POJ 2112 Optimal Milking（二分+最大流）

Posted 2020-09-13 jzdwajue

POJ 2112 Optimal Milking

题目链接

题意：给定一些机器和奶牛，在给定距离矩阵，（不在对角线上为0的值代表不可达），每一个机器能容纳m个奶牛。问全部奶牛都能挤上奶，那么走的距离最大的奶牛的最小值是多少

思路：明显的二分+最大流。注意floyd求出的距离矩阵最大值可能不止200，所以二分的上限要注意

代码：

#include <cstdio>
#include <cstring>
#include <queue>
#include <algorithm>
using namespace std;

const int MAXNODE = 255;
const int MAXEDGE = 100005;

typedef int Type;
const Type INF = 0x3f3f3f3f;

struct Edge {
	int u, v;
	Type cap, flow;
	Edge() {}
	Edge(int u, int v, Type cap, Type flow) {
		this->u = u;
		this->v = v;
		this->cap = cap;
		this->flow = flow;
	}
};

struct Dinic {
	int n, m, s, t;
	Edge edges[MAXEDGE];
	int first[MAXNODE];
	int next[MAXEDGE];
	bool vis[MAXNODE];
	Type d[MAXNODE];
	int cur[MAXNODE];
	vector<int> cut;

	void init(int n) {
		this->n = n;
		memset(first, -1, sizeof(first));
		m = 0;
	}
	void add_Edge(int u, int v, Type cap) {
		edges[m] = Edge(u, v, cap, 0);
		next[m] = first[u];
		first[u] = m++;
		edges[m] = Edge(v, u, 0, 0);
		next[m] = first[v];
		first[v] = m++;
	}

	bool bfs() {
		memset(vis, false, sizeof(vis));
		queue<int> Q;
		Q.push(s);
		d[s] = 0;
		vis[s] = true;
		while (!Q.empty()) {
			int u = Q.front(); Q.pop();
			for (int i = first[u]; i != -1; i = next[i]) {
				Edge& e = edges[i];
				if (!vis[e.v] && e.cap > e.flow) {
					vis[e.v] = true;
					d[e.v] = d[u] + 1;
					Q.push(e.v);
				}
			}
		}
		return vis[t];
	}

	Type dfs(int u, Type a) {
		if (u == t || a == 0) return a;
		Type flow = 0, f;
		for (int &i = cur[u]; i != -1; i = next[i]) {
			Edge& e = edges[i];
			if (d[u] + 1 == d[e.v] && (f = dfs(e.v, min(a, e.cap - e.flow))) > 0) {
				e.flow += f;
				edges[i^1].flow -= f;
				flow += f;
				a -= f;
				if (a == 0) break;
			}
		}
		return flow;
	}

	Type Maxflow(int s, int t) {
		this->s = s; this->t = t;
		Type flow = 0;
		while (bfs()) {
			for (int i = 0; i < n; i++)
				cur[i] = first[i];
			flow += dfs(s, INF);
		}
		return flow;
	}

	void MinCut() {
		cut.clear();
		for (int i = 0; i < m; i += 2) {
			if (vis[edges[i].u] && !vis[edges[i].v])
				cut.push_back(i);
		}
	}
} gao;

const int N = 255;

int n, k, c, m, g[N][N];

bool judge(int len) {
	gao.init(n + 2);
	for (int i = k + 1; i <= n; i++) gao.add_Edge(0, i, 1);
	for (int i = 1; i <= k; i++) {
		gao.add_Edge(i, n + 1, m);
		for (int j = k + 1; j <= n; j++) {
			if (g[j][i] > len) continue;
			gao.add_Edge(j, i, 1);
		}
	}
	return gao.Maxflow(0, n + 1) == c;
}

int main() {
	while (~scanf("%d%d%d", &k, &c, &m)) {
		n = k + c;
		for (int i = 1; i <= n; i++)
			for (int j = 1; j <= n; j++) {
				scanf("%d", &g[i][j]);
				if (i != j && g[i][j] == 0)
					g[i][j] = INF;
			}
		int l = 0, r = 0;
		for (int k = 1; k <= n; k++) {
			for (int i = 1; i <= n; i++) {
				for (int j = 1; j <= n; j++) {
					g[i][j] = min(g[i][j], g[i][k] + g[k][j]);
					if (g[i][j] != INF) r = max(r, g[i][j]);
				}
			}
		}
		while (l < r) {
			int mid = (l + r) / 2;
			if (judge(mid)) r = mid;
			else l = mid + 1;
		}
		printf("%d\n", l);
	}
	return 0;
}