拓扑排序 +Floyd（poj 1094）

 题目：Sorting It All Out

 题意：字母表前n个字母，有m组他们中的大小关系，判断n个字母是否构成唯一序列：

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

思路：判断环好判断，但是判断是否唯一就搞不懂了，后来看了下别人的，

　　　　用的是Floyd传递闭包：如果能构成唯一序列，则定点1~n，必定分布着0~n-1的入度，

　　　　才能保证0个入度的定点排在第一位，1个入度的地点排在第2位，以此类推。

　　　　

#include <iostream>
#include <algorithm>
#include <stdlib.h>
#include <time.h>
#include <cmath>
#include <cstdio>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <stack>
#include <set>


#define c_false ios_base::sync_with_stdio(false); cin.tie(0)
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3f
#define zero_(x,y) memset(x , y , sizeof(x))
#define zero(x) memset(x , 0 , sizeof(x))
#define MAX(x) memset(x , 0x3f ,sizeof(x))
#define swa(x,y) {LL s;s=x;x=y;y=s;}
using namespace std ;
#define N 100

const double PI = acos(-1.0);
typedef long long LL ;

int topo[N],t;
int G[N][N];
int n,m,flag,pos,i,num;
char s[N];
char output[N];

int Floyd(){
    int i, j, k;
    for(i = 0; i<n ;i++)
        for(k = 0; k<n; k++)
            for(j = 0; j<n; j++)
                if(G[k][i] && G[i][j])
                    G[k][j] = 1;
    for(i = 0; i< n; i++){
        if(G[i][i] == 1)
            return 1;
    }
    return 0;
}

int Topsort(){
    int cou, ind, k ,i;
    int degree[N],used[N];
    num = 0;
    zero(used);
    zero(degree);
    for(i = 0; i< n ;i++)
        for(k = 0 ; k< n ;k++)
            if(G[i][k])
                degree[k]++;
        for(i = 0; i< n; i++){
            cou = 0;
            for(k = 0; k< n ; k++)
            if(degree[k] == 0 && !used[k]){
                output[num++] = k + 'A';
                used[k] = 1;
                cou++;
                ind = k;
            }
            if(cou > 1) return 0;
            if(cou == 0) return 1;
            for(k = 0; k < n;k++)
                if(G[ind][k]) degree[k]--;
        }
        output[num] = '\0';
        return 2;
}
int main(){
    //freopen("in.txt","r",stdin);
    //freopen("out.txt","w",stdout);
    while(cin>>n>>m){
        if(n == 0 && m == 0) break;
        flag = 0;
        zero(G);
        for(i = 0;i < m; i++){
            scanf("%s",s);
            G[s[0]-'A'][s[2]-'A'] = 1;
            if(flag != 0) continue;
            flag = Floyd();
            if(flag == 1)
                pos = i;
            if(flag == 0)
                flag = Topsort();
            else continue;
            if(flag == 2)
                pos = i;
        }
        pos++;
        if(flag == 2){
            printf("Sorted sequence determined after %d relations: %s.\n",pos,output);
            continue;
        }
        if(flag == 1){
            printf("Inconsistency found after %d relations.\n",pos);
            continue;
        }
        printf("Sorted sequence cannot be determined.\n");
    }
    return 0;
}