POJ 1094 Sorting It All Out【拓扑排序】

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## Sorting It All Out ##

Time Limit: 1000MS Memory Limit: 10000K  
Total Submissions: 37590 Accepted: 13273

#### 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.

#### Source ####

> East Central North America 2001

#### 题意概括： ####

n表示26个字母的前n个，有m个关系，判断这n个字母能否确定唯一的关系，若能输出Sorted sequence determined after i relations: 关系序列. （i代表第i个关系处判断出的结果）若不能，判断是成环的话输出Inconsistency found after i relations. 若不能判断关系输出Sorted sequence cannot be determined.

#### 解题分析： ####

这道题是一个拓扑排序，每输入一个关系，对相应点的入度进行更新，并进行拓扑排序，直到最后判断出关系。

#### AC代码： ####

#include<stdio.h>
    #include<string.h>
    
    #define N 110
    
    int e[N][N], du[N], d[N], re[N];
    
    int topo(char *s, int n)
    {
        int a = s[0]-'A', b = s[2]-'A';
        int i, j, t = n, flag = 1, coun, top = 0;
        if(!e[a][b]){
            e[a][b] = 1;
            d[b]++;
        }
        for(i = 0; i < n; i++) du[i] = d[i];
        while(t--){
            coun = 0;
            for(i = 0; i < n; i++)
                if(!du[i]){coun++; j = i;}
            if(!coun) return -1;
            else if(coun > 1) flag = 0;//这里只能标记，不能直接return，否则就可能漏掉成环的条件。
            du[j]--;
            re[top++] = j;
            for(i = 0; i < n; i++)
                if(e[j][i]) du[i]--;
        }
        if(flag) return 1;
        return 0;
    }
    
    int main()
    {
        char s[N];
        int i, j, k, n, m, OK;
        while(scanf("%d%d", &n, &m), n || m){
            if(m < n-1){
                while(m--) scanf("%s", s);
                printf("Sorted sequence cannot be determined.\n");
                continue;
            }
            memset(e, 0, sizeof(e));
            memset(d, 0, sizeof(d));
            for(i = OK = 1; i <= m; i++){
                scanf("%s", s);
                if(OK){
                    int a = s[0]-'A', b = s[2]-'A';
                    k = topo(s, n);
                    if(k == -1){
                        OK = 0;
                        printf("Inconsistency found after %d relations.\n", i);
                    }
                    else if(k){
                        printf("Sorted sequence determined after %d relations: ", i);
                        for(j = 0; j < n; j++) printf("%c", re[j]+'A');
                        OK = 0;
                        printf(".\n");
                    }
                }
            }
            if(OK) printf("Sorted sequence cannot be determined.\n");
        }
        return 0;
    }