Problem：
Agu is a cursed place with conflicts of sources between tribes. To avoid the invasion of another tribe, every tribe starts to build their moat.
-
What is a tribe like.
Agu is a square of
$n*m$ grids. Every tribe occupys several grids, for example: . . a b . .
. . c . d .
. . . . . .
$abcd$ compose a tribe, where$a$ and$b$ is connected horizontally,$a$ and$c$ is connected vertically, and$b$ and$d$ is connected diagonally. More importantly, there's no such tribe of which grids have unoccupied grids surrounded, such as:
. . a b c . . .
. d . . e . . .
. . f g . . . .
-
The length of the moat
In principle, every tribe would build their moat as short as possiple for those exposed sides of grids, which means no gird share side with it. For example:
. . . . . .
. a b . . .
. c . d . .
. . . . . .
$abcd$ is a tribe with 16 sides($a$ ,$b$ ,$c$ ,$d$ have four sides), in which the number of exposed is 12. Each exposed side need 1 unit length of moat, therefore the length of the moat needed is 12.
Function Description:
Given the coordinate of a gride$(a, b)$, compute the length of the tribe's moat that the grid belongs to.
Input Format:
The firt line contains 4 integers
Following is an
Constrains
$n \geq 1$ $m\leq 100$ $1\leq a \leq n$ $1 \leq b\leq n$
Output Format:
Return the integer minimum length of the moat.
Sample Input:
-
Sample 1
4 6 3 4
. . . . . .
. # # . . .
. # . # . .
. . . . . .
-
Sample 2
6 4 2 3
. # # #
. # # #
. # # #
. . . #
. . # .
# . . .
-
Sample 3
5 6 1 3
. # # # # .
# . . . . #
. . # # . #
. # . . . #
. . # # # .
Sample Output:
-
Sample 1
12
-
Sample 2
18
-
Sample 3
40
This project requires python 3 with scikit-learn, scipy, numpy installed.