poj——1094——Sorting It All Out(拓扑排序)
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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.
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.
#include <iostream>#include <cstring>#include <cstdio>#include <algorithm>using namespace std;#define MAXN 28bool adj[MAXN][MAXN];int in_degree[MAXN];char str[MAXN];int n,m;int topo_sort(){ int i,j,k; bool flag=true; memset(in_degree,0,sizeof(in_degree)); memset(str,'\0',sizeof(str)); for(i=1; i<=n; i++) { for(j=1; j<=n; j++) if(adj[i][j]) in_degree[j]++; //入度加一 } for(i=1; i<=n; i++) //每次产生一个字符 { k=0; for(j=1; j<=n; j++) { if(in_degree[j]==0) { if(k==0) k=j; else flag=false; //还有入度为零的节点 } } if(k==0) return 0; //没有入度为零的节点,即存在环 in_degree[k]=-1; str[i-1]=k+'A'-1; for(j=1; j<=n; j++) //k指向的节点入度都减一,即去掉A及它相关的边 { if(adj[k][j]) in_degree[j]--; } } if(flag) return 1; //没有入度为零的点,完成排序 else return 2; //排序没有完成}int main(){ int i,a,b,result; char s[4]; // freopen("acm.txt","r",stdin); while(scanf("%d%d",&n,&m),m+n) { memset(adj,false,sizeof(adj)); bool h=false; for(i=1; i<=m; i++) { scanf("%s",s); a=s[0]-'A'+1; b=s[2]-'A'+1; adj[a][b]=true; if(h) continue; //必须有,因为还要继续把剩下的数据都读完 result=topo_sort(); if(result==1) { printf("Sorted sequence determined after %d relations: %s.\n",i,str); h=true; } if(result==0) { printf("Inconsistency found after %d relations.\n",i); //有换存在 h=true; } } if(!h) printf("Sorted sequence cannot be determined.\n"); } return 0;}
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