than ever. 

However, the most important aspect of a break is what comes after it. It’s easy to take a 1-hour break that becomes taking the day off, which then becomes taking the week off, and soon, you realize that you’re not even doing USACO anymore. Take breaks in moderation, and learn the discipline of coming back after your break. It’s perfectly fine to take a break after hard work, but it is not fine to completely stop after an accomplishment. 

Conclusion

In conclusion, sustaining motivation for competitive programming and USACO hinges on a blend of deliberate practice and strategic pacing. Participating in live contests on platforms like Codeforces hones your real-time problem-solving skills, while virtual contests solidify your abilities in a controlled setting. Pushing through tougher problems expands your expertise and resilience, essential for USACO’s challenging environment.

Friendly competition acts as a motivator, turning peer achievements into personal milestones to strive for. Yet, it's equally important to intersperse these efforts with breaks, allowing for mental rejuvenation and a fresh perspective on complex challenges.

By integrating these practices—targeted contests, skill-appropriate challenges, the encouragement of peers, and necessary downtime—you craft a balanced approach to competitive programming. This balance not only keeps your passion for coding alight but also ensures that the journey is as rewarding as the achievements it leads to. Whether you are a beginner or an experienced coder, remember that true motivation thrives in recognizing both the journey itself and the incremental progress made along the way.

"I could have gotten that if I just had more time", How to get those points!

Here’s the video where I discuss the same content: "I could have gotten that if I just had more time", How to get those points!

With the USACO December contest on the horizon, it's crucial to delve deeper into a crucial aspect of competitive programming: content strategy. Often overshadowed by the focus on algorithms and data structures, content strategy and implementation skills play an indispensable role in achieving high scores. In this comprehensive guide, we'll explore the intricacies of content strategy, its impact on your performance, and actionable tips to help you excel in implementing and debugging. Let's dive into the world of content strategy, demystify its components, and unlock its potential for success.

The Significance of Contest Strategy

To underscore the importance of content strategy, it's worth noting that in USACO camp, there is a dedicated lecture to it. This commitment to content strategy underlines its important role in competitive programming. As a coach, I firmly believe in its significance, having witnessed countless instances where content strategy transformed a participant's performance; I’ve even seen situations where a participant took their score from a 233 to a whopping 833 after mastering an effective contest strategy, securing them a spot in Gold!

Understanding the Contest Log

At the heart of contest strategy lies the concept of a contest log. It serves as your compass during the contest, helping you navigate the treacherous waters of problem-solving with precision and efficiency. The contest log is your strategic tool to optimize time management and prioritize tasks effectively.

To create a contest log, break down your contest time into 15-minute increments. At the end of each interval, record what you've been doing. These entries can be as simple as "thinking about P2" to indicate you were thinking about the second problem, "implementing P2" for coding the third problem, or "debugging P1" when looking for where your code goes wrong in the first problem.

Initially, some may find this task distracting, fearing it will disrupt their focus. However, the opposite is true. A few words won't significantly divert your concentration, but they will provide valuable insights. For instance, you might fall through the dangerous path of continuously saying “I’m so close!”, and tunnel vision on debugging. Without the contest log, you might unknowingly squander hours on a single problem.

Identifying Time Leaks

The contest log functions as a time leak detector. It reveals instances where you've unknowingly spent excessive time on a problem. During the excitement of a contest, it's easy to lose track of time. However, the contest log keeps you grounded, making you aware of time leaks that may have otherwise gone unnoticed.

By being conscious of how you allocate your time, you can make more informed decisions. Consider this scenario: you realize you've invested an hour and a half in debugging problem 2. With this awareness, you can choose to cut your losses and allocate the next 30 minutes to other problems. This strategic shift can be the difference between securing partial credit on multiple problems or being stuck in a debugging trench.

Leveraging Task Switching

An important part of a good content strategy is task switching. It involves periodically shifting your focus between different problems. This technique often leads to fresh insights and breakthroughs when you return to a problem after working on others.

To implement task switching effectively, set a rule for yourself: do not spend more than 30 minutes coding or debugging any single problem at the contest's outset. This ensures that you allocate time to every problem, giving you the opportunity to secure partial credit on each. This is especially important for the bronze, silver, and gold divisions, as the goal is to solve two to two and a half problems, emphasizing the significance of partial credits.

Incorporating task switching into your strategy can lead to remarkable results. It's not uncommon for students to return to a problem and suddenly grasp its solution after working on different tasks. The fresh perspective gained through task switching can be a game-changer.

Reading All Problems

Before immersing yourself in coding, invest a minute in reading all the problems thoroughly. While the temptation is strong to begin coding immediately, this approach can be counterproductive. Rushing into problem 1, assuming it's the easiest, might lead to frustration when you realize that it is actually the hardest problem.

By taking the time to read all the problems, you gain a holistic view of the contest. This approach allows you to identify the genuinely easiest problem. Ranking problems from easiest to hardest enables you to tackle the most manageable ones first.

Shortening Implementation Time

When solving problems, always keep in mind the split between the time you come up with the idea, and the time you take to implement. What should you do when you can come up with the ideas relatively quickly, but take many hours to implement, and even longer to debug? I discuss this issue specifically here.

How much time should you aim for?

For problems in the silver divisions and above, dedicating 40 minutes to thinking and 40 minutes to implementing and debugging is a good rule of thumb. This sums up to about 1 hour and 20 minutes per problem, making it feasible to tackle three problems in a contest within four hours. Keep in mind that the time required may vary for easier and more challenging problems, especially in Platinum.

Thus, spending 45 minutes on finding the idea is a good time. However, bronze students should aim to bring their implementation time down to at most 30 minutes, especially for bronze problems which tend to have shorter implementations. 

Tips for shortening implementation time

One way to achieve this is by organizing your code structure before you start coding. Have a clear idea of the sections, functions, and loops your code will include. This planning step can significantly reduce the time spent during implementation and debugging.

Additionally, if you find yourself stuck in debugging and your code is too long (e.g., over 40 lines for a bronze-level problem), consider simplifying sections of your code. Long, complex code is more prone to bugs. Condensing your code to less than 40 lines can often lead to the elimination of unidentifiable bugs. Higher-level competitors tend to code more concisely, so keeping your code clean and compact is a valuable skill.

Using a Debugger

Often, competitive programmers use simple print statements to debug their programs, and while this may be effective for shorter programs, as your code gets longer and longer, print statements can generate lots of confusion, slowing down the debugging process. To avoid losing time in this compartment, try using a debugger.

At its core, a debugger is a software tool designed to assist developers in finding and resolving bugs, glitches, and errors in their code. It provides a controlled environment where you can inspect the inner workings of your program, step through its execution line by line, and examine the values of variables at any given moment. While it might sound complex, debuggers are remarkably user-friendly and can drastically speed up the debugging process. For a comprehensive guide on how to use a debugger, check out Nathan’s video here.

Choosing Your Environment

For this tutorial, we'll be working with VSCode and Java. If you're using a different Integrated Development Environment (IDE) or text editor, the specifics might vary slightly, but the core functions remain the same. Debugging is all about understanding and controlling your code's execution.

Setting Breakpoints

Let's take a look at how to use a debugger effectively. We'll use a USACO Bronze problem from the 2020 February contest called "triangles" as an example. We won’t go into the specifics of the problem, so it’s fine if you aren’t familiar with it. Our goal is to understand how to use a debugger to ensure our code is running correctly.

A breakpoint is essentially a place in the code where we want to stop and check the current state of the variables, so we can see if any of the variables are not as we expected. We can set these breakpoints anywhere in the code. Then, when we debug, the debugger will run the program as normal, until it hits a breakpoint, when it then gives us full control.

Here, you can see that we define a breakpoint in line 15 by hovering to the left of the line number. In other IDEs, this may differ, but in general clicking around the line number will put a red dot, indicating a breakpoint.

The purpose of this breakpoint in line 15 is to check that the input has been properly read into our “points” array.

Once you’ve set breakpoints in all places where you want to check the state of the program, we can get to running the actual debugger.

Navigating the Debugger

To run the debugger in VS Code, simply go to the top right and click on the dropdown next to the run button, and select “Debug Java”.

If you cannot find this option in an IDE such as IntelliJ, try searching up how to run debug on your IDE.

Once you entered the debugger, your IDE will look something like this. It can be a bit overwhelming at first, but let’s explore everything that is going on.

Let's explore the debugger’s features:

• Highlighted Current Line: Line 15 is highlighted, indicating the current execution point.

• Variables Panel: This panel displays the values of all defined variables. For “triangles”, we can check if our points were read in correctly by expanding the "points" menu.

• Hover to Inspect: You can hover over variables in your code to see their current values. For example, hover over "N" to see its value.

Skipping Ahead

Suppose we want to program to continue executing. We can use this menu found at the top of the IDE:

This menu allows us to step forward by clicking on the second icon from the left. Stepping forward means allowing the program to continue its very next line of code, which can be incredibly helpful, as we often want to see how our variables change as the program progresses.

If you’re stuck in a loop, and don’t want to continuously click the “step forward” button, we can skip ahead in the code to a specific point. Define another breakpoint at the line that you want to stop at, and use the “continue” button, which is the first icon from the left.

Exploring Functions

Suppose we are at a line of code where a function is being called. Clicking “step over” will simply go to the next line, not giving us any information about what is going on inside this function.

To read the state of the program inside the function as well, we can use the “step into” feature, which is the 3rd button from the left, when on a line of code that calls a function. Now, you can inspect the variables and calculations happening within that function as well. Similarly, to exit the function, we can use the “step out” feature, which is the 4th button from the left, which goes back to the code that called the function.

Watching Variables

Oftentimes, you will have tons and tons of variables, so keeping track of each one you are interested in can be really tedious. This is solved by another powerful tool: the watch panel, which can be found on the bottom left under the variables panel.

If you click the “+” on the top right of the panel, you can add a variable or expression that you are interested in keeping track of. For example, in the “triangles” problem, we can add “points[i]” to the watch panel, and the debugger will tell us the value of points at index i at every point in time. You can even keep track of a specific property, such as “points[i].x”.

Conditional Breakpoints

Suppose we have a long loop, and we don’t care about every iteration of the loop, just certain iterations. We can use a conditional breakpoint to set this up. To set up a conditional breakpoint, add a breakpoint normally, right click it, and “edit breakpoint”.

Now, we can enter an expression to define when we want this breakpoint to activate, allowing us to only pause the program when we want to.

That covers the essential functions of a debugger that you need to know. Debugging can be a bit overwhelming at first, but with practice, you'll become more efficient at identifying and fixing issues in your code.

Post-Contest Analysis

Content strategy extends its influence beyond the contest itself. After the contest concludes, it's time for a thorough post-contest analysis. This phase is where you consolidate your learning and identify areas for improvement. Post-contest review is much more time-effective for learning than spending your time doing another practice contest instead, as you’ll just make the same mistakes again.

Review your contest log and reflect on your performance. Ask yourself critical questions. Did you allocate too much time to a specific problem? Could I have gotten a problem with better time management? Post-contest analysis serves as a diagnostic tool, revealing your strengths and weaknesses. If you have a coach or mentor, have them review it too, as they can point out things that you might not have thought was a mistake.

The goal of post-contest analysis is not just to dwell on your mistakes but to learn from them. It's an opportunity to fine-tune your strategy for future contests. The insights gained during this phase are invaluable, paving the way for continuous improvement.

Continuous Improvement

The sign of a successful contestant is their commitment to continuous improvement. To foster this growth, implement changes based on your post-contest analysis.

I often witness remarkable score improvements in students who diligently work on their content strategy. Thus, make it a rule to assess your content strategy after each contest; even a five-minute review can lead to significant score enhancements.

Platinum-Specific Strategies

As you progress to the platinum level, the dynamics of content strategy evolve. As the goal shifts more towards one and a half problems, the importance of partial credits becomes even more apparent.

Embrace Partial Scoring

Within Platinum contests, partial credit becomes even more important, as they can substantially boost your overall score. Imagine achieving 75% on one problem, 25% on another, and 25% on the third, which leads to almost one and a half problems already! Since you're not aiming for full solutions as often, allocate more time to partials. This approach can lead to a higher overall score, even if you don't complete any problems.

However, still shoot for the stars; whenever you can, aim for full solves. With proper preparation, you may find full solutions when thinking about how to solve the entire problem, or even if you don’t, you’ll have already found partial solutions without even knowing it.

Strategic Time Allocation

As always, managing time wisely is critical in all divisions, but it is especially important in Platinum, as you also have to balance going for full solves with going for partials. Begin with any problems that you might have the full idea for. Then, as you are nearing the end of the contest, focus on partials, balancing your time among the remaining problems. Time is a precious resource, especially in platinum contests, and should be allocated strategically.

Conclusion

As the upcoming USACO season approaches, remember that content strategy is your secret weapon. It can turn "I could have gotten that if I just had more time" into "I got it because I had a solid content strategy."

Maintain a contest log, organize code before implementing, use a debugger, embrace task switching, read all problems, and conduct post-contest analyses. These steps will significantly enhance your performance. For platinum participants, focus on partial scoring and strategic time allocation to maximize your points.

So, as you prepare for the upcoming contest, make content strategy and faster implementation/debugging a central part of your preparation. It's not just about coding faster but also about coding smarter. Effective content strategy can make all the difference in your journey to USACO success.

Thank you for reading, and best of luck in your USACO journey! May your contest log be your guiding star toward victory.

Nathan, a 4 time USACO Finalist and a USACO Guide developer, reveals how he prepared for USACO

Here’s the full video where I discuss the same content in detail: ”Nathan, a 4 time USACO Finalist and a USACO Guide developer, reveals how he prepared for USACO!"

I recently had the privilege of sitting down with Nathan Wang, a four-time USACO finalist and a USACO Guide developer. Today, we will delve into his remarkable journey through the world of competitive programming.

Introduction

Nathan Wang's journey through the world of competitive programming is nothing short of extraordinary. He has not only achieved the remarkable feat of becoming a four-time USACO finalist but is also a prominent figure within the USACO community. Beyond his impressive competitive achievements, Nathan has played a central role in the development of the USACO guide, a valuable resource for aspiring coders seeking to navigate the challenging waters of competitive programming. Nathan's story is a testament to dedication, passion, and the relentless pursuit of excellence in programming. 

Starting Out

Nathan's fascination with programming began long before he was introduced to USACO. He started programming at a young age, and by the time he reached seventh grade, he was already deeply involved in web development, which he did recreationally.

However, it was only in middle school that he stumbled upon USACO, thanks to his older brother. Intrigued, Nathan decided to participate in his first USACO contest. Surprisingly, his prior programming experience enabled him to excel. The bronze-level contests back then were not as challenging as they are today, which worked to Nathan's advantage. However, on his very first try, he managed to promote himself all the way to the gold level, which still demonstrated Nathan’s immense talent and impressive programming and problem-solving skills.

His Journey to Platinum

Nathan admitted that his journey from gold to platinum wasn't solely backed by rigorous study sessions. In fact, he attributed his advancement to a combination of luck and his foundational knowledge in programming. There was a particular contest where a problem was flawed, and Nathan was among those who managed to solve it before it was removed. This, combined with his scores from other problems, allowed him to advance, even though his solution wasn't entirely correct.

However, luck can only take one so far. Recognizing that he wasn't truly at a platinum level, Nathan decided to invest in his training. He enrolled in a summer program for USACO and honed his skills by solving numerous old USACO problems from the usaco.org website. He believed that continuous practice was key to acquiring the necessary skills to genuinely qualify for the platinum level.

Preparing for Camp

Transitioning from platinum to camp level required Nathan to immerse himself in rigorous practice sessions. He emphasized the importance of mastering foundational concepts like Dynamic Programming (DP) and other algorithms. Nathan’s strategy was straightforward – he tackled old USACO problems, with a focus on the gold and platinum problems to solidify his understanding. In fact, the summer before the season where Nathan went camp, he solved almost every single gold and platinum problem from past contests!

When going through the old problems, Nathan simply went down the list, from the oldest contests to the newest contests. However, one strategy I recommend employing when working on Platinum problems is to sort them based on the number of people who solved them. By reviewing the results, you could prioritize problems with the highest number of solutions first and gradually tackle those with fewer solutions. This method is not perfect, as the difficulty between contests could vary, but it provides a reasonable estimation.

Getting unstuck

Whenever Nathan confronted a problem he couldn't solve, he'd read the solution, ensuring he coded it himself to grasp the concept better. He would spend hours analyzing the often-cryptic solutions, and scour through the code again and again, trying to understand what it was really doing. If a problem was simply way too hard, he would give up and return at a later time. 

Nathan emphasized the importance of persistence, advocating for continuous effort unless one felt utterly stuck. For those who encounter frequent obstacles, he suggests leveraging resources like the USACO forum, a place where one can post questions and receive answers from others in the community. Asking others who are more experienced can really help you get unstuck or even help you see another perspective if you are unable to figure out a problem or understand a solution. 

In the end, Nathan’s priority was to enjoy the process and remain motivated. Participating in USACO was always a highlight for him. During the summer, he would sometimes spend entire weeks just preparing for it.

Nathan’s First Camp Experience

Upon qualifying, Nathan described his experience at the USACO camp as transformative. Before attending, he had considered his journey in competitive programming to be near its end. However, the camp reignited his passion. It was more than just about algorithms and contests; it was a social event. Nathan had a chance to connect with like-minded individuals, learn new concepts, and engage in fun activities like board games.

The camp organizers efficiently split the attendees into two groups – Guernseys and Holsteins. Guernseys consisted of the first-time campers, whereas Holsteins consisted of the returners, who were at camp to compete for a spot on the United States’ International Olympiad of Informatics team. This allowed for a more tailored experience. Nathan, being a Guernsey, had more time dedicated to learning and social activities, making his overall camp experience highly enjoyable, and even the best week of his life up to that point. 

Preparing to return

Returning to USACO camp as a Holsten is much more challenging than reaching camp for the first time, as you are competing to be a candidate for the IOI team. After his first year at camp, Nathan initially didn’t have many expectations and dreams - he was doing USACO and wanted to attend camp mostly for fun. 

However, during camp, a friend Nathan met at camp, who introduced him to a coach. This coach, offering a free service that aspiring competitive programmers could apply for, proved to be a game-changer for Nathan. Eager to seize this opportunity, he wasted no time in enlisting the coach's guidance.

The coach put together problem sets for Nathan to practice. The problem sets were carefully curated, primarily consisting of old Olympiad problems that closely mirrored the difficulty level of the hardest platinum-level USACO problems. The coach's knack for selecting problems that pushed Nathan's limits and providing clear, easy-to-understand solutions was instrumental in driving Nathan's progress.

One key attribute that set Nathan apart was his unwavering motivation. He understood that motivation was essential for continuous improvement. Whenever he encountered a particularly stubborn or frustrating problem, he had a unique approach. Instead of getting stuck for days on end without giving up, he would pivot to a different topic or problem sooner than most would. This strategy, driven by his desire to stay enthusiastic and maintain the joy of practicing, proved to be highly effective.

Nathan's relentless dedication, fueled by his motivating coach and his own intrinsic passion, ultimately paid off. Through his relentless efforts and determination, he secured his place at the USACO camp for a second time, returning as a Holstein.

Continuing to Prepare

At the highest levels of competitive programming, success hinges on one crucial factor: practice. It all boils down to who has devoted the most time and effort to solving a wide array of challenging problems. After mastering the essential algorithms and data structures that could potentially be encountered in competitions like the USACO, the real distinguishing factor becomes a contestant's problem-solving prowess.

Thus, between his second and third appearances at camp, Nathan similarly delved into a mix of old Olympiad-style problems, often under the guidance of the same trusted coach. This continuity in his training regimen allowed him to build on his existing foundation, refine his problem-solving strategies, and cultivate a deeper understanding of the intricacies of competitive programming.

Nathan’s Time Management

Finding time for USACO was never a challenge for Nathan. He never felt overwhelmed with schoolwork and didn't have many extracurricular commitments, as he focused all his energy on USACO. During summers, he opted out of summer programs, freeing up more time for preparation. Even during school hours, if a lecture wasn't captivating his attention, he would mentally work through problem statements he had read earlier. The benefit of this was that even without pen and paper, he could mull over a problem. It became a habit; whether he was eating dinner or in the shower, there was often a problem he was pondering over.

Others have shared similar experiences, bringing printed problems to class only to have them confiscated. But once you memorize the problem statement, no one can stop you from thinking about it. Of course, be sure to respect the teachers and their classes, but if you have a moment or two, why not problem solve?

The Long-term Value of USACO

Regarding summer activities, while many students feel pressured to join recognized summer camps or prioritize other extracurriculars, Nathan personally prioritized USACO. A key factor for him was seeing the long-term value in USACO. Even if he didn't make it to camp, the skills he honed would be invaluable during job searches or internships. Technical programming interviews become significantly easier with the preparation one gets from USACO. It felt like a win-win. Even if he didn't get selected for camp, the skills he gained would make future technical interviews a breeze.

Many have echoed this sentiment. A student mentioned that one of his college courses at Berkeley was primarily about algorithms and problem-solving, and thanks to his preparation, he breezed through it. This highlights USACO’s practicality as an extracurricular activity. While math competitions have their value, they often lack direct practical application. That's one reason Nathan transitioned from math competitions to computer science - advanced math wasn't as appealing to him, and he didn't see its direct practicality. With USACO, he felt he was investing his time wisely, especially since he enjoyed it more.

Furthermore, once you reach a certain division in USACO – whether that's platinum, gold, or silver, depending on your personal goals – you can take the next summer to relax a bit and focus on other extracurriculars. In the context of college admissions, once you achieve a division, you're there forever; you don’t need to maintain your skills. If you qualify for Platinum once, it's there for life, whereas with AMC or AIME, you must continuously qualify.

The USACO Guide

Nathan was in his second year when he started the USACO Guide. His motivation to create the guide stemmed from the existing training pages looking outdated, and wanting to modernize this excellent resource. The idea eventually evolved, and instead of just updating the old training pages, Nathan and his team decided to start from scratch, leading to the USACO guide. By creating his own resource, he had greater flexibility; he could move faster and iterate more quickly. The USACO guide provides a structured set of problems based on topics, making it easier for users to work on areas they're struggling with.

However, while it is called the USACO guide, why are most problems in the guide not from USACO? The goal of the USACO guide is to equip users with algorithms necessary for each division, and sometimes, these algorithms are best trained through repeated practice. Thus, doing additional practice outside of just USACO’s past problems is incredibly beneficial.

For the Platinum division, unlike the other divisions, there is a much more extensive range of topics. However, don’t be intimidated, as even Nathan didn’t memorize all the topics and algorithms. In fact, it is often more time efficient to practice topics that will come up more often, such as dynamic programming, rather than spending time learning obscure techniques that will rarely show up. For dynamic programming in particular, you can always get better and better at it, so it will always be time well spent to practice dynamic programming. 

In general, the USACO guide is meant to provide a foundational understanding, while your skills are meant to be developed through rigorous practice. It’s essential not to get demotivated if unfamiliar topics arise, and in general, prioritize dynamic programming since it's a versatile topic that frequently appears.

How to Most Effectively Use the USACO Guide

For those just starting out in a division, Nathan doesn’t recommend simply going down the list in the USACO Guide, doing all the problems in each category in order. This is because you lose out on vital problem-solving practice. By knowing which category of problems you are doing, you lose the need to come up with the fact that the problem uses that algorithm/data structure. For example, if you are in the “binary search” section of Silver, you automatically know the problems in that section use binary search, whereas in an actual contest, you will not have the information and might miss out on a problem you would otherwise be able to solve.

Instead, Nathan recommends 2 ways to effectively use the USACO Guide. The first way is applicable to those who are already proficient in most topics covered in a division; if there is a particular algorithm/data structure that you lack confidence in in your division, doing the targeted practice in the USACO guide can be incredibly useful and the most efficient way to practice.

The second way is applicable to those who are just starting out in a division. Before you jump right into a divisions’ problems, Nathan recommends learning all of the algorithms from the USACO Guide. Then, after you have a grasp of all the fundamental algorithms and data structures covered in the division, do practice on random problems from the past USACO contests. This avoids the tedious situation where you spend hours and hours on a problem, trying to figure it out, only to realize it simply uses a technique you have never seen before, but still ensures that you get practice in problem-solving. 

Nathan’s Advice for Those Preparing for USACO

Stay motivated. For Nathan, fun and enjoyment were paramount when solving USACO problems. He believes improvement is directly proportional to the number of problems you tackle. Rather than overthinking performance, focus on staying motivated and enjoying the learning process.

How You can Emulate Nathan’s Results

Nathan’s journey is defined by two major factors: repetition, and motivation. If you are able to solve thousands of problems while effectively learning from each and every one of them, you, too, will be able to accomplish what Nathan did. However, it is much easier said than done, so how do you do it?

First, repetition. Doing many practice problems and practice contests are the key to success in competitive programming.

• Where can I find all these practice problems? USACO barely has a few hundred!

  • Fortunately, Codeforces has a problem library of around ~10,000 problems that you can practice with. For the most effective practice, do problems with difficulties just above your skill level. To help choose problems, Codeforces allows you to filter the problem set for certain difficulties. As a general guideline, Bronze problems are around 800-1400, Silver problems are around 1500-2000, Gold problems are around 2100-2500, and Platinum problems are 2500+. However, you should try out the problems for yourself, and measure which difficulty is appropriate for you, regardless of division.

  • Codeforces aside, there are many other online competitive programming platforms that offer a versatile problem set, such as LeetCode and CSES for more standard problems, CodeChef and AtCoder for problems similar to Codeforces’ style, and online judges like oj.uz for Olympiad problems similar to USACO’s style.

  • Additionally, like Nathan, you could invest in a coach or an online course. These external resources are incredibly useful for not only helping you learn competitive programming, but also selecting appropriate problems, tailored to your current level.

• What about practice contests?

  • Many of the aforementioned online platforms offer amazing live contests. Codeforces, LeetCode, AtCoder, and CodeChef all offer contests at least once a week, which are great for practicing your problem solving skills under pressure. Furthermore, these sites have rating systems as well, allowing you to measure your progress and growth.

  • If you have leftover USACO problems that you have not looked at, doing a practice contest with those problems can often be the sole best way to practice. Emulate a contest setting and try your best to solve 3 problems from your division, and you can effectively measure where you are at.

• How do I find the time?

  • If you are truly dedicated to improving at competitive programming, you can always find the time to squeeze in an extra problem. Like mentioned, an effective way to create more time for problem solving that Nathan uses is to always have a problem in mind that you are thinking about. Read a few problem statements, and ponder these as you go through your day while doing monotonous activities.

Second, motivation. It’s easy to burn out doing competitive programming if you do thousands of problems in a short time period. How do you stay motivated, especially during the March-December period when there are no contests?

• One way to stay motivated is to participate in live contests on sites like Codeforces. Competing is always more exciting that just practicing, and while doing problems in a contest, 2, 3 hours can fly by quickly. Even practice contests are very effective, as a time limit will often push you to solve a problem, giving you more concentration. Also, seeing your rating grow on sites like Codeforces can also be a big motivator, as you know you are getting better.

• Another way to stay motivated that Nathan applied is to not get stuck on a problem for too long. Having a problem that you just cannot find the solution to no matter how many hours, days, weeks you spend on it can be incredibly demotivating, so it is often better to simply skip it. Of course, still spend sufficient time thinking about a problem before you skip it.

Conclusion

As you embark on your own journey in competitive programming, remember that every challenge you face is an opportunity for growth. Nathan's story is a testament to the power of persistence, dedication, and a genuine love for problem-solving. So, as you navigate the world of USACO, may his insights and experiences serve as an inspiration for your own path to success.

What is USACO Camp Like?

Here’s the full video where I discuss this in detail: What is USACO Camp Like?

Are you curious about what happens when the most skilled USACO competitors gather to learn and have fun? In this article, we'll take you on a journey through the USACO Camp experience. If you're searching for a unique blend of programming prowess, camaraderie, and memorable moments, you're in the right place.

USACO Camp Overview

USACO Camp stands as a prestigious training program, inviting the top 25 contestants from the Platinum division. Over the course of 10 intense days, participants immerse themselves in a world of learning and competition, with the ultimate goal of securing a spot on the International Olympiad of Informatics (IOI) team. The IOI is a global coding competition where the US has repeatedly excelled in.

Structure

USACO Camp divides participants into two distinct groups: the "Guernseys" and the "Holsteins." Guernseys are the first-time attendees hoping to learn and return as a Holstein, while Holsteins are veterans, and compete for a spot on the IOI team by participating in daily contests.

The exception to this are seniors, who are automatically placed in the Holstein category, as it is their final year to compete for a spot on the IOI team. Becoming a Holstein in your first year at camp is possible, but rare, and requires excellence in USACO’s Platinum contests as well as the USACO Camp contests.

The EGOI finalists follow a similar structure, where those attending camp for the first time are grouped with the Guernseys, and those returning are Holsteins and compete for a spot on the EGOI team. 

Fun Activities

While the heart of USACO Camp is coding, the experience extends far beyond the computer science. Participants create lasting friendships and enjoy a variety of extracurricular activities, including board games, chess, card games, and late-night movie marathons.

The camp even hosts relaxing events, such as mini-golf, ice cream parlor visits, push-up competitions, movie nights, white-water rafting, a trip to Six Flags, ultimate frisbee tournaments, and more. It's not just about coding; it's about connecting with like-minded individuals and creating unforgettable memories.

Guernseys have more leisure time as they primarily focus on classes, attending four lectures and two contests. However, Holsteins take on the pressure of daily contests, along with six lectures.

Further Exploration

 If you want a deeper look into USACO Camp, Melody's YouTube video offers an immersive perspective, showcasing various activities and daily life at Camp.

Conclusion

In summary, USACO Camp offers a remarkable blend of learning, competition, and, most importantly, fun. If the chance arises for you to attend, don't hesitate. It's an opportunity to create lifelong memories and advance your programming skills in an environment where like-minded peers share your passion. Don't miss the chance to experience the unforgettable USACO Camp journey.

How a Student Changed his Strategy to Ace USACO Bronze!

Here’s the full video where I discuss the same content in detail: How a Student Changed his Strategy to Ace USACO Bronze!

Hello, I'm Riya, and in this blog, I'm excited to delve into the strategies that transformed a former USACO bronze competitor's performance from average to perfect. In less than a month, this student went from struggling with bronze-level problems to acing the USACO bronze contest. I'll share the key strategies that led to this remarkable improvement.

Understanding the Challenge: 

Initially, our student had diligently solved every bronze-level problem during practice, but consistently fell short in the actual contests. The critical issue was his reliance on solutions for the harder problems. This common pitfall is discussed in more detail in one of my recent videos, which you can find here. The challenge lies in the fact that problems in the newer contests tend to be in the harder 30%, making it difficult to succeed if you're only comfortable with the older, easier problems.

Strategies for Success

Our primary goal was to strengthen the student's problem-solving skills. To achieve this, we devised a simple yet highly effective strategy. After working on a problem, if he couldn't solve it unaided, we encouraged him not to rush to the solution. Instead, we suggested taking a step back and dedicating 10-15 minutes to reflect on what the barrier was, and how he could get past it in the future. This approach turned out to be far more productive than mindlessly tackling more problems and significantly enhanced his problem-solving abilities.

Tracking Progress

One key tool we used was a Notion page (or a Google Sheet) to track all of the problems solved, marking the ones that required the solution to solve, which is a technique widely employed by top USACO finalists, composed of the top 25 Platinum contestants in the USA. The idea was to log what could have led to an independent solution, allowing the student to continually hone his problem-solving skills.

Expanding Problem Sets 

Our strategy didn't stop at reflection. To progress further, the student needed a broader range of problems to practice with. We went over how to select problems on Codeforces, emphasizing the importance of filtering for problems that match the current skill level. Then, when the student consistently solved these problems independently, we gradually increased the difficulty level. This approach significantly increased the difficulties of problems that he was able to solve without help, suggesting that this incremental process, through a large quantity of problems, had a substantial impact.

Speeding up the Observation Phase

One of the most crucial aspects we tackled was accelerating the observation phase. A powerful method we discussed was the following process: first, solve sample test cases by hand, carefully noting the process you used to solve them. Then, try to create test cases that your process/algorithm would fail at solving, and create a new algorithm to pass that test case, continuing this process until it's impossible to make your solution fail. This approach refines your problem-solving skills and guides you toward more efficient solutions. However, it's also vital to be aware of time limits, particularly when dealing with problems with tighter limits (where N is large).

Conclusion

These strategies were the most important and effective ones discussed in the original video with the student, which you can watch here. If you're committed to improving your USACO bronze score, I highly recommend watching the video and applying these techniques.