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Problem 5: The Knapsack Challenge (0/1 Knapsack)

Problem Statement

Given n items, each with a weight and a value, determine the maximum total value that can be put in a knapsack of capacity W. You cannot break an item — either pick the complete item or don't pick it (0/1 property).

Input Format

  • An integer W (knapsack capacity).
  • Arrays weights and values of length n.

Constraints

  • 1 <= n <= 100
  • 1 <= W <= 1000

Example

Input: W = 50, weights = [10, 20, 30], values = [60, 100, 120]
Output: 220
Explanation: Take items with weights 20 and 30 (values 100 + 120 = 220).