Copied Hungarian Algorithm from Wikipedia

I still do not understand it tho...

Author: EduMenges

4/CMakeLists.txt

@@ -0,0 +1,2 @@
+add_executable(hungarian_algorithm hungarian_algorithm.cpp)
+target_link_libraries(hungarian_algorithm PRIVATE mimalloc)

4/hungarian_algorithm.cpp

@@ -0,0 +1,103 @@
+#if __has_include(<mimalloc-new-delete.h>)
+#include <mimalloc-new-delete.h>
+#endif
+
+#if __has_include(<mdspan>)
+#include <mdspan>
+#else
+#include "util/mdspan.hpp"
+#endif
+
+#include <algorithm>
+#include <iostream>
+#include <limits>
+#include <vector>
+
+using namespace std;
+
+using Weight = int32_t;
+
+constexpr int INF = numeric_limits<Weight>::max();
+
+pair<Weight, vector<int>> hungarian(const vector<vector<Weight>>& cost) {
+    auto n = cost.size();
+    vector<int> u(n, 0); // Labels do U
+    vector<int> v(n, 0); // Labels do V
+    vector<int> match_left(n, -1);
+    vector<int> match_right(n, -1);
+
+    for (int i = 0; i < n; ++i) {
+        vector<int> effective_costs(n, INF);
+        vector<int> predecessors(n, -1);
+        vector used(n, false);
+
+        int marked_i = i;
+        int marked_j = -1;
+        int j;
+
+        while (true) {
+            j = -1;
+            for (int k = 0; k < n; ++k) {
+                if (!used[k]) {
+                    auto effective_cost = cost[marked_i][k] - u[marked_i] - v[k];
+                    if (effective_cost < effective_costs[k]) {
+                        effective_costs[k] = effective_cost;
+                        predecessors[k] = marked_j;
+                    }
+                    if (j == -1 || effective_costs[k] < effective_costs[j])
+                        j = k;
+                }
+            }
+
+            int delta = effective_costs[j];
+            for (int k = 0; k < n; ++k) {
+                if (used[k]) {
+                    u[match_right[k]] += delta;
+                    v[k] -= delta;
+                } else {
+                    effective_costs[k] -= delta;
+                }
+            }
+            u[i] += delta;
+
+            used[j] = true;
+            marked_j = j;
+            if (match_right[j] == -1) {
+                break;
+            }
+            marked_i = match_right[j];
+        }
+
+        while (predecessors[j] != -1) {
+            match_right[j] = match_right[predecessors[j]];
+            j = predecessors[j];
+        }
+        match_right[j] = i;
+    }
+
+    // Monta match_left
+    int total_weight = 0;
+    for (int j = 0; j < n; ++j) {
+        if (match_right[j] != -1) {
+            match_left[match_right[j]] = j;
+            total_weight += cost[match_right[j]][j];
+        }
+    }
+
+    return {total_weight, match_left};
+}
+
+int main() {
+    vector<vector<Weight>> weight = {{10, 19, 8}, {10, 18, 7}, {5, 7, 9}};
+
+    auto [max_weight, match] = hungarian(weight);
+
+    cout << "Emparelhamento ótimo (máximo peso):\n";
+    for (int i = 0; i < match.size(); ++i) {
+        cout << "Vértice " << i << " emparelhado com " << match[i]
+             << " (peso: " << weight[i][match[i]] << ")\n";
+    }
+    cout << "Peso total do emparelhamento: " << max_weight << endl;
+
+    return 0;
+}

CMakeLists.txt

@@ -37,3 +37,4 @@ find_package(OpenMP REQUIRED)
 add_subdirectory(1)
 add_subdirectory(2)
 add_subdirectory(3)
+add_subdirectory(4)