Graph/Matching/HungarianLMH.h

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• Last update: 2022-01-06 04:03:40+08:00
• Link: https://codeforces.com/contest/1437/problem/C
• Link: https://judge.yosupo.jp/problem/assignment

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• Graph/tests/matching_bipartite_weighted.test.cpp

Code

// Index from 1
// Min cost matching
// Usage: init(); for[i,j,cost] addEdge(i, j, cost)
//
// Tested:
// - SGU 210
// - SGU 206
// - https://codeforces.com/contest/1437/problem/C
// - https://judge.yosupo.jp/problem/assignment

#define arg __arg
long long c[MN][MN];
long long fx[MN], fy[MN];
int mx[MN], my[MN];
int trace[MN], qu[MN], arg[MN];
long long d[MN];
int front, rear, start, finish;

void init() {
    FOR(i,1,N) {
        fy[i] = mx[i] = my[i] = 0;
        FOR(j,1,N) c[i][j] = inf;
    }
}

void addEdge(int i, int j, long long cost) {
    c[i][j] = min(c[i][j], cost);
}

inline long long getC(int i, int j) {
    return c[i][j] - fx[i] - fy[j];
}

void initBFS() {
    front = rear = 1;
    qu[1] = start;
    memset(trace, 0, sizeof trace);
    FOR(j,1,N) {
        d[j] = getC(start, j);
        arg[j] = start;
    }
    finish = 0;
}

void findAugPath() {
    while (front <= rear) {
        int i = qu[front++];
        FOR(j,1,N) if (!trace[j]) {
            long long w = getC(i, j);
            if (!w) {
                trace[j] = i;
                if (!my[j]) {
                    finish = j;
                    return ;
                }
                qu[++rear] = my[j];
            }
            if (d[j] > w) {
                d[j] = w;
                arg[j] = i;
            }
        }
    }
}

void subx_addy() {
    long long delta = inf;
    FOR(j,1,N)
        if (trace[j] == 0 && d[j] < delta) delta = d[j];

    // xoay
    fx[start] += delta;
    FOR(j,1,N)
        if (trace[j]) {
            int i = my[j];
            fy[j] -= delta;
            fx[i] += delta;
        }
        else d[j] -= delta;

    FOR(j,1,N)
        if (!trace[j] && !d[j]) {
            trace[j] = arg[j];
            if (!my[j]) { finish = j; return ; }
            qu[++rear] = my[j];
        }
}

void enlarge() {
    do {
        int i = trace[finish];
        int next = mx[i];
        mx[i] = finish;
        my[finish] = i;
        finish = next;
    } while (finish);
}

long long mincost() {
    FOR(i,1,N) fx[i] = *min_element(c[i]+1, c[i]+N+1);
    FOR(j,1,N) {
        fy[j] = c[1][j] - fx[1];
        FOR(i,1,N) {
            fy[j] = min(fy[j], c[i][j] - fx[i]);
        }
    }
    FOR(i,1,N) {
        start = i;
        initBFS();
        while (finish == 0) {
            findAugPath();
            if (!finish) subx_addy();
        }
        enlarge();
    }
    long long res = 0;
    FOR(i,1,N) res += c[i][mx[i]];
    return res;
}

#line 1 "Graph/Matching/HungarianLMH.h"
// Index from 1
// Min cost matching
// Usage: init(); for[i,j,cost] addEdge(i, j, cost)
//
// Tested:
// - SGU 210
// - SGU 206
// - https://codeforces.com/contest/1437/problem/C
// - https://judge.yosupo.jp/problem/assignment

#define arg __arg
long long c[MN][MN];
long long fx[MN], fy[MN];
int mx[MN], my[MN];
int trace[MN], qu[MN], arg[MN];
long long d[MN];
int front, rear, start, finish;

void init() {
    FOR(i,1,N) {
        fy[i] = mx[i] = my[i] = 0;
        FOR(j,1,N) c[i][j] = inf;
    }
}

void addEdge(int i, int j, long long cost) {
    c[i][j] = min(c[i][j], cost);
}

inline long long getC(int i, int j) {
    return c[i][j] - fx[i] - fy[j];
}

void initBFS() {
    front = rear = 1;
    qu[1] = start;
    memset(trace, 0, sizeof trace);
    FOR(j,1,N) {
        d[j] = getC(start, j);
        arg[j] = start;
    }
    finish = 0;
}

void findAugPath() {
    while (front <= rear) {
        int i = qu[front++];
        FOR(j,1,N) if (!trace[j]) {
            long long w = getC(i, j);
            if (!w) {
                trace[j] = i;
                if (!my[j]) {
                    finish = j;
                    return ;
                }
                qu[++rear] = my[j];
            }
            if (d[j] > w) {
                d[j] = w;
                arg[j] = i;
            }
        }
    }
}

void subx_addy() {
    long long delta = inf;
    FOR(j,1,N)
        if (trace[j] == 0 && d[j] < delta) delta = d[j];

    // xoay
    fx[start] += delta;
    FOR(j,1,N)
        if (trace[j]) {
            int i = my[j];
            fy[j] -= delta;
            fx[i] += delta;
        }
        else d[j] -= delta;

    FOR(j,1,N)
        if (!trace[j] && !d[j]) {
            trace[j] = arg[j];
            if (!my[j]) { finish = j; return ; }
            qu[++rear] = my[j];
        }
}

void enlarge() {
    do {
        int i = trace[finish];
        int next = mx[i];
        mx[i] = finish;
        my[finish] = i;
        finish = next;
    } while (finish);
}

long long mincost() {
    FOR(i,1,N) fx[i] = *min_element(c[i]+1, c[i]+N+1);
    FOR(j,1,N) {
        fy[j] = c[1][j] - fx[1];
        FOR(i,1,N) {
            fy[j] = min(fy[j], c[i][j] - fx[i]);
        }
    }
    FOR(i,1,N) {
        start = i;
        initBFS();
        while (finish == 0) {
            findAugPath();
            if (!finish) subx_addy();
        }
        enlarge();
    }
    long long res = 0;
    FOR(i,1,N) res += c[i][mx[i]];
    return res;
}

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