poj2186 Popular Cows
2015-01-01 12:59
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有向图中,寻找所有点都能到达的点集大小
做法:1缩点2.统计scc图的出度,出度为1的点仅有一个u,则ans=sccnum[u],否则ans=0
姊妹命题:寻找能到达所有点的点集大小
把出度统计改为入度统计即可
#include<iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<math.h>
#include<vector>
#include<stack>
#define ll long long
#define INF 0x3f3f3f3f
#define maxn 20000
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
int n,m;
vector<int> g[maxn];
int pre[maxn],lowin[maxn],sccno[maxn],sccnum[maxn],scc_cnt,dfs_clock;
stack<int> S;
int out[maxn],out_cnt,ans;
void build(){
for(int i=1;i<=n;i++) g[i].clear();
for(int i=1;i<=m;i++){
int a,b;
scanf("%d%d",&a,&b);
g[a].push_back(b);
}
}
void dfs(int u){
lowin[u]=pre[u]=++dfs_clock;
S.push(u);
for(int i=0;i<g[u].size();i++){
int v=g[u][i];
if(!pre[v]){ dfs(v);lowin[u]=min(lowin[u],lowin[v]); }
else if(!sccno[v]) lowin[u]=min(lowin[u],pre[v]);
}
if(lowin[u]==pre[u]){
scc_cnt++;
for(;;){
int x=S.top();S.pop();
sccno[x]=scc_cnt;
sccnum[scc_cnt]++;
if(x==u) break;
}
}
}
void find_scc(){
mem(pre,0),mem(sccno,0),mem(sccnum,0),dfs_clock=scc_cnt=0;
for(int i=1;i<=n;i++) if(!pre[i]) dfs(i);
}
void scc_caldegree(){
mem(out,0);
for(int u=1;u<=n;u++){
for(int i=0;i<g[u].size();i++){
int v=g[u][i];
if(sccno[u]!=sccno[v]) out[sccno[u]]++;
}
}
}
int main(){
//freopen("a.txt","r",stdin);
scanf("%d%d",&n,&m);
build();
find_scc();
scc_caldegree();
out_cnt=0;
for(int i=1;i<=scc_cnt;i++){
if(!out[i])
if(!out_cnt) { out_cnt=1;ans=sccnum[i]; }
else { ans=0;break; }
}
printf("%d\n",ans);
}
做法:1缩点2.统计scc图的出度,出度为1的点仅有一个u,则ans=sccnum[u],否则ans=0
姊妹命题:寻找能到达所有点的点集大小
把出度统计改为入度统计即可
#include<iostream>
#include<stdio.h>
#include<string.h>
#include<algorithm>
#include<math.h>
#include<vector>
#include<stack>
#define ll long long
#define INF 0x3f3f3f3f
#define maxn 20000
#define mem(a,b) memset(a,b,sizeof(a))
using namespace std;
int n,m;
vector<int> g[maxn];
int pre[maxn],lowin[maxn],sccno[maxn],sccnum[maxn],scc_cnt,dfs_clock;
stack<int> S;
int out[maxn],out_cnt,ans;
void build(){
for(int i=1;i<=n;i++) g[i].clear();
for(int i=1;i<=m;i++){
int a,b;
scanf("%d%d",&a,&b);
g[a].push_back(b);
}
}
void dfs(int u){
lowin[u]=pre[u]=++dfs_clock;
S.push(u);
for(int i=0;i<g[u].size();i++){
int v=g[u][i];
if(!pre[v]){ dfs(v);lowin[u]=min(lowin[u],lowin[v]); }
else if(!sccno[v]) lowin[u]=min(lowin[u],pre[v]);
}
if(lowin[u]==pre[u]){
scc_cnt++;
for(;;){
int x=S.top();S.pop();
sccno[x]=scc_cnt;
sccnum[scc_cnt]++;
if(x==u) break;
}
}
}
void find_scc(){
mem(pre,0),mem(sccno,0),mem(sccnum,0),dfs_clock=scc_cnt=0;
for(int i=1;i<=n;i++) if(!pre[i]) dfs(i);
}
void scc_caldegree(){
mem(out,0);
for(int u=1;u<=n;u++){
for(int i=0;i<g[u].size();i++){
int v=g[u][i];
if(sccno[u]!=sccno[v]) out[sccno[u]]++;
}
}
}
int main(){
//freopen("a.txt","r",stdin);
scanf("%d%d",&n,&m);
build();
find_scc();
scc_caldegree();
out_cnt=0;
for(int i=1;i<=scc_cnt;i++){
if(!out[i])
if(!out_cnt) { out_cnt=1;ans=sccnum[i]; }
else { ans=0;break; }
}
printf("%d\n",ans);
}
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