hdu 3435 A new Graph Game

http://acm.hdu.edu.cn/showproblem.php?pid=3435

　　题意是，从一个给定的图里得到一个或以上的哈密顿回路，使得所有边权之和最小。子图不能只有一个点。

　　很容易想到用KM最优匹配，将自环全都设置为不连通，然后一次KM匹配就可以完成了！这次的KM算法不能只用一个slack来记录松弛的大小，必须要用多个slack，以空间来换时间。于是我就顺便更新我的KM模板了~！

AC代码：

/*
 * Author: Lyon
 * Problem: hdu 3435
 */

#include <cstdio>
#include <cstring>
#include <cassert>
#include <algorithm>

using namespace std;
const int inf = 100000000;
const int maxn = 1001;

int lx[maxn], ly[maxn], mat[maxn][maxn], match[maxn];
bool vx[maxn], vy[maxn];
//int slack;
int sl[maxn];

bool dfs(int x, int n){
    vx[x] = true;
    for (int y = 1; y <= n; y++){
        if (vy[y]) continue;

        int t = lx[x] + ly[y] - mat[x][y];

        if (t){
            //slack = min(slack, t);
            sl[y] = min(sl[y], t);
        }
        else{
            vy[y] = true;
            if (~match[y] && !dfs(match[y], n)) continue;
            match[y] = x;

            return true;
        }
    }

    return false;
}

int km(int n){
    for (int i = 1; i <= n; i++){
        match[i] = -1;
        lx[i] = -inf;
        ly[i] = 0;
        for (int j = 1; j <= n; j++){
            lx[i] = max(lx[i], mat[i][j]);
        }
    }
    for (int x = 1; x <= n; x++){
        for (int i = 1; i <= n; i++){
            sl[i] = inf;
        }

        int minsl;

        while (true){
            for (int i = 1; i <= n; i++){
                vx[i] = vy[i] = false;
            }
            //slack = inf;
            if (dfs(x, n)) break;
            minsl = inf;
            for (int i = 1; i <= n; i++){
                if (!vy[i]) minsl = min(minsl, sl[i]);
            }
            for (int i = 1; i <= n; i++){
                if (vx[i]) lx[i] -= minsl;
                if (vy[i]) ly[i] += minsl;
                else sl[i] -= minsl;
            }
            /*
            for (int i = 1; i <= n; i++){
                if (vx[i]) lx[i] -= slack;
                if (vy[i]) ly[i] += slack;
            }
            */
        }
    }

    int ret = 0;

    for (int i = 1; i <= n; i++){
        if (~match[i]) ret += mat[match[i]][i];
        if (ret <= -inf) return -1;
    }

    return -ret;
}

void makeGraph(int n, int m){
    for (int i = 1; i <= n; i++){
        for (int j = 1; j <= n; j++){
            mat[i][j] = -inf;
        }
    }
    while (m--){
        int a, b, c;

        scanf("%d%d%d", &a, &b, &c);
        if (a == b) continue;
        mat[a][b] = mat[b][a] = max(-c, mat[a][b]);
    }
}

int main(){
    int n, m, T;

    scanf("%d", &T);
    for (int i = 1; i <= T; i++){
        scanf("%d%d", &n, &m);
        makeGraph(n, m);

        int ans = km(n);

        printf("Case %d: ", i);
        if (~ans){
            printf("%d\n", ans);
        }
        else puts("NO");
    }

    return 0;
}

——written by Lyon