Count Simple Paths

AtCoder

IDabc284_e

Time2000ms

Memory256MB

Difficulty—

You are given a simple undirected graph with $N$ vertices numbered $1$ to $N$ and $M$ edges numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and vertex $v_i$. The degree of each vertex is at most $10$. Let $K$ be the number of simple paths (paths without repeated vertices) starting from vertex $1$. Print $\min(K, 10^6)$. ## Constraints * $1 \leq N \leq 2 \times 10^5$ * $0 \leq M \leq \min \left(2 \times 10^5, \frac{N(N-1)}{2}\right)$ * $1 \leq u_i, v_i \leq N$ * The given graph is simple. * The degree of each vertex in the given graph is at most $10$. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_M$ $v_M$ [samples]

Samples

Input #1

4 2
1 2
2 3

Output #1

3

We have the following three paths that count. (Note that a path of length $0$ also counts.)

*   Vertex $1$;
*   vertex $1$, vertex $2$;
*   vertex $1$, vertex $2$, vertex $3$.

Input #2

Output #2

Input #3

Output #3

API Response (JSON)

{
  "problem": {
    "name": "Count Simple Paths",
    "description": {
      "content": "You are given a simple undirected graph with $N$ vertices numbered $1$ to $N$ and $M$ edges numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and vertex $v_i$. The degree of each vertex is at most $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc284_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a simple undirected graph with $N$ vertices numbered $1$ to $N$ and $M$ edges numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and vertex $v_i$. The degree of each vertex is at most $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments