poj 2186 Popular Cows【tarjan求scc个数&&缩点】【求一个图中可以到达其余所有任意点的点的个数】

Popular Cows

Time Limit: 2000MS		Memory Limit: 65536K
Total Submissions: 27698		Accepted: 11148

Description

Every cow's dream is to become the most popular cow in the herd. In a herd of N (1 <= N <= 10,000) cows, you are given up to M (1 <= M <= 50,000) ordered pairs of the form (A, B) that tell you that cow A thinks that cow B is popular. Since popularity is transitive, if A thinks B is popular and B thinks C is popular, then A will also think that C is 
popular, even if this is not explicitly specified by an ordered pair in the input. Your task is to compute the number of cows that are considered popular by every other cow. 

Input

* Line 1: Two space-separated integers, N and M 

* Lines 2..1+M: Two space-separated numbers A and B, meaning that A thinks B is popular. 

Output

* Line 1: A single integer that is the number of cows who are considered popular by every other cow. 

Sample Input

3 3
1 2
2 1
2 3

Sample Output

1

Hint

Cow 3 is the only cow of high popularity. 

题意：有n头牛，已知m个关系即牛a认为牛b是受欢迎，现在问你在n头牛里有多少头牛被 除它外所有的牛认为是受欢迎的。

题解：

一：出度为0的SCC有0个，显然易见，该图就是一个强连通图，所有牛都满足条件；

二：出度为0的SCC有1个，满足条件的只有这一个SCC里面的牛；

三：出度为0的SCC超过1个，无论如何，出度超过0的SCC之间是无法连通的，所以没有牛满足。

 

?

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147

#include<stdio.h> #include<string.h> #include<algorithm> #include<vector> #include<stack> #define MAX 50010 #define INF 0x3f3f3f using namespace std; struct node {     int beg,end,next; }edge[MAX]; int low[MAX],dfn[MAX]; int n,m,ans; int sccno[MAX],instack[MAX]; int dfsclock,scccnt; vector<int>newmap[MAX]; vector<int>scc[MAX]; int head[MAX]; int out[MAX]; stack<int>s; int sum,sumout,ant; void init() {     ans=0;     memset(head,-1,sizeof(head)); } void add(int u,int v) {     edge[ans].beg=u;     edge[ans].end=v;     edge[ans].next=head[u];     head[u]=ans++; } void getmap() {     int a,b,i;     while(m--)     {         scanf("%d%d",&a,&b);         add(a,b);     } } void tarjan(int u) {     int v,i,j;     s.push(u);     instack[u]=1;     dfn[u]=low[u]=++dfsclock;     for(i=head[u];i!=-1;i=edge[i].next)     {         v=edge[i].end;         if(!dfn[v])         {             tarjan(v);             low[u]=min(low[u],low[v]);         }         else if(instack[v])             low[u]=min(low[u],dfn[v]);     }     if(dfn[u]==low[u])     {         scccnt++;         while(1)         {             v=s.top();             s.pop();             instack[v]=0;             sccno[v]=scccnt;             if(v==u)             break;         }     } } void find(int l,int r) {     memset(low,0,sizeof(low));     memset(dfn,0,sizeof(dfn));     memset(instack,0,sizeof(instack));     memset(sccno,0,sizeof(sccno));     dfsclock=scccnt=0;     for(int i=l;i<=r;i++)     {         if(!dfn[i])             tarjan(i);     } } void suodian() {     int i;     ant=0;     for(i=1;i<=scccnt;i++)     {         newmap[i].clear();         out[i]=0;     }     for(i=0;i<ans;i++)     {         int u=sccno[edge[i].beg];         int v=sccno[edge[i].end];         if(u!=v)         {             newmap[u].push_back(v);             out[u]++;         }     } } void solve() {     int i,j;     sumout=0;sum=0;     for(i=1;i<=scccnt;i++)     {         if(!out[i])         {             sumout++;             ant=i;         }     }     if(sumout==0)     {         printf("%d\n",n);         return ;     }     else if(sumout==1)     {         for(i=1;i<=n;i++)             if(sccno[i]==ant)                 sum++;         printf("%d\n",sum);     }     else     printf("0\n"); } int main() {     int t;     while(scanf("%d%d",&n,&m)!=EOF)     {         init();         getmap();         find(1,n);         suodian();         solve();     }     return 0; }