Score : 600 points
Given is a directed graph G with N vertices and M edges.
The vertices are numbered 1 to N, and the i-th edge is directed from Vertex A_i to Vertex B_i.
It is guaranteed that the graph contains no self-loops or multiple edges.
Determine whether there exists an induced subgraph (see Notes) of G such that the in-degree and out-degree of every vertex are both 1. If the answer is yes, show one such subgraph.
Here the null graph is not considered as a subgraph.
For a directed graph G = (V, E), we call a directed graph G' = (V', E') satisfying the following conditions an induced subgraph of G:
Input is given from Standard Input in the following format:
N M A_1 B_1 A_2 B_2 : A_M B_M
If there is no induced subgraph of G that satisfies the condition, print -1
.
Otherwise, print an induced subgraph of G that satisfies the condition, in the following format:
K v_1 v_2 : v_K
This represents the induced subgraph of G with K vertices whose vertex set is \{v_1, v_2, \ldots, v_K\}. (The order of v_1, v_2, \ldots, v_K does not matter.) If there are multiple subgraphs of G that satisfy the condition, printing any of them is accepted.
4 5 1 2 2 3 2 4 4 1 4 3
3 1 2 4
The induced subgraph of G whose vertex set is \{1, 2, 4\} has the edge set \{(1, 2), (2, 4), (4, 1)\}. The in-degree and out-degree of every vertex in this graph are both 1.
4 5 1 2 2 3 2 4 1 4 4 3
-1
There is no induced subgraph of G that satisfies the condition.
6 9 1 2 2 3 3 4 4 5 5 6 5 1 5 2 6 1 6 2
4 2 3 4 5