Knapsack Problem
0-1 Knapsack Problem Description: There are $N$ items and one knapsack with a maximum capacity of $V$. Each item can be selected at most once (i.e., either take it or leave it). The $i\text{-th}$ item has a volume of $v_i$ and a value of $w_i$. Your task is to select a subset of items to put into the knapsack such that: The total volume of the selected items does not exceed the knapsack's capacity V. The total value of the selected items is maximized. Output the maximum possible total value achievable under these constraints. ...