Added hungarian algorithm

Author: fredbr

graph/hungarian.cpp

@@ -0,0 +1,88 @@
+#include <bits/stdc++.h>
+
+using namespace std;
+
+constexpr int inf = numeric_limits<int>::max();
+
+struct Hungarian {
+    Hungarian(int n_, int m_) :
+            n(n_), m(m_), at(1), u(n_+1), v(m_+1), p(m_+1), way(m_+1) {}
+
+    Hungarian(vector<vector<int>> const& v) :
+            n((int)v.size() - 1), m((int)v[0].size() - 1), at(1),
+            u(n+1), v(m+1), p(m+1), way(m+1) 
+    {
+        for (int i = 1; i <= n; i++) {
+            add_row(v[i]);
+        }
+    }
+
+    void add_row(vector<int> const& a) {
+        p[0] = at++;
+        int j0 = 0;
+        vector<int> minv (m+1, inf);
+        vector<char> used (m+1, false);
+
+        do {
+            used[j0] = true;
+            int i0 = p[j0],  delta = inf,  j1;
+            for (int j = 1; j <= m; j++) {
+                if (!used[j]) {
+                    int cur = a[j] - u[i0] - v[j];
+                    if (cur < minv[j])
+                        minv[j] = cur,  way[j] = j0;
+                    if (minv[j] < delta)
+                        delta = minv[j],  j1 = j;
+                }
+            }
+            for (int j = 0; j <= m; j++) {
+                if (used[j])
+                    u[p[j]] += delta,  v[j] -= delta;
+                else
+                    minv[j] -= delta;
+            }
+            j0 = j1;
+        } while (p[j0] != 0);
+        
+        do {
+            int j1 = way[j0];
+            p[j0] = p[j1];
+            j0 = j1;
+        } while (j0);
+    }
+
+    vector<int> get_ans() {
+        vector<int> ans (at);
+        for (int j=1; j <= m; j++) {
+            ans[p[j]] = j;
+        }
+        return ans;
+    }
+
+private:
+    int n, m, at;
+    vector<int> u, v, p, way;
+};
+
+int main() {
+    int n = 3, m = 4;
+
+    Hungarian h(n, m);
+
+    auto print_ans = [] (auto& h) {
+        auto res = h.get_ans();
+        for (int i = 1; i < (int)res.size(); i++) {
+            cout << res[i] << " ";
+        }
+        cout << "\n";
+    };
+
+    h.add_row({0, 1, 2, 3, 1});
+    print_ans(h);
+    
+    h.add_row({0, 1, 2, 3, 1});
+    print_ans(h);
+    
+    h.add_row({0, 1, 2, 3, 0});
+    print_ans(h);
+}