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0/1 Knapsack Problem

0/1 Knapsack Problem

Optimize value within weight constraints using dynamic programming for resource allocation.

Family: Dynamic Programming Status: 📋 Planned

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Overview

The 0/1 Knapsack problem is a fundamental optimization problem in computer science. Given a set of items,

each with a weight and value, determine the maximum value that can be obtained by selecting items such that the total weight does not exceed a given capacity.

This problem is a classic example of dynamic programming and has applications in resource allocation, portfolio optimization, and cutting stock problems.

Related Algorithms in Dynamic Programming:

  • Coin Change Problem - Find the minimum number of coins needed to make a given amount using dynamic programming.

  • Fibonacci Sequence - Classic sequence where each number is the sum of the two preceding ones, demonstrating recursion, memoization, and dynamic programming.