flow - Hungarian

#include <bits/stdc++.h>
using namespace std;

const int N = 55;

typedef int Type;
const Type INF = 0x3f3f3f3f;

struct Hungary {
    int n, m;                 // left and right side dimension
    Type g[N][N];             // Given Matrix
    Type Lx[N], Ly[N], slack[N];
    int left[N], right[N];    // Matching vertex of other side
    bool S[N], T[N];          // Status of Left and right

    void init(int n, int m) {
        this->n = n;
        this->m = m;
        memset(g, 0, sizeof(g));
    }
    bool dfs(int i) {
        S[i] = true;
        for (int j = 0; j < m; j++) {
            if (T[j]) continue;
            Type tmp = Lx[i] + Ly[j] - g[i][j];
            if (!tmp) {
                T[j] = true;
                if (left[j] == -1 || dfs(left[j])) {
                    left[j] = i;
                    right[i] = j;
                    return true;
                }
            } else slack[j] = min(slack[j], tmp);
        }
        return false;
    }

    void update() {
        Type a = INF;
        for (int i = 0; i < m; i++)
            if (!T[i]) a = min(a, slack[i]);
        for (int i = 0; i < n; i++)
            if (S[i]) Lx[i] -= a;
        for (int i = 0; i < m; i++)
            if (T[i]) Ly[i] += a;
    }

    Type km() {
        memset(left, -1, sizeof(left));
        memset(right, -1, sizeof(right));
        memset(Ly, 0, sizeof(Ly));
        for (int i = 0; i < n; i++) {
            Lx[i] = -INF;
            for (int j = 0; j < m; j++)
                Lx[i] = max(Lx[i], g[i][j]);
        }
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) slack[j] = INF;
            while (1) {
                memset(S, false, sizeof(S));
                memset(T, false, sizeof(T));
                if (dfs(i)) break;
                else update();
            }
        }
        Type ans = 0;
        for (int i = 0; i < n; i++) {
            //if (right[i] == -1) return -1;
            //if (g[i][right[i]] == -INF) return -1;
            ans += g[i][right[i]];
        }
        return ans;
    }
} h;