[] Tarjan shrink graph theory point: poj2186 Popular Cows

condensing point tarjan

Condensing point is used in graph theory techniques, when having a conductive path contribution, it may be a new strongly connected components shrink to a point, because the points within a strongly connected component can reach each other. The number of points within a strongly connected components can be stained by recording, with the same number of points is the color of the number of points in the strongly connected component.

Example: poj2186 Popular Cows

Tell your cattle have n, m a relationship of worship, and worship is transitive, if a worship b, b worship c, then a worship c, several cows have been seeking finally all cattle worship.

Sample Input

3 3

1 2

2 1

2 3

Sample Output

1

answer:

When the entire first consider the case of FIG acyclic (DAG), and when there is a cow worship all cattle, to consider only the number of point 0 (the degree of a certain number of points greater than or equal to 0 1), if it is 1, then a solution, if greater than 1, no solution;
if there FIG ring, then after a tarjan FIG identify strongly connected component, the point for point v u connected if their colors the same, they are described in the same strongly connected component, considered u, v in a super point, not shown in the statistics of u; if they are different in color, then these two points belong to different strongly connected components , can be added so that the degree of u 1.
statistics at completion, for each color (i.e., all strongly connected components) statistical point of 0 degree, to obtain the number of worship all cow "super-point." Note that the "super spot" If the point is greater than 1 points strongly connected component of the configuration, will have the number of points in the strongly connected component added answers, plus 1 instead.

#include<cstdio>
#include<vector>
#include<cstring>
using namespace std;

int n,m;
const int maxn=10010;
int dfn[maxn],low[maxn],cnt[maxn],color[maxn],degree[maxn],vis[maxn];
int tot;
int st[maxn],top;
int tmp,ans;
int deep;
vector<int> g[maxn];

void tarjan(int u)
{
    dfn[u]=++deep;
    low[u]=deep;
    vis[u]=1;
    st[++top]=u;
    int sz=g[u].size();
    for(int i=0;i<sz;i++)
    {
        int v=g[u][i];
        if(!dfn[v])
        {
            tarjan(v);
            low[u]=min(low[u],low[v]);
        }
        else
        {
            if(vis[v])
            low[u]=min(low[u],low[v]);
        }
    }
    if(dfn[u]==low[u])
    {
        color[u]=++tot;
        vis[u]=0;
        while(st[top]!=u)
        {
            color[st[top]]=tot;
            vis[st[top--]]=0;
        }
        top--;
    }
}

int main()
{
    while(~scanf("%d%d",&n,&m))
    {
        memset(vis,0,sizeof(vis));
        memset(dfn,0,sizeof(dfn));
        memset(color,0,sizeof(color));
        memset(degree,0,sizeof(degree));
        memset(low,0,sizeof(low));
        memset(cnt,0,sizeof(cnt));
        memset(st,0,sizeof(st));
        for(int i=1;i<=m;i++)
        {
            int x,y;
            scanf("%d%d",&x,&y);
            g[x].push_back(y);
        }
        for(int i=1;i<=n;i++)
            if(!dfn[i])tarjan(i);
        for(int i=1;i<=n;i++)
        {
            int sz=g[i].size();
            for(int j=0;j<sz;j++)
            {
                int v=g[i][j];
                if(color[i]!=color[v])
                    degree[color[i]]++;
            }
            cnt[color[i]]++;
        }
        for(int i=1;i<=tot;i++)
            if(degree[i]==0) tmp++,ans=cnt[i];
        if(tmp>1) printf("0\n");
        else printf("%d\n",ans); 
    }
    return 0;
}