[kuangbin带你飞]专题四 最短路练习 H - Cow Contest （floyed传递背包）

H - Cow Contest

题目链接：https://vjudge.net/contest/66569#problem/H

题目：

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
题意：给出n,m，n是n头牛，m是m对关系，a,b，在前的即为a打败了b，一开始没看懂让我们求啥，然后百度发现用到了传递闭包，有向图的传递背包算法
其中包括了floyed传递背包算法，就是1跟2有关系，2跟3有关系，1也就跟3有关系，算这些牛中能确立多少等级关系，一旦一头牛和其他牛都存在胜负关系，
那么就确立一个等级关系，最后for循环遍历一下就可算出几个等级关系

//
// Created by hanyu on 2019/7/20.
//
#include <iostream>
#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;
const int maxn=105;
#define MAX 0x3f3f3f3f

int road[maxn][maxn];
int main()
{
    int n,m;
    scanf("%d%d",&n,&m);
    int front,to;
    memset(road,MAX,sizeof(road));
    for(int i=1;i<=n;i++)
        road[i][i]=0;//自己和自己不成立关系
    for(int i=1;i<=m;i++)
    {
        scanf("%d%d",&front,&to);
        road[front][to]=1;//单向图
        road[to][front]=-1;//反向不成立
    }
    for(int k=1;k<=n;k++)
    {
        for(int i=1;i<=n;i++)
        {
            for(int j=1;j<=n;j++)
            {
                if(road[i][k]==road[k][j]&&road[i][k]!=MAX)
                {
                    road[i][j]=road[i][k];
                }
            }
        }
    }//Floyd 传递闭包算法
    int cnt,sum=0;
    for(int i=1;i<=n;i++)
    {
        cnt=0;
        for(int j=1;j<=n;j++)
        {
            if(i!=j&&road[i][j]!=MAX)
            {
                cnt++;
            }//遍历每头牛和其他牛的关系
        }
        if(cnt==n-1)//如果关系达到n-1，即和自身之外的其他牛都确定了关系，则可确定等级
            sum++;
    }
    printf("%d\n",sum);
    return 0;
}