poj 1094拓扑排序+flody

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 22332		Accepted: 7705

Description

An ascending sorted sequence of distinct values is one in which some form of a less-than operator is used to order the elements from smallest to largest. For example, the sorted sequence A, B, C, D implies that A < B, B < C and C < D. in this problem, we will give you a set of relations of the form A < B and ask you to determine whether a sorted order has been specified or not.

Input

Input consists of multiple problem instances. Each instance starts with a line containing two positive integers n and m. the first value indicated the number of objects to sort, where 2 <= n <= 26. The objects to be sorted will be the first n characters of the uppercase alphabet. The second value m indicates the number of relations of the form A < B which will be given in this problem instance. Next will be m lines, each containing one such relation consisting of three characters: an uppercase letter, the character "<" and a second uppercase letter. No letter will be outside the range of the first n letters of the alphabet. Values of n = m = 0 indicate end of input.

Output

For each problem instance, output consists of one line. This line should be one of the following three:

Sorted sequence determined after xxx relations: yyy...y.
Sorted sequence cannot be determined.
Inconsistency found after xxx relations.

where xxx is the number of relations processed at the time either a sorted sequence is determined or an inconsistency is found, whichever comes first, and yyy...y is the sorted, ascending sequence.

Sample Input

4 6
A<B
A<C
B<C
C<D
B<D
A<B
3 2
A<B
B<A
26 1
A<Z
0 0

Sample Output

Sorted sequence determined after 4 relations: ABCD.
Inconsistency found after 2 relations.
Sorted sequence cannot be determined.

 

// 首先。有拓扑排序检查是不是有环的存在，要是没有环的话，用flody传递闭包

再判断序列是不是唯一的。

而判断序列是不是唯一的方法是：

n个结点的出度分别是0,1,2,3,4...n-1，是的话就说明是唯一的

 

代码：

#include<cstdio>
#include<iostream>
#include<queue>
#include<cmath>
#include<cstring>
#include<string>
#include<algorithm>
#include<stack>
using namespace std;
typedef long long LL;
#define clr(x) memset(x,0,sizeof(x));
#define sf scanf
#define pf printf
int map[35][35];
int path[35];
bool vis[35];
int cnt[35];
int N,M;
const int INF=1<<29;
void flody(){//传递闭包
	for(int k2=0;k2<N;k2++)
		for(int i1=0;i1<N;i1++)
			for(int j3=0;j3<N;j3++){
				if(map[k2][i1]&&map[i1][j3])
					map[k2][j3]=1;
			}
}
void updata(int u){
	for(int i=0;i<N;i++){
		if(map[u][i]) --cnt[i];
	}
	cnt[u]--;
}
bool topSort(){
	clr(cnt);
	for(int i=0;i<N;i++)
		for(int j=0;j<N;j++){
			if(map[i][j]) ++cnt[j];
		}
		for(int i=0;i<N;i++){
			int u=-1;
			for(int j=0;j<N;j++){
				if(!cnt[j]){
					u=j;
					break;
				}
			}
			if(u==-1) return true;
			path[i]=u;
			updata(u);
		}
		return false;
}
bool judge(){
	clr(vis);
	for(int i=0;i<N;i++){
		int out=0;
		for(int j=0;j<N;j++){
			if(map[i][j]) out++;
		}
		if(vis[out]) return false;
		vis[out]=true;
	}
	return true;
}
int main(){
	while(sf("%d%d",&N,&M)!=EOF&&N+M){
		bool flag=false;
		char str[5];
		clr(map);
		for(int i=1;i<=M;i++){
			sf("%s",&str);
			if(flag) continue;
			int x=str[0]-'A';
			int y=str[2]-'A';
			if(map[x][y]) continue;
			map[x][y]=1;
			if(topSort()){
				pf("Inconsistency found after %d relations.\n",i);
				flag=true;
				continue;
			}
			flody();
			if(judge()){
				pf("Sorted sequence determined after %d relations: ",i);
				for(int j=0;j<N;j++) pf("%c",path[j]+'A');
				pf(".\n");flag=true;
			}
		}
		if(!flag) 
			pf("Sorted sequence cannot be determined.\n");
	}
	return 0;
}