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Added Descriptions to Classic DP Problems #1269

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Added Descriptions to Classic DP Problems #1269

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Expand Up @@ -130,19 +130,21 @@ That's it. That's the basics of dynamic programming: Don't repeat work you've do
One of the tricks to getting better at dynamic programming is to study some of the classic examples.

## Classic Dynamic Programming Problems
- 0-1 Knapsack
- Subset Sum
- Longest Increasing Subsequence
- Counting all possible paths from top left to bottom right corner of a matrix
- Longest Common Subsequence
- Longest Path in a Directed Acyclic Graph (DAG)
- Coin Change
- Longest Palindromic Subsequence
- Rod Cutting
- Edit Distance
- Bitmask Dynamic Programming
- Digit Dynamic Programming
- Dynamic Programming on Trees
| Name | Description | Example Poblems |
| ---------------------------------------------- | ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ | ----------------------------------------------------------------------------------------------------------------------------------------------- |
| 0-1 Knapsack | 0-1 Knapsack | given a set of items, each with a weight and a value, and a knapsack with a maximum capacity. | [D - Knapsack 1 (](https://atcoder.jp/contests/dp/tasks/dp_d)[atcoder.jp](http://atcoder.jp)[)](https://atcoder.jp/contests/dp/tasks/dp_d) |
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| Subset Sum | you are given a set of integers and a target sum. The task is to determine whether there exists a subset of the given set whose elements sum up to the target sum. | |
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| Longest Increasing Subsequence | It's a problem that asks for the length of the longest subsequence of a given sequence such that all elements of the subsequence are sorted in increasing order. | [Longest Increasing Subsequence - LeetCode](https://leetcode.com/problems/longest-increasing-subsequence/description/) |
| Counting all possible paths in a matrix. | Solved using dynamic programming or recursion with memoization. | [Unique Paths - LeetCode](https://leetcode.com/problems/unique-paths/description/) |
| Longest Common Subsequence | Given two sequences (usually strings), the task is to find the length of the longest subsequence that is common to both sequences. | [F - LCS (](https://atcoder.jp/contests/dp/tasks/dp_f)[atcoder.jp](http://atcoder.jp)[)](https://atcoder.jp/contests/dp/tasks/dp_f) |
| Longest Path in a Directed Acyclic Graph (DAG) | Unlike finding the longest path in a general graph, which is an NP-hard problem, finding the longest path in a DAG can be solved efficiently using dynamic programming. | [G - Longest Path (](https://atcoder.jp/contests/dp/tasks/dp_g)[atcoder.jp](http://atcoder.jp)[)](https://atcoder.jp/contests/dp/tasks/dp_g) |
| Longest Palindromic Subsequence | Finding the Longest Palindromic Subsequence (LPS) of a given string. | [Longest Palindromic Subsequence - LeetCode](https://leetcode.com/problems/longest-palindromic-subsequence/description/) |
| Rod Cutting | It involves finding the maximum revenue that can be obtained by cutting a rod of length n into smaller pieces and selling them. | |
| Edit Distance | It involves finding the minimum number of operations required to transform one string into another, where the allowed operations are insertion, deletion, or substitution of a single character. | [CSES - Edit Distance](https://cses.fi/problemset/task/1639) |
| Bitmask Dynamic Programming | Bitmask Dynamic Programming is a technique used to solve combinatorial optimization problems, where the state can be represented compactly using bitmasks. | [Problem - F - Codeforces](https://codeforces.com/contest/1043/problem/F) |
| Digit Dynamic Programming | Digit Dynamic Programming is a technique used to solve problems related to digits of a number. | [SPOJ.com](http://SPOJ.com) [- Problem PR003004](https://www.spoj.com/problems/PR003004/) |
| Dynamic Programming on Trees | A technique used to solve various problems related to trees, such as finding the longest path, computing subtree properties, or counting certain structures within the tree. | [P - Independent Set (](https://atcoder.jp/contests/dp/tasks/dp_p)[atcoder.jp](http://atcoder.jp)[)](https://atcoder.jp/contests/dp/tasks/dp_p) |
| Range Dynamic Programming | Range Dynamic Programming is a technique used to solve problems where you need to find optimal solutions for subranges within a given range or array. | |

Of course, the most important trick is to practice.

Expand All @@ -151,3 +153,7 @@ Of course, the most important trick is to practice.
* [LeetCode - 118. Pascal's Triangle](https://leetcode.com/problems/pascals-triangle/description/)
* [LeetCode - 1025. Divisor Game](https://leetcode.com/problems/divisor-game/description/)

## Dp Contests
* [Atcoder - Educational DP Contest](https://atcoder.jp/contests/dp/tasks)
* [CSES - Dynamic Programming](https://cses.fi/problemset/list/)