Shapes

AtCoder

IDabc218_c

Time2000ms

Memory256MB

Difficulty—

We have two figures $S$ and $T$ on a two-dimensional grid with square cells. $S$ lies within a grid with $N$ rows and $N$ columns, and consists of the cells where $S_{i,j}$ is `#`. $T$ lies within the same grid with $N$ rows and $N$ columns, and consists of the cells where $T_{i,j}$ is `#`. Determine whether it is possible to exactly match $S$ and $T$ by $90$\-degree rotations and translations. ## Constraints * $1 \leq N \leq 200$ * Each of $S$ and $T$ consists of `#` and `.`. * Each of $S$ and $T$ contains at least one `#`. ## Input Input is given from Standard Input in the following format: $N$ $S_{1,1}S_{1,2}\ldots S_{1,N}$ $\vdots$ $S_{N,1}S_{N,2}\ldots S_{N,N}$ $T_{1,1}T_{1,2}\ldots T_{1,N}$ $\vdots$ $T_{N,1}T_{N,2}\ldots T_{N,N}$ [samples]

Samples

Input #1

5
.....
..#..
.###.
.....
.....
.....
.....
....#
...##
....#

Output #1

Yes

We can match $S$ to $T$ by rotating it $90$\-degrees counter-clockwise and translating it.

Input #2

5
#####
##..#
#..##
#####
.....
#####
#..##
##..#
#####
.....

Output #2

No

It is impossible to match them by $90$\-degree rotations and translations.

Input #3

4
#...
..#.
..#.
....
#...
#...
..#.
....

Output #3

Yes

Each of $S$ and $T$ may not be connected.

Input #4

4
#...
.##.
..#.
....
##..
#...
..#.
....

Output #4

No

Note that it is not allowed to rotate or translate just a part of a figure; it is only allowed to rotate or translate a whole figure.

API Response (JSON)

{
  "problem": {
    "name": "Shapes",
    "description": {
      "content": "We have two figures $S$ and $T$ on a two-dimensional grid with square cells. $S$ lies within a grid with $N$ rows and $N$ columns, and consists of the cells where $S_{i,j}$ is `#`.   $T$ lies within t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc218_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have two figures $S$ and $T$ on a two-dimensional grid with square cells.\n$S$ lies within a grid with $N$ rows and $N$ columns, and consists of the cells where $S_{i,j}$ is `#`.  \n$T$ lies within t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments