HDU 3081 Marriage Match II（二分+最大流）

HDU 3081 Marriage Match II

题目链接

题意：n个女孩n个男孩，每个女孩可以和一些男孩配对，然后有些女孩是朋友，满足这个朋友圈里面的人，如果有一个能和某个男孩配对，其他就都可以，然后每轮要求每个女孩匹配到一个男孩，且每轮匹配到的都不同，问最多能匹配几轮

思路：二分轮数k，然后建图为，源点连向女孩，男孩连向汇点容量都为k，然后女孩和男孩之间连边为，有关系的连边容量1，这样一个匹配对应一条边，且不会重复，每次判断最大流是否等于n * k即可

代码：

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

const int MAXNODE = 205;
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 = 105;

int t, n, m, f, g

, parent
;

int find(int x) {
return x == parent[x] ? x : parent[x] = find(parent[x]);
}

bool judge(int k) {
int s = 0, t = n * 2 + 1;
gao.init(t + 1);
for (int i = 1; i <= n; i++) {
gao.add_Edge(s, i, k);
gao.add_Edge(i + n, t, k);
for (int j = 1; j <= n; j++)
if (g[i][j]) gao.add_Edge(i, j + n, 1);
}
return gao.Maxflow(s, t) == n * k;
}

int main() {
scanf("%d", &t);
while (t--) {
scanf("%d%d%d", &n, &m, &f);
memset(g, 0, sizeof(g));
for (int i = 1; i <= n; i++) parent[i] = i;
int u, v;
while (m--) {
scanf("%d%d", &u, &v);
g[u][v] = 1;
}
while (f--) {
scanf("%d%d", &u, &v);
int pa = find(u);
int pb = find(v);
if (pa != pb) parent[pa] = pb;
}
for (int i = 1; i <= n; i++)
for (int j = 1; j <= n; j++) {
if (find(i) == find(j)) {
for (int k = 1; k <= n; k++)
g[i][k] |= g[j][k];
}
}
int l = 1, r = n + 1;
while (l < r) {
int mid = (l + r) / 2;
if (judge(mid)) l = mid + 1;
else r = mid;
}
printf("%d\n", l - 1);
}
return 0;
}