题目描述：
LeetCode 694. Number of Distinct Islands
Given a non-empty 2D array grid of 0's and 1's, an island is a group of 1'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 of distinct islands. 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 given grid does not exceed 50.
题目大意：
给定二维格子grid，上下左右相邻的1组成岛屿，求不同的岛屿种类（岛屿可以平移变换，但是不可以旋转或者对称变换）。
解题思路：
BFS + Map
利用BFS可以求出某个岛屿的所有点坐标，用top, left表示这些坐标的最上和最左。
将所有坐标(x, y) 变换为 (x - top, y - left)，即可实现平移变换。
Python代码：
class Solution(object):
def numDistinctIslands(self, grid):
"""
:type grid: List[List[int]]
:rtype: int
"""
islands = set()
for x in range(len(grid)):
for y in range(len(grid[0])):
if grid[x][y]:
islands.add(self.bfs(grid, x, y))
return len(islands)
def bfs(self, grid, x, y):
w, h = len(grid), len(grid[0])
dxs = [1, 0, -1, 0]
dys = [0, 1, 0, -1]
queue = [(x, y)]
grid[x][y] = 0
ans = []
while queue:
x, y = queue.pop(0)
ans.append((x, y))
for dx, dy in zip(dxs, dys):
nx, ny = x + dx, y + dy
if 0 <= nx < w and 0 <= ny < h:
if grid[nx][ny]:
grid[nx][ny] = 0
queue.append((nx, ny))
top = min(x for x, y in ans)
left = min(y for x, y in ans)
return tuple((x - top) * h + y - left for x, y in sorted(ans))
本文链接：http://bookshadow.com/weblog/2017/10/08/leetcode-number-of-distinct-islands/
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