Create Unbounded_knapsack.cpp

dynamic_programming/Unbounded_knapsack.cpp

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+/**
+ * @file
+ * @brief Unbounded Knapsack problem using Dynamic Programming
+ * @details 
+ * The Unbounded Knapsack problem allows you to take unlimited quantities of each item. The goal is to maximize the total 
+ * value without exceeding the given knapsack capacity. Unlike the 0/1 knapsack, where each item can be taken only once, 
+ * in this variation, you can pick any item as many times as needed, as long as the total weight stays within the knapsack's capacity. 
+ * 
+ * @task Given a set of N items, each with a weight and a value, represented by the array `wt` and `val` respectively, and a knapsack 
+ * with a weight limit W, the task is to fill the knapsack in such a way that the maximum profit is obtained. Return the maximum profit.
+ * 
+ * Note: Each item can be taken any number of times.
+ *
+ * @author [Sanskruti Yeole](https://github.com/yeolesanskruti)
+ * @see dynamic_programming/Unbounded_knapsack.cpp
+ */
+
+#include <iostream>
+#include <vector>
+#include <cassert>
+#include <cstdint> // for std::uint16_t
+
+/**
+ * @brief Recursive function to calculate the maximum value that can be obtained
+ *        using an unbounded knapsack approach.
+ *
+ * @param i Current index in the value and weight vectors.
+ * @param W Remaining capacity of the knapsack.
+ * @param val Vector of values corresponding to the items.
+ * @param wt Vector of weights corresponding to the items.
+ * @param dp 2D vector for memoization to avoid redundant calculations.
+ * @return The maximum value that can be obtained for the given index and capacity.
+ */
+int KnapSackFilling(std::uint16_t i, std::uint16_t W, const std::vector<std::uint16_t>& val, const std::vector<std::uint16_t>& wt, std::vector<std::vector<int>>& dp) {
+    if (i == 0) {
+        if (wt[0] <= W) {
+            return (W / wt[0]) * val[0];
+        } else {
+            return 0;
+        }
+    }
+    if (dp[i][W] != -1) return dp[i][W];
+
+    int nottake = KnapSackFilling(i - 1, W, val, wt, dp);
+    int take = 0;
+    if (W >= wt[i]) {
+        take = val[i] + KnapSackFilling(i, W - wt[i], val, wt, dp);
+    }
+    return dp[i][W] = std::max(take, nottake);
+}
+
+/**
+ * @brief Wrapper function to initiate the unbounded knapsack calculation.
+ *
+ * @param N Number of items.
+ * @param W Maximum weight capacity of the knapsack.
+ * @param val Vector of values corresponding to the items.
+ * @param wt Vector of weights corresponding to the items.
+ * @return The maximum value that can be obtained for the given capacity.
+ */
+int unboundedKnapsack(std::uint16_t N, std::uint16_t W, const std::vector<std::uint16_t>& val, const std::vector<std::uint16_t>& wt) {
+    std::vector<std::vector<int>> dp(N, std::vector<int>(W + 1, -1));
+    return KnapSackFilling(N - 1, W, val, wt, dp);
+}
+
+/**
+ * @brief Function to run test cases for the unbounded knapsack implementation.
+ */
+void test_cases() {
+    std::uint16_t N = 4; // Number of items
+    std::vector<std::uint16_t> wt = {1, 3, 4, 5}; // Weights of the items
+    std::vector<std::uint16_t> val = {6, 1, 7, 7}; // Values of the items
+    std::uint16_t W = 8; // Maximum capacity of the knapsack
+
+    // Test the function and assert the expected output
+    assert(unboundedKnapsack(N, W, val, wt) == 48);
+    std::cout << "All test cases passed!" << std::endl;
+}
+
+int main() {
+    test_cases();
+    return 0;
+}