HDU 3157 Crazy Circuits（有源汇上下界最小流）

HDU 3157 Crazy Circuits

题目链接

题意：一个电路板，上面有N个接线柱(标号1~N)，还有两个电源接线柱 + -。给出一些线路，每一个线路有一个下限值求一个能够让全部部件正常工作的总电流 没有则输出impossible

思路：

有源汇有上下界求最小流，建模方法为：

按无源汇先建图，跑超级源汇ss->tt一次。然后增加t->s，容量INF的边，在跑一次ss->tt，假设是满流。就有解，解为t->s边的当前流量

顺带写个最大流的，最大流就先把t->s增加直接跑一下。t->s的流量就是了

代码：

#include <cstdio>

#include <cstring>

#include <queue>

#include <algorithm>

using namespace std;

const int MAXNODE = 65;

const int MAXEDGE = 10005;

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];

	Type flow;

	int cur[MAXNODE];

	void init(int n) {

		this->n = n;

		memset(first, -1, sizeof(first));

		m = 0;

		flow = 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;

		while (bfs()) {

			for (int i = 0; i < n; i++)

				cur[i] = first[i];

			flow += dfs(s, INF);

		}

		return flow;

	}

	bool judge(int s) {

		for (int i = first[s]; i + 1; i = next[i])

			if (edges[i].flow != edges[i].cap) return false;

		return true;

	}

} gao;

const int N = 65;

int n, m, s, t, ss, tt, du[N];

char c[15];

int main() {

	while (~scanf("%d%d", &n, &m) && n || m) {

		gao.init(n + 4);

		s = 0; t = n + 1; ss = n + 2; tt = n + 3;

		int u, v, w;

		memset(du, 0, sizeof(du));

		while (m--) {

			scanf("%s", c);

			if (c[0] == '+') u = s;

			else sscanf(c, "%d", &u);

			scanf("%s", c);

			if (c[0] == '-') v = t;

			else sscanf(c, "%d", &v);

			scanf("%d", &w);

			gao.add_Edge(u, v, INF);

			du[u] -= w;

			du[v] += w;

		}

		for (int i = s; i <= t; i++) {

			if (du[i] > 0) gao.add_Edge(ss, i, du[i]);

			if (du[i] < 0) gao.add_Edge(i, tt, -du[i]);

		}

		gao.Maxflow(ss, tt);

		gao.add_Edge(t, s, INF);

		gao.Maxflow(ss, tt);

		if (!gao.judge(ss)) printf("impossible\n");

		else printf("%d\n", gao.edges[gao.m - 2].flow);

	}

	return 0;

}