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.

gre.jpg

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
5
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:
3 4
分析：
判断顶点序列是否为拓扑序列。依次判断顶点序列中的顶点，若顶点入度为0，则顶点符合输出要求；不为1，则说明不符合要求，则不是拓扑序列。如果所有顶点都是在满足入度为0的情况下输出，那么顶点序列为拓扑序列。

参考代码：

#include<vector>
#include<iostream>
using namespace std;
vector<vector<int>>graph;
vector<int>in, intemp, v;
int n, m;
int main() {
	int a, b, query, vex, flag;
	scanf_s("%d%d", &n, &m);
	graph.resize(n + 2);
	in.resize(n + 2, 0);
	intemp.resize(n + 2, 0);
	for (int i = 1; i <= m; i++) {
		scanf_s("%d%d", &a, &b);
		graph[a].push_back(b);
		intemp[b]++;
	}
	scanf_s("%d", &query);
	for (int i = 0; i < query; i++) {
		in = intemp; flag = 1;
		for (int j = 1; j <= n; j++) {
			scanf_s("%d", &vex);
			if (flag) {
				if (in[vex] == 0)
					for (int w = 0; w < graph[vex].size(); w++) {
						in[graph[vex][w]]--;
					}
				else flag = 0;
			}
		}
		if (!flag)v.push_back(i);
	}
	flag = 0;
	for (auto val : v) {
		if (flag)cout << " ";
		cout << val; flag = 1;
	}

	return 0;
}