👀 Views: 22 💬 Answers: 1 📅 Created: 2025-06-06

dynamic-programming algorithms python Python

I'm maintaining legacy code that I'm dealing with Does anyone know how to I'm trying to implement I'm currently trying to implement a dynamic programming solution for the 0/1 Knapsack question in Python, but I'm working with issues with the calculated maximum value... My approach involves using a 2D list to store the results, but the output is not what I expect. I've set up the question with weights and values as follows: ```python weights = [1, 2, 3] values = [10, 15, 40] capacity = 6 ``` I expect that the maximum value I can achieve with a knapsack of capacity 6 should be 55 (items 2 and 3), but my implementation only returns 40. Here is the code I've written so far: ```python def knapsack(weights, values, capacity): n = len(values) dp = [[0 for _ in range(capacity + 1)] for _ in range(n + 1)] for i in range(n + 1): for w in range(capacity + 1): if i == 0 or w == 0: dp[i][w] = 0 elif weights[i - 1] <= w: dp[i][w] = max(values[i - 1] + dp[i - 1][w - weights[i - 1]], dp[i - 1][w]) else: dp[i][w] = dp[i - 1][w] return dp[n][capacity] max_value = knapsack(weights, values, capacity) print(max_value) # Expected output: 55 ``` Despite following the dynamic programming approach, I'm not sure where I went wrong. I've double-checked the indices, and it seems correct, but I'm getting the wrong maximum value. Could someone guide to identify the scenario in my implementation? I'm using Python 3.9, and I've verified that the input values are being passed correctly. Any insights would be appreciated! What would be the recommended way to handle this? My team is using Python for this application. How would you solve this? This is part of a larger web app I'm building. Has anyone dealt with something similar? The project is a microservice built with Python. Is there a simpler solution I'm overlooking?