POJ 1094 Sorting It All Out (拓扑排序)

 

Sorting It All Out

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 28766		Accepted: 9965

 

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

题目链接：http://poj.org/problem?id=1094

题目大意：根据给出的点的大小关系，判断是否能够确定所有点构成的有序序列，不能输出在第几个关系后出现矛盾

题目分析：拓扑排序，排完后三种情况
1.图中存在环，则关系矛盾
2.图中不存在环，但排序出来的序列中元素个数小于总的元素个数，则序列不能够确定
3.图中不存在环，排序出的序列中元素个数等于总的元素个数，则序列被唯一确定

#include <cstdio>
#include <cstring>
#include <queue>
using namespace std;
int const MAX = 30;
int m, n, len, mp[MAX][MAX], ind[MAX], tmp[MAX];
char seq[MAX], s[5];
bool determined, inconsistency;

int TopoSort() {
    bool flag = false;
    len = 0;
    memcpy(tmp, ind, sizeof(ind));
    queue <int> q;
    for (int i = 0; i < n; i++) {
        if (tmp[i] == 0) {
            q.push(i);
        }
    }
    while (!q.empty()) {
        if (q.size() > 1) {
            flag = true;
        }
        int u = q.front();
        q.pop();
        seq[len++] = u + 'A';
        for (int v = 0; v < n; v++) {
            if (mp[u][v]) {
                tmp[v] --;
                if (tmp[v] == 0) {
                    q.push(v);
                }
            }  
        }
    }
    if (len != n) {
        return 1;
    }
    if(flag) {
        return 2;
    }
    return 0;
}

void Init() {
    determined = false;
    inconsistency = false;
    memset(mp, 0, sizeof(mp));
    memset(ind, 0, sizeof(ind));
}
 
int main() {
    while (scanf("%d %d", &n, &m) != EOF && m && n) {
        Init();
        for (int i = 1; i <= m; i++) {
            scanf("%s", s);
            if (!determined && !inconsistency) {
                int x = s[0] - 'A';
                int y = s[2] - 'A';
                if(mp[y][x]) {
                    inconsistency = true;
                    printf("Inconsistency found after %d relations.\n", i);
                    continue;
                }
                if (!mp[x][y]) {
                    mp[x][y] = 1;
                    ind[y]++;
                }
                int res = TopoSort();
                if (res == 0) {
                    seq[len] = '\0';
                    printf("Sorted sequence determined after %d relations: %s.\n", i, seq);
                    determined = true;
                } else if (res == 1) {
                    printf("Inconsistency found after %d relations.\n", i);
                    inconsistency = true;
                }
            }
        }
        if (!determined && !inconsistency) {
            printf("Sorted sequence cannot be determined.\n");
        }
    }
}