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:给出了N个排名,分给N头牛,每头牛占一个,给出M对合乎逻辑的牛u KO 牛v的信息,问能确定几头牛的排名?
题解:只要一头牛确定了和其他所有牛的关系,这头牛的排名就是确定的,用floyd做一个传递闭包。
代码:
//============================================================================ // Name : POJ.cpp // Author : // Version : // Copyright : Your copyright notice // Description : Hello World in C++, Ansi-style //============================================================================ /* * floyed算法,传递闭包。如果一个点和其余点的关系都是确定的,则这个的排名是确定的 */ #include <iostream> #include <string.h> #include <algorithm> #include <stdio.h> using namespace std; const int MAXN=110; int d[MAXN][MAXN]; int main() { int n,m; while(scanf("%d%d",&n,&m)==2) { memset(d,0,sizeof(d)); int u,v; while(m--) { scanf("%d%d",&u,&v); d[u][v]=1; } for(int k=1;k<=n;k++) for(int i=1;i<=n;i++) for(int j=1;j<=n;j++) d[i][j] = d[i][j]||(d[i][k]&&d[k][j]); int ans=0; int j; for(int i=1;i<=n;i++) { for(j=1;j<=n;j++) { if(i==j)continue; if(d[i][j]==0&&d[j][i]==0)break;//关系不确定,只要一边关系确定就行,因为题目规定不冲突 } if(j>n)ans++; } printf("%d\n",ans); } return 0; }