Teaching Yourself Dynamic Programming for Competitive Programming

Dynamic Programming (DP) is a crucial tool in competitive programming that allows you to solve complex problems by breaking them down into simpler subproblems. If you are a beginner in competitive programming and have been reading about dynamic programming, you're already on the right path! Here are some resources and tips to help you master DP.

Understanding Dynamic Programming

Dynamic programming differs from recursive backtracking in that it memorizes results of overlapping subproblems to avoid redundant computations. This technique can significantly improve the efficiency of your solutions, especially in competitive programming where performance matters.

Learning Resources

There are several excellent resources available to help you learn dynamic programming. Here are a few of the top ones:

TopCoder

TopCoder is a well-known competitive programming platform that has an extensive library of dynamic programming tutorials. These tutorials are comprehensive and well-explained, making them ideal for beginners. Additionally, TopCoder hosts regular contests where you can apply your skills and improve your understanding of DP.

GeeksforGeeks

GeeksforGeeks is another invaluable resource for learning DP. This site offers detailed explanations of standard DP problems, along with code examples and sample solutions. This can be incredibly useful as you progress through your learning journey.

Quora

Quora is an excellent platform to ask questions and get insights on dynamic programming. Michal Danilaks is a well-known figure on Quora who offers clear and concise explanations of DP concepts. Following him can provide you with additional insights and tips.

The Coin Problem Example

One of the classic dynamic programming problems is the Coin Change Problem. In this problem, you are given a list of coin denominations and a target amount. Your goal is to determine the minimum number of coins required to make up the target amount. Here's an example implementation:

long long maxamount(long long n) {
    long long max;
    // When no of coins is Zero
    if (n  0) return 0;
    // Use a global array to remember if you have already know value for a particular n
    if (store[n] ! 0) {
        return store[n]; // return answer without calculating in O1
    }
    // If result was not already saved you have to calculate it
    max  maxamount(n / 2)   maxamount(n / 3)   maxamount(n / 4);
    // dont forget to store the results for future reference
    store[n]  max;
    // finally return the result to the main function
    return max;
}

Note that this code may not handle large values of n (e.g., > 10^7) directly. For larger values, you may need to use a more efficient storage mechanism or tailor the approach based on the problem constraints.

Additional Resources

Here are a few more resources you might find helpful:

SPOJ Problems

If you're looking for more practice, SPOJ () offers a wide range of dynamic programming problems that you can solve. Some example problems include:

FARIDA - A classic DP problem that teaches you the importance of recursion and memoization. NFURY - This problem focuses on optimizing the use of memoization to solve large data sets efficiently. WACHOVIA - A problem that requires you to apply dynamic programming principles to a real-world scenario. TRT - An interesting challenge that tests your understanding of DP in a slightly more complex setting.

Conclusion

Dynamic programming is a powerful technique, and mastering it can significantly enhance your competitive programming skills. By following these resources and practicing regularly, you can become proficient in solving DP problems. Happy coding and learning!