Score : $200$ points

问题描述

你被给定一个包含 $N$ 个顶点和 $M$ 条边的简单无向图。顶点编号为 $1, \dots, N$，第 $i$-条 $(1 \leq i \leq M)$ 边连接顶点 $U_i$ 和顶点 $V_i$。

求满足以下所有条件的整数元组 $(a, b, c)$ 的数量：

• $1 \leq a < b < c \leq N$
• 存在一条连接顶点 $a$ 和顶点 $b$ 的边。
• 存在一条连接顶点 $b$ 和顶点 $c$ 的边。
• 存在一条连接顶点 $c$ 和顶点 $a$ 的边。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

You are given a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, \dots, N$, and the $i$-th $(1 \leq i \leq M)$ edge connects Vertex $U_i$ and Vertex $V_i$.

Find the number of tuples of integers $a, b, c$ that satisfy all of the following conditions:

• $1 \leq a \lt b \lt c \leq N$
• There is an edge connecting Vertex $a$ and Vertex $b$.
• There is an edge connecting Vertex $b$ and Vertex $c$.
• There is an edge connecting Vertex $c$ and Vertex $a$.

Constraints

• $3 \leq N \leq 100$
• $1 \leq M \leq \frac{N(N - 1)}{2}$
• $1 \leq U_i \lt V_i \leq N \, (1 \leq i \leq M)$
• $(U_i, V_i) \neq (U_j, V_j) \, (i \neq j)$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$

$U_1$ $V_1$

$\vdots$

$U_M$ $V_M$

Output

Print the answer.

Sample Input 1

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

Sample Output 1

2

$(a, b, c) = (1, 4, 5), (2, 3, 5)$ satisfy the conditions.

Sample Input 2

3 1
1 2

Sample Output 2

0

Sample Input 3

7 10
1 7
5 7
2 5
3 6
4 7
1 5
2 4
1 3
1 6
2 7

Sample Output 3

4

update @ 2024/3/10 11:05:47