POJ 2112 Optimal Milking【网络流+二分+最短路】

求使所有牛都可以被挤牛奶的条件下牛走的最长距离。

Floyd求出两两节点之间的最短路，然后二分距离。

构图：

将每一个milking machine与源点连接，边权为最大值m，每个cow与汇点连接，边权为1，然后根据二分的距离x，将g[i][j] < x的milking machine节点i与cow节点j连接，边权为1，其他的赋值为零。

最大流的结果是可以被挤奶的cow数量，判断是否等于总的cow总量即可。

#include <iostream>#include <cstring>#include <vector>#include <cstdio>#include <algorithm>using namespace std;#define N 240#define INF 0x3f3f3f3fclass Dinic {public:    int n, s, t, l[N], c[N][N], e[N];    int flow(int maxf = INF) {        int left = maxf;        while (build()) left -= push(s, left);        return maxf - left;    }    int push(int x, int f) {        if (x == t) return f;        int &y = e[x], sum = f;        for (; y<n; y++)            if (c[x][y] > 0 && l[x]+1==l[y]) {                int cnt = push(y, min(sum, c[x][y]));                c[x][y] -= cnt;                c[y][x] += cnt;                sum -= cnt;                if (!sum) return f;            }        return f-sum;    }    bool build() {        int m = 0;        memset(l, -1, sizeof(l));        l[e[m++]=s] = 0;        for (int i=0; i<m; i++) for (int y=0; y<n; y++)            if (c[e[i]][y] > 0 && l[y]<0) l[e[m++]=y] = l[e[i]] + 1;        memset(e, 0, sizeof(e));        return l[t] >= 0;    }} net;int g[N][N], n, k, c, m;bool ok(int x) {    memset(net.c, 0, sizeof(net.c));    net.s = 0, net.t = n + 1, net.n = n + 2;    for (int i=1; i<=k; i++) net.c[0][i] = m;    for (int i=k+1; i<=n; i++) net.c[i][net.t] = 1;    for (int i=1; i<=k; i++)        for (int j=k+1; j<=n; j++)            if (g[i][j] <= x) net.c[i][j] = 1;            else net.c[i][j] = 0;    return net.flow() == c;}int main() {    while (scanf("%d%d%d", &k, &c, &m) == 3) {        n = k + c;        for (int i=1; i<=n; i++)            for (int j=1; j<=n; j++) {                scanf(" %d", &g[i][j]);                if (g[i][j] == 0 && i != j) g[i][j] = INF;            }        for (int p=1; p<=n; p++) for (int i=1; i<=n; i++)            for (int j=1; j<=n; j++) g[i][j] = min(g[i][j], g[i][p] + g[p][j]);        int l = 0, r = INF, mid, ans;        while (l <= r) {            mid = (l + r) >> 1;            if (ok(mid)) {                ans = mid;                r = mid -1;            } else l = mid + 1;        }        cout << ans << endl;    }    return 0;}