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| 1 | +/** |
| 2 | + * @file |
| 3 | + * @brief [Gale Shapley Algorithm](https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm) |
| 4 | + * @details |
| 5 | + * This implementation utilizes the Gale-Shapley algorithm to find stable matches. |
| 6 | + * |
| 7 | + * **Gale Shapley Algorithm** aims to find a stable matching between two equally sized |
| 8 | + * sets of elements given an ordinal preference for each element. The algorithm was |
| 9 | + * introduced by David Gale and Lloyd Shapley in 1962. |
| 10 | + * |
| 11 | + * Reference: |
| 12 | + * [Wikipedia](https://en.wikipedia.org/wiki/Gale%E2%80%93Shapley_algorithm) |
| 13 | + * [Wikipedia](https://en.wikipedia.org/wiki/Stable_matching_problem) |
| 14 | + * |
| 15 | + * @author [B Karthik](https://github.com/BKarthik7) |
| 16 | + */ |
| 17 | + |
| 18 | +#include <iostream> /// for std::u32int_t |
| 19 | +#include <vector> /// for std::vector |
| 20 | +#include <algorithm> /// for std::find |
| 21 | +#include <cassert> /// for assert |
| 22 | + |
| 23 | +/** |
| 24 | + * @namespace |
| 25 | + * @brief Greedy Algorithms |
| 26 | + */ |
| 27 | +namespace greedy_algorithms { |
| 28 | +/** |
| 29 | + * @namespace |
| 30 | + * @brief Functions for the Gale-Shapley Algorithm |
| 31 | + */ |
| 32 | +namespace stable_matching { |
| 33 | +/** |
| 34 | + * @brief The main function that finds the stable matching between two sets of elements |
| 35 | + * using the Gale-Shapley Algorithm. |
| 36 | + * @note This doesn't work on negative preferences. the preferences should be continuous integers starting from |
| 37 | + * 0 to number of preferences - 1. |
| 38 | + * @param primary_preferences the preferences of the primary set should be a 2D vector |
| 39 | + * @param secondary_preferences the preferences of the secondary set should be a 2D vector |
| 40 | + * @returns matches the stable matching between the two sets |
| 41 | + */ |
| 42 | +std::vector<std::uint32_t> gale_shapley(const std::vector<std::vector<std::uint32_t>>& secondary_preferences, const std::vector<std::vector<std::uint32_t>>& primary_preferences) { |
| 43 | + std::uint32_t num_elements = secondary_preferences.size(); |
| 44 | + std::vector<std::uint32_t> matches(num_elements, -1); |
| 45 | + std::vector<bool> is_free_primary(num_elements, true); |
| 46 | + std::vector<std::uint32_t> proposal_index(num_elements, 0); // Tracks the next secondary to propose for each primary |
| 47 | + |
| 48 | + while (true) { |
| 49 | + int free_primary_index = -1; |
| 50 | + |
| 51 | + // Find the next free primary |
| 52 | + for (std::uint32_t i = 0; i < num_elements; i++) { |
| 53 | + if (is_free_primary[i]) { |
| 54 | + free_primary_index = i; |
| 55 | + break; |
| 56 | + } |
| 57 | + } |
| 58 | + |
| 59 | + // If no free primary is found, break the loop |
| 60 | + if (free_primary_index == -1) break; |
| 61 | + |
| 62 | + // Get the next secondary to propose |
| 63 | + std::uint32_t secondary_to_propose = primary_preferences[free_primary_index][proposal_index[free_primary_index]]; |
| 64 | + proposal_index[free_primary_index]++; |
| 65 | + |
| 66 | + // Get the current match of the secondary |
| 67 | + std::uint32_t current_match = matches[secondary_to_propose]; |
| 68 | + |
| 69 | + // If the secondary is free, match them |
| 70 | + if (current_match == -1) { |
| 71 | + matches[secondary_to_propose] = free_primary_index; |
| 72 | + is_free_primary[free_primary_index] = false; |
| 73 | + } else { |
| 74 | + // Determine if the current match should be replaced |
| 75 | + auto new_proposer_rank = std::find(secondary_preferences[secondary_to_propose].begin(), |
| 76 | + secondary_preferences[secondary_to_propose].end(), |
| 77 | + free_primary_index); |
| 78 | + auto current_match_rank = std::find(secondary_preferences[secondary_to_propose].begin(), |
| 79 | + secondary_preferences[secondary_to_propose].end(), |
| 80 | + current_match); |
| 81 | + |
| 82 | + // If the new proposer is preferred over the current match |
| 83 | + if (new_proposer_rank < current_match_rank) { |
| 84 | + matches[secondary_to_propose] = free_primary_index; |
| 85 | + is_free_primary[free_primary_index] = false; |
| 86 | + is_free_primary[current_match] = true; // Current match is now free |
| 87 | + } |
| 88 | + } |
| 89 | + } |
| 90 | + |
| 91 | + return matches; |
| 92 | +} |
| 93 | +} // namespace stable_matching |
| 94 | +} // namespace greedy_algorithms |
| 95 | + |
| 96 | +/** |
| 97 | + * @brief Self-test implementations |
| 98 | + * @returns void |
| 99 | + */ |
| 100 | +static void tests() { |
| 101 | + // Test Case 1 |
| 102 | + std::vector<std::vector<std::uint32_t>> primary_preferences = {{0, 1, 2, 3}, {2, 1, 3, 0}, {1, 2, 0, 3}, {3, 0, 1, 2}}; |
| 103 | + std::vector<std::vector<std::uint32_t>> secondary_preferences = {{1, 0, 2, 3}, {3, 0, 1, 2}, {0, 2, 1, 3}, {1, 2, 0, 3}}; |
| 104 | + assert(greedy_algorithms::stable_matching::gale_shapley(secondary_preferences, primary_preferences) == std::vector<std::uint32_t>({0, 2, 1, 3})); |
| 105 | + |
| 106 | + // Test Case 2 |
| 107 | + primary_preferences = {{0, 2, 1, 3}, {2, 3, 0, 1}, {3, 1, 2, 0}, {2, 1, 0, 3}}; |
| 108 | + secondary_preferences = {{1, 0, 2, 3}, {3, 0, 1, 2}, {0, 2, 1, 3}, {1, 2, 0, 3}}; |
| 109 | + assert(greedy_algorithms::stable_matching::gale_shapley(secondary_preferences, primary_preferences) == std::vector<std::uint32_t>({0, 3, 1, 2})); |
| 110 | + |
| 111 | + // Test Case 3 |
| 112 | + primary_preferences = {{0, 1, 2}, {2, 1, 0}, {1, 2, 0}}; |
| 113 | + secondary_preferences = {{1, 0, 2}, {2, 0, 1}, {0, 2, 1}}; |
| 114 | + assert(greedy_algorithms::stable_matching::gale_shapley(secondary_preferences, primary_preferences) == std::vector<std::uint32_t>({0, 2, 1})); |
| 115 | + |
| 116 | + // Test Case 4 |
| 117 | + primary_preferences = {}; |
| 118 | + secondary_preferences = {}; |
| 119 | + assert(greedy_algorithms::stable_matching::gale_shapley(secondary_preferences, primary_preferences) == std::vector<std::uint32_t>({})); |
| 120 | +} |
| 121 | + |
| 122 | +/** |
| 123 | + * @brief Main function |
| 124 | + * @returns 0 on exit |
| 125 | + */ |
| 126 | +int main() { |
| 127 | + tests(); // Run self-test implementations |
| 128 | + return 0; |
| 129 | +} |
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