Number of Distinct Islands

Given a non-empty 2D arraygridof 0's and 1's, anislandis a group of1's (representing land) connected 4-directionally (horizontal or vertical.) You may assume all four edges of the grid are surrounded by water.

Count the number ofdistinctislands. An island is considered to be the same as another if and only if one island can be translated (and not rotated or reflected) to equal the other.

Example 1:

11000
11000
00011
00011

Given the above grid map, return

1

.

Example 2:

11011
10000
00001
11011

Given the above grid map, return

3

.

Notice that:

11
1

and

 1
11

are considered different island shapes, because we do not consider reflection / rotation.

Note:The length of each dimension in the givengriddoes not exceed 50.

分析

和题二的区别就是二8个方向，这里只要相同。

每次dfs得到一个联通块，然后在本块里的所有坐标-minx, -miny。加入set。结果就set长度

class Solution:
    def numDistinctIslands(self, grid: List[List[int]]) -> int:
        if not grid or not grid[0]:
            return 0
        n, m = len(grid), len(grid[0])        
        d = [-1, 0, 1, 0, -1]

        ss = set()

        def dfs(i,j,q):
            q.append((i,j))
            if grid[i][j] == -1:
                return
            grid[i][j] = -1
            nxy = [(i + d[k], j + d[k + 1]) for k in range(4)]
            for nx,ny in nxy:
                if 0<= nx < n and 0<= ny< m and grid[nx][ny] == 1:
                    q.append((nx,ny))
                    dfs(nx,ny,q)

        for i in range(n):        
            for j in range(m):
                if grid[i][j] == 1:
                    q = []
                    dfs(i, j, q)
                    if q:
                        mini,minj = min(x for x,y in q), min(y for x,y in q)
                        f = tuple(sorted((x-mini, y-minj) for x, y in q))
                        ss.add(f)

        return len(ss)