| Name| Description/Example|

| ----------------------------------------------| -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|

|[0-1 Knapsack](dynamic_programming/knapsack.md)| Given $W$, $N$, and $N$ items with weights $w_i$ and values $v_i$, what is the maximum $\sum_{i=1}^{k} v_i$ for each subset of items of size $k$ ($1 \le k \le N$) while ensuring $\sum_{i=1}^{k} w_i \le W$?|

|[0-1 Knapsack](knapsack.md)| Given $W$, $N$, and $N$ items with weights $w_i$ and values $v_i$, what is the maximum $\sum_{i=1}^{k} v_i$ for each subset of items of size $k$ ($1 \le k \le N$) while ensuring $\sum_{i=1}^{k} w_i \le W$?|

| Subset Sum| Given $N$ integers and $T$, determine whether there exists a subset of the given set whose elements sum up to the $T$.|

|[Longest Increasing Subsequence (LIS)](dynamic_programming/longest_increasing_subsequence.md)| You are given an array containing $N$ integers. Your task is to determine the LIS in the array, i.e., a subsequence where every element is larger than the previous one.|

|[Longest Increasing Subsequence (LIS)](longest_increasing_subsequence.md)| You are given an array containing $N$ integers. Your task is to determine the LIS in the array, i.e., a subsequence where every element is larger than the previous one.|

| Counting Paths in a 2D Array| Given $N$ and $M$, count all possible distinct paths from $(1,1)$ to $(N, M)$, where each step is either from $(i,j)$ to $(i+1,j)$ or $(i,j+1)$.|

| Longest Common Subsequence| You are given strings $s$ and $t$. Find the length of the longest string that is a subsequence of both $s$ and $t$.|

| Longest Path in a Directed Acyclic Graph (DAG)| Finding the longest path in Directed Acyclic Graph (DAG).|

| Edit Distance| The edit distance between two strings is the minimum number of operations required to transform one string into the other. Operations are["Add", "Remove", "Replace"]|

*[Bitmask Dynamic Programming](dynamic_programming/profile-dynamics.md)

*[Bitmask Dynamic Programming](profile-dynamics.md)

* Digit Dynamic Programming

* Dynamic Programming on Trees