| 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](../dynamic_programming/knapsack.md)| Given $N$items with weights $w_i$ and values $v_i$ and maximum weight $W$, 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.|

| 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 $(i,j+1)$.|