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The 0-1 Knapsack Problem is a classic optimization problem where you are given n items, each with a weight and a value, and a knapsack with a maximum capacity W. The goal is to maximize the total value of items placed in the knapsack without exceeding its capacity. The "0-1" means each item can either be taken entirely or not at all.
A dynamic programming approach is efficient here because the problem exhibits overlapping subproblems and optimal substructure.
Bottom-Up Dynamic Programming Implementation (Python)
def knapSack(W, wt, val, n):# Create DP table with dimensions (n+1) x (W+1)K = [[0 for _ in range(W + 1)] for _ in range(n + 1)]# Build table K[][] in bottom-up mannerfor i in range(1, n + 1):for w in range(1, W + 1):if wt[i - 1] <= w:K[i][w] = max(val[i - 1] + K[i - 1][w - wt[i - 1]],K[i - 1][w])else:K[i][w] = K[i - 1][w]return K[n][W]# Example usageprofit = [60, 100, 120]weight = [10, 20, 30]W = 50n = len(profit)print("Maximum Profit:", knapSack(W, weight, profit, n))コピーしました。✕コピーOutput:
Python Program for 0-1 Knapsack Problem - GeeksforGeeks
2025年7月23日 · Python Program for 0-1 Knapsack Problem using Recursion: A simple solution is to consider all subsets of items and calculate the total weight and profit of all subsets.
geeksforgeeks.org の検索結果のみを表示Java Program 0-1 Knapsack Problem
Java Program for 0-1 Knapsack Problem using Recursion: A simple solution is to consider all subsets of items and calculate the total weight and profit of all sub…
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- When analyzing 0/1 Knapsack problem using Dynamic programming, you can find some noticeable points. The value of the knapsack algorithm depends on two factors: 1. How many packages are being considered 2. The remaining weight which the knapsack can store. Therefore, you have two variable quantities. With dynamic programming, you have useful informa...
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2025年9月10日 · By the end of this article, you will be able to understand how to solve the problem of 0-1 and fractional knapsack using dynamic programming …
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