Connect Cities

AtCoder

IDabl_c

Time2000ms

Memory256MB

Difficulty—

There are $N$ cities numbered $1$ through $N$, and $M$ bidirectional roads numbered $1$ through $M$. Road $i$ connects City $A_i$ and City $B_i$. Snuke can perform the following operation zero or more times: * Choose two distinct cities that are not directly connected by a road, and build a new road between the two cities. After he finishes the operations, it must be possible to travel from any city to any other cities by following roads (possibly multiple times). What is the minimum number of roads he must build to achieve the goal? ## Constraints * $2 \leq N \leq 100,000$ * $1 \leq M \leq 100,000$ * $1 \leq A_i < B_i \leq N$ * No two roads connect the same pair of cities. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $A_1$ $B_1$ $:$ $A_M$ $B_M$ [samples]

Samples

Input #1

3 1
1 2

Output #1

1

Initially, there are three cities, and there is a road between City $1$ and City $2$.
Snuke can achieve the goal by building one new road, for example, between City $1$ and City $3$. After that,

*   We can travel between $1$ and $2$ directly.
*   We can travel between $1$ and $3$ directly.
*   We can travel between $2$ and $3$ by following both roads ($2$ - $1$ - $3$).

API Response (JSON)

{
  "problem": {
    "name": "Connect Cities",
    "description": {
      "content": "There are $N$ cities numbered $1$ through $N$, and $M$ bidirectional roads numbered $1$ through $M$. Road $i$ connects City $A_i$ and City $B_i$. Snuke can perform the following operation zero or more",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abl_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ cities numbered $1$ through $N$, and $M$ bidirectional roads numbered $1$ through $M$. Road $i$ connects City $A_i$ and City $B_i$.\nSnuke can perform the following operation zero or more...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments