UVA 1212 - Duopoly

题目链接

题意：两个公司，每个公司都有n个开价租用一些频道，一个频道只能租给一个公司，现在要求出一个分配方案使得收益最大

思路：最小割，源点连到第一个公司，第二个公司连到汇点，容量均为价钱，然后第一个公司和第二个公司有冲突的就连一条边容量为无穷大，然后求这个图的最小割就是去掉最小多少使得图原图不会冲突了，然后用总金额减去最小割的值即可

代码：

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

const int MAXNODE = 6005;
const int MAXEDGE = 320005;

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 = 300005;
int T, n1, n2, vis[N];

int main() {
	int cas = 0;
	scanf("%d", &T);
	while (T--) {
		int sum = 0;
		gao.init(0);
		memset(vis, 0, sizeof(vis));
		scanf("%d", &n1);
		int a, b;
		char c;
		for (int i = 1; i <= n1; i++) {
			scanf("%d", &a);
			sum += a;
			gao.add_Edge(0, i, a);
			while ((c = getchar()) != '\n') {
				scanf("%d", &b);
				vis[b] = i;
			}
		}
		scanf("%d", &n2);
		gao.n = n1 + n2 + 2;
		int t = n1 + n2 + 1;
		for (int i = n1 + 1; i <= n1 + n2; i++) {
			scanf("%d", &a);
			sum += a;
			gao.add_Edge(i, t, a);
			while ((c = getchar()) != '\n') {
				scanf("%d", &b);
				if (vis[b] != 0) gao.add_Edge(vis[b], i, INF);
			}
		}
		printf("Case %d:\n", ++cas);
		printf("%d\n", sum - gao.Maxflow(0, t));
		if (T) printf("\n");
	}
	return 0;
}

UVA 1212 - Duopoly（最小割）