RGB Coloring 2

AtCoder

IDabc199_d

Time2000ms

Memory256MB

Difficulty—

We have a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$. Edge $i$ connects Vertex $A_i$ and Vertex $B_i$. Find the number of ways to paint each vertex in this graph red, green, or blue so that the following condition is satisfied: * two vertices directly connected by an edge are always painted in different colors. Here, it is not mandatory to use all the colors. ## Constraints * $1 \le N \le 20$ * $0 \le M \le \frac{N(N - 1)}{2}$ * $1 \le A_i \le N$ * $1 \le B_i \le N$ * The given graph is simple (that is, has no multi-edges and no self-loops). ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $A_2$ $B_2$ $A_3$ $B_3$ $\hspace{15pt} \vdots$ $A_M$ $B_M$ [samples]

Samples

Input #1

Output #1

6

Let $c_1, c_2, c_3$ be the colors of Vertices $1, 2, 3$ and `R`, `G`, `B` denote red, green, blue, respectively. There are six ways to satisfy the condition:

*   $c_1c_2c_3 = $ `RGB`
*   $c_1c_2c_3 = $ `RBG`
*   $c_1c_2c_3 = $ `GRB`
*   $c_1c_2c_3 = $ `GBR`
*   $c_1c_2c_3 = $ `BRG`
*   $c_1c_2c_3 = $ `BGR`

Input #2

3 0

Output #2

27

Since the graph has no edge, we can freely choose the colors of the vertices.

Input #3

Output #3

0

There may be no way to satisfy the condition.

Input #4

20 0

Output #4

3486784401

The answer may not fit into the $32$\-bit signed integer type.

API Response (JSON)

{
  "problem": {
    "name": "RGB Coloring 2",
    "description": {
      "content": "We have a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$.   Edge $i$ connects Vertex $A_i$ and Vertex $B",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc199_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1$ through $N$, and the edges are numbered $1$ through $M$.  \nEdge $i$ connects Vertex $A_i$ and Vertex $B...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments