Moving Pieces on Graph

AtCoder

IDarc191_d

Time2000ms

Memory256MB

Difficulty—

You are given a simple connected undirected graph with $N$ vertices and $M$ edges, where the vertices are numbered $1$ to $N$ and the edges are numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and vertex $v_i$ in both directions. Initially, there is a piece A on vertex $S$ and a piece B on vertex $T$. Here, $S$ and $T$ are given as input. You may perform the following operation any number of times in any order: * Choose either piece A or piece B, and move it from its current vertex to an adjacent vertex via an edge. However, you cannot make a move that results in both pieces ending up on the same vertex. Your goal is to reach the state in which piece A is on vertex $T$ and piece B is on vertex $S$. Determine whether this is possible, and if it is, find the minimum number of operations required to achieve it. ## Constraints * $2 \le N \le 2\times 10^5$ * $\displaystyle N-1 \le M \le \min\left(\frac{N(N-1)}{2},\,2\times 10^5\right)$ * $1 \le u_i < v_i \le N$ * The given graph is simple and connected. * $1 \le S, T \le N$ * $S \neq T$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $N$ $M$ $S$ $T$ $u_1$ $v_1$ $u_2$ $v_2$ $\vdots$ $u_M$ $v_M$ [samples]

Samples

Input #1

Output #1

3

For example, the following sequence of operations completes the goal in three moves:

1.  Move piece A to vertex $2$.
    *   Piece A is on vertex $2$, piece B is on vertex $4$.
2.  Move piece B to vertex $3$.
    *   Piece A is on vertex $2$, piece B is on vertex $3$.
3.  Move piece A to vertex $4$.
    *   Piece A is on vertex $4$, piece B is on vertex $3$.

It is impossible to complete the goal in fewer than three moves, so print $3$.

Input #2

2 1 1 2
1 2

Output #2

\-1

No matter how you move the pieces, you cannot achieve the goal.

Input #3

Output #3

API Response (JSON)

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  "problem": {
    "name": "Moving Pieces on Graph",
    "description": {
      "content": "You are given a simple connected undirected graph with $N$ vertices and $M$ edges, where the vertices are numbered $1$ to $N$ and the edges are numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc191_d"
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  "statements": [
    {
      "statement_type": "Markdown",
      "content": "You are given a simple connected undirected graph with $N$ vertices and $M$ edges, where the vertices are numbered $1$ to $N$ and the edges are numbered $1$ to $M$. Edge $i$ connects vertex $u_i$ and ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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