Uniqueness of Topological Order

题目描述

This is a problem given in the Graduate Entrance Exam in 2023: Given a directed graph G, you are supposed to tell if there exists a unique topological order of its vertices.

输入格式

Each input file contains one test case. For each case, the first line gives two positive integers $n (≤10^4)$, the number of vertices in the graph, and $m (≤10^5)$, 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 $n$. It is guaranteed that no duplicated edge is given.

输出格式

Output the vertices with the smallest in-degree in the first line, in ascending order. Then if there exists a unique topological order of all the vertices, first print in a line Yes and then output the topological sequence in the next line. Or if the answer is no, just print in a line No. All the numbers in a line must be separated by exactly $1$ space, and there must be no extra space at the beginning or the end of the line.

样例 #1

样例输入 #1

6 9
2 1
1 3
5 2
5 4
2 3
2 6
3 4
6 4
6 1

样例输出 #1

5
Yes
5 2 6 1 3 4