Close Group

AtCoder

IDabc187_f

Time3000ms

Memory256MB

Difficulty—

Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \dots, N$, and the $i$\-th edge connects Vertices $A_i$ and $B_i$. Find the minimum possible number of connected components in the graph after removing zero or more edges so that the following condition will be satisfied: **Condition:** For every pair of vertices $(a, b)$ such that $1 \le a < b \le N$, if Vertices $a$ and $b$ belong to the same connected component, there is an edge that directly connects Vertices $a$ and $b$. ## Constraints * All values in input are integers. * $1 \le N \le 18$ * $0 \le M \le \frac{N(N - 1)}{2}$ * $1 \le A_i < B_i \le N$ * $(A_i, B_i) \neq (A_j, B_j)$ for $i \neq j$. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $\vdots$ $A_M$ $B_M$ [samples]

Samples

Input #1

3 2
1 2
1 3

Output #1

2

Without removing edges, the pair $(2, 3)$ violates the condition. Removing one of the edges disconnects Vertices $2$ and $3$, satisfying the condition.

Input #2

Output #2

Input #3

Output #3

Input #4

18 0

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Close Group",
    "description": {
      "content": "Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \\dots, N$, and the $i$\\-th edge connects Vertices $A_i$ and $B_i$. Find the minimum possible number",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc187_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a simple undirected graph with $N$ vertices and $M$ edges. The vertices are numbered $1, 2, \\dots, N$, and the $i$\\-th edge connects Vertices $A_i$ and $B_i$.\nFind the minimum possible number...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments