implementing Dynamic Programming Approach for Knapsack solution in C++ - Memory Limit Exceeded scenarios
I recently switched to Hey everyone, I'm running into an issue that's driving me crazy... I've tried everything I can think of but This might be a silly question, but I'm currently working on a 0/1 Knapsack question using a dynamic programming approach in C++. My implementation is intended to handle weights and values of items, and I'm allocating a 2D vector for the DP table. However, I'm working with a 'memory limit exceeded' behavior when I try to run tests with larger inputs (e.g., 100 items with weights and values up to 1000). Here’s a snippet of the code I’ve written: ```cpp #include <iostream> #include <vector> #include <algorithm> using namespace std; int knapsack(int W, vector<int>& weights, vector<int>& values, int n) { vector<vector<int>> dp(n + 1, vector<int>(W + 1)); for (int i = 1; i <= n; i++) { for (int w = 0; w <= W; w++) { if (weights[i - 1] <= w) { dp[i][w] = max(dp[i - 1][w], dp[i - 1][w - weights[i - 1]] + values[i - 1]); } else { dp[i][w] = dp[i - 1][w]; } } } return dp[n][W]; } int main() { int n = 100; // Number of items int W = 1000; // Maximum weight capacity vector<int> weights(n, 10); vector<int> values(n, 10); cout << "Maximum value: " << knapsack(W, weights, values, n) << endl; return 0; } ``` I’ve attempted to optimize it by switching to a 1D DP array to reduce space complexity, but I’m still working with the same scenario. This is my modified version: ```cpp int knapsack(int W, vector<int>& weights, vector<int>& values, int n) { vector<int> dp(W + 1); for (int i = 0; i < n; i++) { for (int w = W; w >= weights[i]; w--) { dp[w] = max(dp[w], dp[w - weights[i]] + values[i]); } } return dp[W]; } ``` Even with this change, I still run into memory issues when I increase the number of items or the weight limit. I’ve also checked my environment settings (using g++ version 9.3.0) to ensure that there aren’t any limits set on memory allocation. Does anyone have suggestions on how to optimize this further or alternate approaches that might help in handling larger datasets without hitting memory limits? My development environment is Ubuntu. What's the best practice here? This issue appeared after updating to C++ 3.9. Hoping someone can shed some light on this. This is part of a larger REST API I'm building.