Add 0/1 Knapsack Problem implementation in C++

Author: Saujanya77

CPP/algorithms/dynamic_programming/knapsack_problem.cpp

@@ -0,0 +1,74 @@
+/*
+ * Algorithm: 0/1 Knapsack Problem
+ * Language: C++
+ * Description: Given weights and values of n items, determine the maximum value
+ *              that can be put in a knapsack of capacity W. Each item can be 
+ *              included at most once (0/1 property).
+ * Time Complexity: O(n * W) where n = number of items, W = knapsack capacity
+ * Space Complexity: O(n * W)
+ */
+
+#include <iostream>
+#include <vector>
+#include <algorithm>
+
+using namespace std;
+
+/**
+ * Function to solve 0/1 Knapsack problem using DP
+ *
+ * @param weights vector of item weights
+ * @param values vector of item values
+ * @param capacity maximum capacity of the knapsack
+ * @return maximum total value that fits in the knapsack
+ */
+int knapsack01(const vector<int> &weights, const vector<int> &values, int capacity) {
+    int n = weights.size();
+
+    // DP table initialization (n+1 x capacity+1)
+    vector<vector<int>> dp(n + 1, vector<int>(capacity + 1, 0));
+
+    // Fill DP table
+    for (int i = 1; i <= n; i++) {
+        for (int w = 0; w <= capacity; w++) {
+            if (weights[i - 1] <= w) {
+                // Take maximum of including or excluding current item
+                dp[i][w] = max(dp[i - 1][w], values[i - 1] + dp[i - 1][w - weights[i - 1]]);
+            } else {
+                // Cannot include current item
+                dp[i][w] = dp[i - 1][w];
+            }
+        }
+    }
+
+    return dp[n][capacity]; // Maximum value achievable
+}
+
+/**
+ * Test function for 0/1 Knapsack implementation
+ */
+void testKnapsack() {
+    vector<pair<vector<int>, vector<int>>> testCases = {
+        {{1, 2, 3, 8}, {10, 20, 30, 90}}, // Items 1-4
+        {{3, 2, 1}, {50, 40, 60}},        // Smaller knapsack
+        {{5, 4, 6, 3}, {10, 40, 30, 50}}  // Random test
+    };
+    vector<int> capacities = {10, 5, 10};
+
+    for (int i = 0; i < testCases.size(); i++) {
+        int maxVal = knapsack01(testCases[i].first, testCases[i].second, capacities[i]);
+        cout << "Test Case " << i + 1 << ":\n";
+        cout << "Weights: ";
+        for (auto w : testCases[i].first) cout << w << " ";
+        cout << "\nValues: ";
+        for (auto v : testCases[i].second) cout << v << " ";
+        cout << "\nKnapsack Capacity: " << capacities[i] << "\n";
+        cout << "Maximum Value: " << maxVal << "\n\n";
+    }
+}
+
+int main() {
+    cout << "Testing 0/1 Knapsack Problem Implementation\n\n";
+    testKnapsack();
+    return 0;
+}