题目链接:https://onlinejudge.org/index.php?option=com_onlinejudge&Itemid=8&page=show_problem&category=0&problem=4535&mosmsg=Submission+received+with+ID+26565007
点的容量问题可以用拆点解决,于是将每个点拆成两个点,连容量为 \(1\) 的边,原来的边容量为无穷大,
表示只能割点,割点的代价为 \(1\),枚举点对,其中使得点对不连通的最小割的最小值即为答案
特殊情况:当点对之间两两都有边时,最小割为无穷大,此时的点连通度为 \(n\)
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn = 510;
const int INF = 1000000007;
int n, m;
int u[maxn], v[maxn];
int h[maxn], cnt = 1;
struct E{
int to, cap, next;
}e[maxn * maxn * 10];
void add(int u, int v, int c){
e[++cnt].to = v;
e[cnt].cap = c;
e[cnt].next = h[u];
h[u] = cnt;
}
int s,t;
int vis[maxn], d[maxn], cur[maxn];
bool BFS() {
memset(vis, 0, sizeof(vis));
queue<int> Q;
Q.push(s);
vis[s] = 1;
d[s] = 0;
while(!Q.empty()) {
int u = Q.front(); Q.pop();
for(int i = h[u]; i != -1 ; i = e[i].next) {
if(!vis[e[i].to] && e[i].cap) {
vis[e[i].to] = 1;
d[e[i].to] = d[u] + 1;
Q.push(e[i].to);
}
}
}
return vis[t];
}
int DFS(int x, int a) {
if(x == t || a == 0) return a;
int flow = 0, f;
for(int &i = cur[x]; i != -1 ; i = e[i].next) {
if(d[x] + 1 == d[e[i].to] && (f = DFS(e[i].to, min(a, e[i].cap))) > 0) {
e[i].cap -= f;
e[i^1].cap += f;
flow += f;
a -= f;
if(a == 0) break;
}
}
return flow;
}
int Maxflow() {
int flow = 0;
while(BFS()) {
memcpy(cur, h, sizeof(h));
flow += DFS(s, INF);
}
return flow;
}
ll read(){ ll s = 0, f = 1; char ch = getchar(); while(ch < '0' || ch > '9'){ if(ch == '-') f = -1; ch = getchar(); } while(ch >= '0' && ch <= '9'){ s = s * 10 + ch - '0'; ch = getchar(); } return s * f; }
int main(){
int kase = 0; int flag = 0;
while(scanf("%d%d", &n, &m) == 2){
memset(h, -1, sizeof(h)); cnt = 1;
for(int i = 1 ; i <= m ; ++i){
scanf(" (%d,%d)", &u[i], &v[i]);
++u[i], ++v[i];
}
int ans = INF;
for(int ss = 1 ; ss <= n ; ++ss){
for(int tt = 1 ; tt <= n ; ++tt){
if(ss == tt) continue;
memset(h, -1, sizeof(h)); cnt = 1;
for(int i = 1 ; i <= n ; ++i){
add(i, i + n, 1);
add(i + n, i, 0);
}
for(int i = 1 ; i <= m ; ++i){
add(u[i] + n, v[i], INF);
add(v[i], u[i] + n, 0);
add(v[i] + n, u[i], INF);
add(u[i], v[i] + n, 0);
}
s = ss + n, t = tt;
ans = min(ans, Maxflow());
}
}
if(ans == INF) ans = n;
printf("%d\n", ans);
}
return 0;
}