The Grove
시간 제한1초메모리 제한1024 MB
나무 숲이 하나 있는 격자에서 8방향 이동으로 숲을 한 바퀴 도는 닫힌 경로를 찾고 최소 걸음 수를 구한다.
문제
The pasture contains a small, contiguous grove of trees that has no 'holes' in the middle of the it. Bessie wonders: how far is it to walk around that grove and get back to my starting position? She's just sure there is a way to do it by going from her start location to successive locations by walking horizontally, vertically, or diagonally and counting each move as a single step. Just looking at it, she doesn't think you could pass 'through' the grove on a tricky diagonal. Your job is to calculate the minimum number of steps she must take.
Happily, Bessie lives on a simple world where the pasture is represented by a grid with R rows and C columns (1 ≤ R ≤ 50, 1 ≤ C ≤ 50). Here's a typical example where '.' is pasture (which Bessie may traverse), 'X' is the grove of trees, '*' represents Bessie's start and end position, and '+' marks one shortest path she can walk to circumnavigate the grove (i.e., the answer):
...+...
..+X+..
.+XXX+.
..+XXX+
..+X..+
...+++*
The path shown is not the only possible shortest path; Bessie might have taken a diagonal step from her start position and achieved a similar length solution. Bessie is happy that she's starting 'outside' the grove instead of in a sort of 'harbor' that could complicate finding the best path.
입력
- Line 1: Two space-separated integers: R and C
- Lines 2..R+1: Line i+1 describes row i with C characters (with no spaces between them).
출력
- Line 1: The single line contains a single integer which is the smallest number of steps required to circumnavigate the grove.