【PAT甲级】1146 Topological Order

1146 Topological Order

This is a problem given in the Graduate Entrance Exam in 2018: Which of the following is NOT a topological order obtained from the given directed graph? Now you are supposed to write a program to test each of the options.

Input Specification:

Each input file contains one test case. For each case, the first line gives two positive integers N (≤ 1,000), the number of vertices in the graph, and M (≤ 10,000), the number of directed edges. Then M lines follow, each gives the start and the end vertices of an edge. The vertices are numbered from 1 to N. After the graph, there is another positive integer K (≤ 100). Then K lines of query follow, each gives a permutation of all the vertices. All the numbers in a line are separated by a space.

Output Specification:

Print in a line all the indices of queries which correspond to “NOT a topological order”. The indices start from zero. All the numbers are separated by a space, and there must no extra space at the beginning or the end of the line. It is graranteed that there is at least one answer.

Sample Input:

6 8
1 2
1 3
5 2
5 4
2 3
2 6
3 4
6 4
6
5 2 3 6 4 1
1 5 2 3 6 4
5 1 2 6 3 4
5 1 2 3 6 4
5 2 1 6 3 4
1 2 3 4 5 6

Sample Output:

0 4 5

代码

#include<bits/stdc++.h>
using namespace std;
const int N = 1010, M = 10010;
struct Edge {
int a, b;
}e[M];
int p[N];
int main()
{
int n, m;
cin >> n >> m;
//输入每条有向边
for (int i = 0; i < m; i++)    cin >> e[i].a >> e[i].b;
//开始查询
bool is_first = true; //输出行末不能有空格
int k;
cin >> k;
for (int i = 0; i < k; i++)
{
//输入每个序列
for (int j = 1; j <= n; j++)
{
int x;
cin >> x;
p[x] = j; //记录每个点所在序列下标
}
//遍历每条边，判断是否都满足拓扑序列规则
bool success = true;
for (int i = 0; i < m; i++)
if (p[e[i].a] > p[e[i].b])
{
success = false;
break;
}
//输出不是拓扑序列的询问编号
if (!success)
{
if (is_first)    is_first = false;
else    cout << " ";
cout << i;
}
}
cout << endl;
return 0;
}

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