Forest

AtCoder

IDapc001_d

Time2000ms

Memory256MB

Difficulty—

You are given a forest with $N$ vertices and $M$ edges. The vertices are numbered $0$ through $N-1$. The edges are given in the format $(x_i,y_i)$, which means that Vertex $x_i$ and $y_i$ are connected by an edge. Each vertex $i$ has a value $a_i$. You want to add edges in the given forest so that the forest becomes connected. To add an edge, you choose two different vertices $i$ and $j$, then span an edge between $i$ and $j$. This operation costs $a_i + a_j$ dollars, and afterward neither Vertex $i$ nor $j$ can be selected again. Find the minimum total cost required to make the forest connected, or print `Impossible` if it is impossible. ## Constraints * $1 ≤ N ≤ 100,000$ * $0 ≤ M ≤ N-1$ * $1 ≤ a_i ≤ 10^9$ * $0 ≤ x_i,y_i ≤ N-1$ * The given graph is a forest. * All input values are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $a_0$ $a_1$ $..$ $a_{N-1}$ $x_1$ $y_1$ $x_2$ $y_2$ $:$ $x_M$ $y_M$ [samples]

Samples

Input #1

7 5
1 2 3 4 5 6 7
3 0
4 0
1 2
1 3
5 6

Output #1

7

If we connect vertices $0$ and $5$, the graph becomes connected, for the cost of $1 + 6 = 7$ dollars.

Input #2

5 0
3 1 4 1 5

Output #2

Impossible

We can't make the graph connected.

Input #3

1 0
5

Output #3

0

The graph is already connected, so we do not need to add any edges.

API Response (JSON)

{
  "problem": {
    "name": "Forest",
    "description": {
      "content": "You are given a forest with $N$ vertices and $M$ edges. The vertices are numbered $0$ through $N-1$. The edges are given in the format $(x_i,y_i)$, which means that Vertex $x_i$ and $y_i$ are connecte",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "apc001_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a forest with $N$ vertices and $M$ edges. The vertices are numbered $0$ through $N-1$. The edges are given in the format $(x_i,y_i)$, which means that Vertex $x_i$ and $y_i$ are connecte...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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