我又回来了!!!!
这是典型的求最小可相交路径覆盖
我们先求闭包,利用闭包连边,然后求解最小不可相交路径就可以了。
什么?如何求解最小不可相交路径覆盖?
点数-最大匹配数
代码如下:
#include<iostream>
#include<algorithm>
#include<cstring>
#include<queue>
using namespace std;
const int max_n = 550;
const int inf = 2e9;
struct edge{
int to,next;
}E[max_n*max_n*max_n];
int head[max_n];
int cnt=1;
void add(int from,int to){
E[cnt].to=to;E[cnt].next = head[from];
head[from]=cnt++;
}
int leftTo[max_n], rightTo[max_n];
int distleft[max_n], distright[max_n];
int dist;
bool seacherpath(int left_tot, int right_tot) {
fill(distleft, distleft + left_tot + 1, -1);
fill(distright, distright + right_tot + 1, -1);
queue<int> que;dist = inf;
for (int i = 1;i <= left_tot;++i)
if (leftTo[i] == -1)
que.push(i);
while (!que.empty()) {
int u = que.front();que.pop();
if (distleft[u] > dist)break;
for (int i = head[u];i;i = E[i].next) {
int v = E[i].to;
if (distright[v] != -1)continue;
distright[v] = distleft[u] + 1;
if (rightTo[v] == -1)dist = distright[v];
else {
distleft[rightTo[v]] = distright[v] + 1;
que.push(rightTo[v]);
}
}
}return dist != inf;
}
bool matchpath(int u) {
for (int i = head[u];i;i = E[i].next) {
int v = E[i].to;
if (distright[v] != distleft[u] + 1)continue;
if (distright[v] == dist && rightTo[v] != -1)continue;
distright[v] = -1;
if (rightTo[v] == -1 || matchpath(rightTo[v])) {
leftTo[u] = v;
rightTo[v] = u;
return true;
}
}return false;
}
int HK(int left_tot, int right_tot) {
fill(leftTo, leftTo + left_tot + 1, -1);
fill(rightTo, rightTo + right_tot + 1, -1);
int ans = 0;
while (seacherpath(left_tot, right_tot)) {
for (int i = 1;i <= left_tot;++i)
if (leftTo[i] == -1 && matchpath(i))
++ans;
}return ans;
}
bool tr[550][550];
int main(){
int n,m;
while(scanf("%d %d",&n,&m)){
if (n==m&&n==0)break;
fill(head,head+n+5,0);
for (int i=1;i<=n;++i)
for (int j=1;j<=n;++j)
tr[i][j]=0;
cnt=1;
for (int i=1,u,v;i<=m;++i){
scanf("%d %d",&u,&v);
tr[u][v]=1;
}
for (int k=1;k<=n;++k)
for (int i=1;i<=n;++i)
for (int j=1;j<=n;++j)
tr[i][j]=tr[i][k]&tr[k][j]|tr[i][j];
for (int i=1;i<=n;++i)
for (int j=1;j<=n;++j)
if (tr[i][j])
add(i,j);
printf("%d\n",n-HK(n,n));
}
}
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