poj 1094（拓扑排序）

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Sorting It All Out

Time Limit: 1000MS Memory Limit: 10000KTotal Submissions: 26943 Accepted: 9309

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 6A<BA<CB<CC<DB<DA<B3 2A<BB<A26 1A<Z0 0

Sample Output

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

Source

East Central North America 2001

这是做的拓扑排序的第一题。

题意：输入n和m，n 表示给出的字符的个数，然后输入m行 字符之间的关系，每输入一行便要判断是不是有环，是不是有n个字符唯一的排列顺序。若全部输入完毕后没有唯一的排列顺序，也没有环便输出 Sorted sequence cannot be determined.

分析：每输入一行 字符间的关系便调用拓扑排序的函数判断，在拓扑排序中，先定义一个flag=1，如果有环，直接返回0；如果不唯一，则改变flag的值；有唯一情况时，保存入度为0的字符。循环完毕后，返回flag的值。

    在主函数中如果调用的函数返回1，那么表示有唯一排序，输出字符串；如果返回0，表示有环，停止循环。如果已输入m行，判断结果返回-1，那么输出 Sorted sequence cannot be determined.

#include <stdio.h>#include <string.h>int map[30][30];//记录图int ans[30];//记录结果int into[30];//记录入度int into1[30];//同上int n,m;int topu(){int i;int k;int flag=1;for(int j=1;j<=n;j++)//将入度保存到另一个数组中 ，确保into数组不变； {  into1[j]=into[j];}for(i=1;i<=n;i++){int count=0;for(int j=1;j<=n;j++)//找是否存在入度为0的点 {if(into1[j]==0){ count++; k=j;}}if(count>1)flag= -1;//入度为0的点不唯一，所以顺序也不唯一 if(count==0)return 0;//不存在入度为0的点，有环；          ans[i]=k;         into1[k]=-1;           for(int j=1;j<=n;j++)//将从这个字符出发的到达其他的节点的入度减1；            {              if(map[k][j]==1)              into1[j]--;           }}return flag;}int main(){while(scanf("%d%d",&n,&m),m,n){memset(map,0,sizeof(map));//清空数组 memset(ans,0,sizeof(ans));memset(into,0,sizeof(into));char a[5];int i;int flag=0;    for(i=1;i<=m;i++){scanf("%s",&a);if(flag)continue; //已经输出过了，所以continue int x=a[0]-'A'+1;int y=a[2]-'A'+1;if(!map[x][y])//消除重边 {map[x][y]=1;into[y]++;}int ans1=topu();//调用拓扑排序 if(ans1==0){printf("Inconsistency found after %d relations.\n",i);flag=1;}if(ans1==1){printf("Sorted sequence determined after %d relations: ",i);for(int j=1;j<=n;j++)printf("%c",ans[j]+'A'-1);printf(".\n");flag=1;}}if(!flag)//表示没有输出过 printf("Sorted sequence cannot be determined.\n");}return 0;}