Teleport Maze

AtCoder

IDabc436_d

Time2000ms

Memory256MB

Difficulty—

There is a maze consisting of a grid with $H$ rows and $W$ columns. Let $(i,j)$ denote the cell at the $i$\-th row from the top and $j$\-th column from the left. The type of cell $(i,j)$ is given as a character $S_{i,j}$, where each character has the following meaning: * `.` : Empty cell * `#` : Obstacle cell * Lowercase English letter (`a` - `z`): Warp cell In the maze, you can perform the following two types of actions any number of times in any order: * Walk: Move from the current cell to a cell that is one cell away in one of the four directions (up, down, left, right). However, you cannot move to an obstacle cell or outside the grid. * Warp: When you are at a warp cell, move to any warp cell with the same character written on it. Determine whether it is possible to move from cell $(1,1)$ to cell $(H,W)$, and if possible, find the minimum total number of actions required. ## Constraints * $1\leq H,W \leq 1000$ * $H\times W \geq 2$ * $H$ and $W$ are integers. * $S_{i,j}$ is `.`, `#`, or a lowercase English letter. * $S_{1,1}\neq$ `#` * $S_{H,W}\neq$ `#` ## Input The input is given from Standard Input in the following format: $H$ $W$ $S_{1,1}S_{1,2}\dots S_{1,W}$ $\vdots$ $S_{H,1}S_{H,2}\dots S_{H,W}$ [samples]

Samples

Input #1

3 4
..a.
####
ba#b

Output #1

5

You can move from cell $(1,1)$ to cell $(3,4)$ by performing actions as follows:

1.  Move from cell $(1,1)$ to cell $(1,2)$ by walking.
2.  Move from cell $(1,2)$ to cell $(1,3)$ by walking.
3.  Move from cell $(1,3)$ to cell $(3,2)$ by warping.
4.  Move from cell $(3,2)$ to cell $(3,1)$ by walking.
5.  Move from cell $(3,1)$ to cell $(3,4)$ by warping.

The total number of actions is $5$, which is the minimum.

Input #2

3 4
..a.
####
b.#b

Output #2

\-1

It is impossible to move from cell $(1,1)$ to cell $(3,4)$.

Input #3

4 4
xxxx
xxxx
xxxx
xxxx

Output #3

Input #4

7 11
u..#y..#...
k..#.z.#.k.
iju#...#x..
###########
..x#.t.#..n
abc#y..#...
..z#..t#.y.

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Teleport Maze",
    "description": {
      "content": "There is a maze consisting of a grid with $H$ rows and $W$ columns. Let $(i,j)$ denote the cell at the $i$\\-th row from the top and $j$\\-th column from the left. The type of cell $(i,j)$ is given as a",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc436_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There is a maze consisting of a grid with $H$ rows and $W$ columns. Let $(i,j)$ denote the cell at the $i$\\-th row from the top and $j$\\-th column from the left. The type of cell $(i,j)$ is given as a...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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