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| 1 | +/** |
| 2 | + * @file |
| 3 | + * @brief Implementation of the Unbounded 0/1 Knapsack Problem |
| 4 | + * |
| 5 | + * @details |
| 6 | + * The Unbounded 0/1 Knapsack problem allows taking unlimited quantities of each item. |
| 7 | + * The goal is to maximize the total value without exceeding the given knapsack capacity. |
| 8 | + * Unlike the 0/1 knapsack, where each item can be taken only once, in this variation, |
| 9 | + * any item can be picked any number of times as long as the total weight stays within |
| 10 | + * the knapsack's capacity. |
| 11 | + * |
| 12 | + * Given a set of N items, each with a weight and a value, represented by the arrays |
| 13 | + * `wt` and `val` respectively, and a knapsack with a weight limit W, the task is to |
| 14 | + * fill the knapsack to maximize the total value. |
| 15 | + * |
| 16 | + * @note weight and value of items is greater than zero |
| 17 | + * |
| 18 | + * ### Algorithm |
| 19 | + * The approach uses dynamic programming to build a solution iteratively. |
| 20 | + * A 2D array is used for memoization to store intermediate results, allowing |
| 21 | + * the function to avoid redundant calculations. |
| 22 | + * |
| 23 | + * @author [Sanskruti Yeole](https://github.com/yeolesanskruti) |
| 24 | + * @see dynamic_programming/0_1_knapsack.cpp |
| 25 | + */ |
| 26 | + |
| 27 | +#include <iostream> // Standard input-output stream |
| 28 | +#include <vector> // Standard library for using dynamic arrays (vectors) |
| 29 | +#include <cassert> // For using assert function to validate test cases |
| 30 | +#include <cstdint> // For fixed-width integer types like std::uint16_t |
| 31 | + |
| 32 | +/** |
| 33 | + * @namespace dynamic_programming |
| 34 | + * @brief Namespace for dynamic programming algorithms |
| 35 | + */ |
| 36 | +namespace dynamic_programming { |
| 37 | + |
| 38 | +/** |
| 39 | + * @namespace Knapsack |
| 40 | + * @brief Implementation of unbounded 0-1 knapsack problem |
| 41 | + */ |
| 42 | +namespace unbounded_knapsack { |
| 43 | + |
| 44 | +/** |
| 45 | + * @brief Recursive function to calculate the maximum value obtainable using |
| 46 | + * an unbounded knapsack approach. |
| 47 | + * |
| 48 | + * @param i Current index in the value and weight vectors. |
| 49 | + * @param W Remaining capacity of the knapsack. |
| 50 | + * @param val Vector of values corresponding to the items. |
| 51 | + * @note "val" data type can be changed according to the size of the input. |
| 52 | + * @param wt Vector of weights corresponding to the items. |
| 53 | + * @note "wt" data type can be changed according to the size of the input. |
| 54 | + * @param dp 2D vector for memoization to avoid redundant calculations. |
| 55 | + * @return The maximum value that can be obtained for the given index and capacity. |
| 56 | + */ |
| 57 | +std::uint16_t KnapSackFilling(std::uint16_t i, std::uint16_t W, |
| 58 | + const std::vector<std::uint16_t>& val, |
| 59 | + const std::vector<std::uint16_t>& wt, |
| 60 | + std::vector<std::vector<int>>& dp) { |
| 61 | + if (i == 0) { |
| 62 | + if (wt[0] <= W) { |
| 63 | + return (W / wt[0]) * val[0]; // Take as many of the first item as possible |
| 64 | + } else { |
| 65 | + return 0; // Can't take the first item |
| 66 | + } |
| 67 | + } |
| 68 | + if (dp[i][W] != -1) return dp[i][W]; // Return result if available |
| 69 | + |
| 70 | + int nottake = KnapSackFilling(i - 1, W, val, wt, dp); // Value without taking item i |
| 71 | + int take = 0; |
| 72 | + if (W >= wt[i]) { |
| 73 | + take = val[i] + KnapSackFilling(i, W - wt[i], val, wt, dp); // Value taking item i |
| 74 | + } |
| 75 | + return dp[i][W] = std::max(take, nottake); // Store and return the maximum value |
| 76 | +} |
| 77 | + |
| 78 | +/** |
| 79 | + * @brief Wrapper function to initiate the unbounded knapsack calculation. |
| 80 | + * |
| 81 | + * @param N Number of items. |
| 82 | + * @param W Maximum weight capacity of the knapsack. |
| 83 | + * @param val Vector of values corresponding to the items. |
| 84 | + * @param wt Vector of weights corresponding to the items. |
| 85 | + * @return The maximum value that can be obtained for the given capacity. |
| 86 | + */ |
| 87 | +std::uint16_t unboundedKnapsack(std::uint16_t N, std::uint16_t W, |
| 88 | + const std::vector<std::uint16_t>& val, |
| 89 | + const std::vector<std::uint16_t>& wt) { |
| 90 | + if(N==0)return 0; // Expect 0 since no items |
| 91 | + std::vector<std::vector<int>> dp(N, std::vector<int>(W + 1, -1)); // Initialize memoization table |
| 92 | + return KnapSackFilling(N - 1, W, val, wt, dp); // Start the calculation |
| 93 | +} |
| 94 | + |
| 95 | +} // unbounded_knapsack |
| 96 | + |
| 97 | +} // dynamic_programming |
| 98 | + |
| 99 | +/** |
| 100 | + * @brief self test implementation |
| 101 | + * @return void |
| 102 | + */ |
| 103 | +static void tests() { |
| 104 | + // Test Case 1 |
| 105 | + std::uint16_t N1 = 4; // Number of items |
| 106 | + std::vector<std::uint16_t> wt1 = {1, 3, 4, 5}; // Weights of the items |
| 107 | + std::vector<std::uint16_t> val1 = {6, 1, 7, 7}; // Values of the items |
| 108 | + std::uint16_t W1 = 8; // Maximum capacity of the knapsack |
| 109 | + // Test the function and assert the expected output |
| 110 | + assert(unboundedKnapsack(N1, W1, val1, wt1) == 48); |
| 111 | + std::cout << "Maximum Knapsack value " << unboundedKnapsack(N1, W1, val1, wt1) << std::endl; |
| 112 | + |
| 113 | + // Test Case 2 |
| 114 | + std::uint16_t N2 = 3; // Number of items |
| 115 | + std::vector<std::uint16_t> wt2 = {10, 20, 30}; // Weights of the items |
| 116 | + std::vector<std::uint16_t> val2 = {60, 100, 120}; // Values of the items |
| 117 | + std::uint16_t W2 = 5; // Maximum capacity of the knapsack |
| 118 | + // Test the function and assert the expected output |
| 119 | + assert(unboundedKnapsack(N2, W2, val2, wt2) == 0); |
| 120 | + std::cout << "Maximum Knapsack value " << unboundedKnapsack(N2, W2, val2, wt2) << std::endl; |
| 121 | + |
| 122 | + // Test Case 3 |
| 123 | + std::uint16_t N3 = 3; // Number of items |
| 124 | + std::vector<std::uint16_t> wt3 = {2, 4, 6}; // Weights of the items |
| 125 | + std::vector<std::uint16_t> val3 = {5, 11, 13};// Values of the items |
| 126 | + std::uint16_t W3 = 27;// Maximum capacity of the knapsack |
| 127 | + // Test the function and assert the expected output |
| 128 | + assert(unboundedKnapsack(N3, W3, val3, wt3) == 27); |
| 129 | + std::cout << "Maximum Knapsack value " << unboundedKnapsack(N3, W3, val3, wt3) << std::endl; |
| 130 | + |
| 131 | + // Test Case 4 |
| 132 | + std::uint16_t N4 = 0; // Number of items |
| 133 | + std::vector<std::uint16_t> wt4 = {}; // Weights of the items |
| 134 | + std::vector<std::uint16_t> val4 = {}; // Values of the items |
| 135 | + std::uint16_t W4 = 10; // Maximum capacity of the knapsack |
| 136 | + assert(unboundedKnapsack(N4, W4, val4, wt4) == 0); |
| 137 | + std::cout << "Maximum Knapsack value for empty arrays: " << unboundedKnapsack(N4, W4, val4, wt4) << std::endl; |
| 138 | + |
| 139 | + std::cout << "All test cases passed!" << std::endl; |
| 140 | + |
| 141 | +} |
| 142 | + |
| 143 | +/** |
| 144 | + * @brief main function |
| 145 | + * @return 0 on successful exit |
| 146 | + */ |
| 147 | +int main() { |
| 148 | + tests(); // Run self test implementation |
| 149 | + return 0; |
| 150 | +} |
| 151 | + |
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