【题目描述】
N (1 ≤ N ≤ 100) cows, conveniently numbered 1…N, are participating in a programming contest. As we all know, some cows code better than others. Each cow has a certain constant skill rating that is unique among the competitors.
The contest is conducted in several head-to-head rounds, each between two cows. If cow A has a greater skill level than cow B (1 ≤ A ≤ N; 1 ≤ B ≤ N; A ≠ B), then cow A will always beat cow B.
Farmer John is trying to rank the cows by skill level. Given a list the results of M (1 ≤ M ≤ 4,500) two-cow rounds, determine the number of cows whose ranks can be precisely determined from the results. It is guaranteed that the results of the rounds will not be contradictory.
Input
-
Line 1: Two space-separated integers: N and M
-
Lines 2…M+1: Each line contains two space-separated integers that describe the competitors and results (the first integer, A, is the winner) of a single round of competition: A and B
Output -
Line 1: A single integer representing the number of cows whose ranks can be determined
Sample Input
5 5
4 3
4 2
3 2
1 2
2 5
Sample Output
2
【题目分析】
需要将题目转化成图的问题,假如我们我打赢看作一条有向边,那么对于每个节点,我们判断其他节点能否到达他(比他厉害)或者他能否到达其他节点(比他菜),如果所有节点都可以,那么他的排名就是唯一确定的,所以我们用一个Floyed判断一下
【AC代码】
#include<cstdio>
#include<cstring>
#include<cstdlib>
#include<algorithm>
#include<iostream>
#include<cmath>
#include<climits>
#include<queue>
#include<vector>
#include<set>
#include<map>
using namespace std;typedef long long ll;
const int MAXN=105;
bool a[MAXN][MAXN],flag;
int n,m,ans;void Floyed()
{for(int k=1;k<=n;k++){for(int i=1;i<=n;i++){for(int j=1;j<=n;j++){a[i][j]=a[i][j] || (a[i][k] && a[k][j]);}}}
}int main()
{int u,v;while(~scanf("%d%d",&n,&m)){memset(a,0,sizeof(a));ans=0;for(int i=0;i<m;++i){scanf("%d%d",&u,&v);a[u][v]=true;}Floyed();for(int i=1;i<=n;i++){flag=true;for(int j=1;j<=n;j++){if(i==j) continue;if(!a[i][j] && !a[j][i]){flag=false;break;}}if(flag) ans++;}printf("%d\n",ans);}return 0;
}