unbounded_0_1_knapsack.cpp

/**
 * @file
 * @brief Implementation of the Unbounded 0/1 Knapsack Problem
 * 
 * @details 
 * The Unbounded 0/1 Knapsack problem allows taking 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, 
 * any item can be picked any number of times as long as the total weight stays within 
 * the knapsack's capacity.
 * 
 * Given a set of N items, each with a weight and a value, represented by the arrays 
 * `wt` and `val` respectively, and a knapsack with a weight limit W, the task is to 
 * fill the knapsack to maximize the total value.
 *
 * @note weight and value of items is greater than zero 
 *
 * ### Algorithm
 * The approach uses dynamic programming to build a solution iteratively. 
 * A 2D array is used for memoization to store intermediate results, allowing 
 * the function to avoid redundant calculations.
 * 
 * @author [Sanskruti Yeole](https://github.com/yeolesanskruti)
 * @see dynamic_programming/0_1_knapsack.cpp
 */

#include <iostream>  // Standard input-output stream
#include <vector>   // Standard library for using dynamic arrays (vectors)
#include <cassert>  // For using assert function to validate test cases
#include <cstdint>  // For fixed-width integer types like std::uint16_t

/**
 * @namespace dynamic_programming
 * @brief Namespace for dynamic programming algorithms
 */
namespace dynamic_programming {

/**
 * @namespace Knapsack
 * @brief Implementation of unbounded 0-1 knapsack problem
 */
namespace unbounded_knapsack {

/**
 * @brief Recursive function to calculate the maximum value obtainable 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.
 * @note "val" data type can be changed according to the size of the input.
 * @param wt Vector of weights corresponding to the items.
 * @note "wt" data type can be changed according to the size of the input.
 * @param dp 2D vector for memoization to avoid redundant calculations.
 * @return The maximum value that can be obtained for the given index and capacity.
 */
std::uint16_t 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]; // Take as many of the first item as possible
        } else {
            return 0; // Can't take the first item
        }
    }
    if (dp[i][W] != -1) return dp[i][W]; // Return result if available

    int nottake = KnapSackFilling(i - 1, W, val, wt, dp); // Value without taking item i
    int take = 0;
    if (W >= wt[i]) {
        take = val[i] + KnapSackFilling(i, W - wt[i], val, wt, dp); // Value taking item i
    }
    return dp[i][W] = std::max(take, nottake); // Store and return the maximum value
}

/**
 * @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.
 */
std::uint16_t unboundedKnapsack(std::uint16_t N, std::uint16_t W, 
                      const std::vector<std::uint16_t>& val, 
                      const std::vector<std::uint16_t>& wt) {
    if(N==0)return 0; // Expect 0 since no items
    std::vector<std::vector<int>> dp(N, std::vector<int>(W + 1, -1)); // Initialize memoization table
    return KnapSackFilling(N - 1, W, val, wt, dp); // Start the calculation
}

} // unbounded_knapsack

} // dynamic_programming

/**
 * @brief self test implementation
 * @return void
 */
static void tests() {
    // Test Case 1
    std::uint16_t N1 = 4;  // Number of items
    std::vector<std::uint16_t> wt1 = {1, 3, 4, 5}; // Weights of the items
    std::vector<std::uint16_t> val1 = {6, 1, 7, 7}; // Values of the items
    std::uint16_t W1 = 8; // Maximum capacity of the knapsack
    // Test the function and assert the expected output
    assert(unboundedKnapsack(N1, W1, val1, wt1) == 48);
    std::cout << "Maximum Knapsack value " << unboundedKnapsack(N1, W1, val1, wt1) << std::endl;

    // Test Case 2
    std::uint16_t N2 = 3; // Number of items
    std::vector<std::uint16_t> wt2 = {10, 20, 30}; // Weights of the items
    std::vector<std::uint16_t> val2 = {60, 100, 120}; // Values of the items
    std::uint16_t W2 = 5; // Maximum capacity of the knapsack
    // Test the function and assert the expected output
    assert(unboundedKnapsack(N2, W2, val2, wt2) == 0);
    std::cout << "Maximum Knapsack value " << unboundedKnapsack(N2, W2, val2, wt2) << std::endl;

    // Test Case 3
    std::uint16_t N3 = 3; // Number of items
    std::vector<std::uint16_t> wt3 = {2, 4, 6}; // Weights of the items
    std::vector<std::uint16_t> val3 = {5, 11, 13};// Values of the items 
    std::uint16_t W3 = 27;// Maximum capacity of the knapsack 
    // Test the function and assert the expected output
    assert(unboundedKnapsack(N3, W3, val3, wt3) == 27);
    std::cout << "Maximum Knapsack value " << unboundedKnapsack(N3, W3, val3, wt3) << std::endl;

    // Test Case 4
    std::uint16_t N4 = 0; // Number of items
    std::vector<std::uint16_t> wt4 = {}; // Weights of the items
    std::vector<std::uint16_t> val4 = {}; // Values of the items 
    std::uint16_t W4 = 10; // Maximum capacity of the knapsack
    assert(unboundedKnapsack(N4, W4, val4, wt4) == 0); 
    std::cout << "Maximum Knapsack value for empty arrays: " << unboundedKnapsack(N4, W4, val4, wt4) << std::endl;
  
    std::cout << "All test cases passed!" << std::endl;

}

/**
 * @brief main function
 * @return 0 on successful exit
 */
int main() {
    tests(); // Run self test implementation 
    return 0;
}