题目传送门：http://www.lydsy.com/JudgeOnline/problem.php?id=4519
分治+最小割
具体来说，假设随便选两个点来做一次最小割x
那么左右点被分成了两个点集，而任意一对存在于不同点集的点的最小割与x的割相等
于是只用考虑每个点集内部的点，接下来的事就是坚持信仰了
#include<bits/stdc++.h>
#define LL long long
#define abs(x) ((x)>0?(x):-(x))
using namespace std;
const int N = 850+9;
const int M = 8500*2+9;
const int INF = 100000000;
int head[N],nxt[M],to[M],flow[M],cur[N];
int n,m,vout[N*N],cnt,id[N],dis[N],pur,T=1;
queue<int> que;
inline void Add_Edge(int u, int v, int w) {
to[++T] = v; nxt[T] = head[u]; head[u] = T; flow[T] = w;
to[++T] = u; nxt[T] = head[v]; head[v] = T; flow[T] = w;
}
inline int read(){
char c=getchar(); int ret=0,f=1;
while (c<'0'||c>'9') {if(c=='-')f=-1;c=getchar();}
while (c<='9'&&c>='0') ret=ret*10+c-'0',c=getchar();
return ret*f;
}
inline bool BFS(int s, int t) {
memset(dis,-1,sizeof(dis));
que.push(s); dis[s] = 0;
while (!que.empty()) {
int w = que.front(); que.pop();
for (int i=head[w];i;i=nxt[i]) if (flow[i] && !~dis[to[i]])
dis[to[i]] = dis[w] + 1, que.push(to[i]);
}
return ~dis[t];
}
int DFS(int w, int f) {
if (w == pur) return f;
else {
int ret = 0;
for (int &i=cur[w];i;i=nxt[i]) if (flow[i] && dis[to[i]] == dis[w] + 1) {
int tmp = DFS(to[i], min(f, flow[i]));
flow[i] -= tmp; flow[i^1] += tmp;
ret += tmp; f -= tmp; if (!f) return ret;
}
return ret;
}
}
inline int Dinic(int s, int t){
int ret = 0; pur = t;
while (BFS(s,t)) {
memcpy(cur,head,sizeof(head));
ret += DFS(s,INF);
} return ret;
}
void SIGN(int w) {
dis[w] = 1;
for (int i=head[w];i;i=nxt[i])
if (!~dis[to[i]] && flow[i]) SIGN(to[i]);
}
void solve(int l , int r){
if (l >= r) return ;
static int tmp[N]; int L=l-1, R=r+1;
for (int i=2;i<=T;i+=2) flow[i] = flow[i^1] = flow[i] + flow[i^1] >> 1;
vout[++cnt] = Dinic(id[l],id[r]);
memset(dis,-1,sizeof(dis)); SIGN(id[l]);
for (int i=l;i<=r;i++)
if (~dis[id[i]]) tmp[++L] = id[i];
else tmp[--R] = id[i];
for (int i=l;i<=r;i++) id[i] = tmp[i];
solve(l,L); solve(R,r);
}
int main(){
n = read(); m = read();
for (int i=1,u,v,w;i<=m;i++) u = read(), v = read(), w = read(), Add_Edge(u,v,w);
for (int i=1;i<=n;i++) id[i] = i; solve(1,n);
int tot = 0; sort(vout+1,vout+1+cnt);
for (int i=1;i<=cnt;i++) if (vout[i] != vout[i-1]) tot++;
printf("%d\n",tot);
return 0;
}
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