Knapsack Problem Dynamic Programming Visualizer

Algorithm Steps

Knapsack Problem

0/1 Knapsack Problem finds the maximum value that can be obtained with given weight capacity, where each item can be taken at most once.

Dynamic Programming Approach:

• Create DP table: dp[i][w] = max value with first i items and weight w
• Base case: dp[0][w] = 0 (no items, no value)
• For each item: choose max of including or excluding it
• If weight ≤ w: dp[i][w] = max(dp[i-1][w], dp[i-1][w-weight] + value)
• Else: dp[i][w] = dp[i-1][w]
• Traceback to find selected items

Time Complexity: O(n×W) where n = items, W = capacity