This series of videos are focused on explaining dynamic programming by illustrating the application of DP through the use of selected problems from platforms like Codeforces, Codechef, SPOJ, CSES and Atcoder.
After going through this series, you should find yourself confident in approaching dynamic programming problems and also implementing them in a reasonable amount of time.
I will also live code and submit the solutions to the problem on the coding platform from where the problem comes.
Some Basic elements of Dynamic Programming
Some general ideas and my thoughts about DP to help you get started:
Part 1: https://youtu.be/24hk2qW_BCU
1. What is Divide and Conquer?
2. What is Dynamic Programming?
3. Types of DP problems.
Part 2: https://youtu.be/yfgKw6BUZUk
1. What is a DP-state?
2. Characterizing a DP-state.
3. What is a recurrence?
4. Top Down v/s Bottom Up.
Part 3: https://youtu.be/X-3HklSPx6k
1. Directed Acyclic Graph(DAG) Representation of DP solution
2. Visualizing Top-Down and Bottom-Up.
3. Evaluation order for bottom-up codes.
4. Analyzing the space and time complexity for a DP solution(derivation).
Problem 1: Dice Combinations
Problem 2: Coin Combinations I
Problem 3: Coin Combinations II
Problem 4: Removing Digits
Problem 5: Grid Paths
Problem 6: Book Shop
Problem 7: Array Description
Problem 8: Edit Distance
Problem 9: Rectangle Cutting
Problem 10: Two Sets II
Problem 11: Beautiful Array
Problem 12: Number of Valid Arrays
Problem 13: Longest Increasing Subsequence O(NlogN)
Problem 14: Projects
Problem 15: Beauty of Tree
Problem 16: Catch Some
Problem 17: Vasya and Binary Strings
Problem 18: Counting Towers
I am quite confident that many beginners/intermediates will definitely enjoy watching this series on dynamic programming and it will definitely help in getting better at dynamic programming and problem solving in general. I have tried to teach in a way such that not many prior prerequisites are required to understand the explanations even to the harder problems.
If people find this helpful then I will make sure that this list of problems will keep growing, cheers!
Link for introduction to DP on Trees: https://codeforces.com/blog/entry/79857
UPD: Added 2 more problems from CSES: Projects and Removing digits.
UPD: Added 3 parts on basic elements of DP to get you started.
UPD: I have also started a series on DP with bitmasking(starting from the very basics) and in the future will make a separate blog for both Digit DP series and DP with bitmasking series, till then interested people can check: Dynamic Programming with bitmasking
UPD: added solution to problem Vasya and Binary Strings
UPD: added solution to problem Counting towers from CSES