LeetCode题解(0711)：不同岛屿的数量II(Python)

题目：​​原题链接​​（困难）

标签：哈希表、图、广度优先搜索、深度优先搜索

解法一：

class Solution:
    def numDistinctIslands(self, grid: List[List[int]]):
        visited = set()
        islands = set()

        size1, size2 = len(grid), len(grid[0])
        for i1 in range(size1):
            for i2 in range(size2):
                if grid[i1][i2] == 0 or (i1, i2) in visited:
                    continue

                land, min1, min2, max1, max2 = {(i1, i2)}, i1, i2, i1, i2
                pos_list = collections.deque([(i1, i2)])
                while pos_list:
                    i3, i4 = pos_list.popleft()
                    if i3 + 1 < size1 and grid[i3 + 1][i4] == 1 and (i3 + 1, i4) not in land:
                        land.add((i3 + 1, i4))
                        pos_list.append((i3 + 1, i4))
                        max1 = max(max1, i3 + 1)
                    if i4 + 1 < size2 and grid[i3][i4 + 1] == 1 and (i3, i4 + 1) not in land:
                        land.add((i3, i4 + 1))
                        pos_list.append((i3, i4 + 1))
                        max2 = max(max2, i4 + 1)
                    if i3 - 1 >= 0 and grid[i3 - 1][i4] == 1 and (i3 - 1, i4) not in land:
                        land.add((i3 - 1, i4))
                        pos_list.append((i3 - 1, i4))
                        min1 = min(min1, i3 - 1)
                    if i4 - 1 >= 0 and grid[i3][i4 - 1] == 1 and (i3, i4 - 1) not in land:
                        land.add((i3, i4 - 1))
                        pos_list.append((i3, i4 - 1))
                        min2 = min(min2, i4 - 1)

                island = []
                for i3 in range(min1, max1 + 1):
                    row = []
                    for i4 in range(min2, max2 + 1):
                        if (i3, i4) in land:
                            row.append("1")
                        else:
                            row.append("0")
                    island.append("".join(row))
                island = " ".join(island)

                visited |= land
                islands.add(island)

        return islands

    def numDistinctIslands2(self, grid: List[List[int]]) -> int:
        # 对角线翻转
        def reverse_diagonal(source):
            source = source.split(" ")
            ss1, ss2 = len(source), len(source[0])
            result = []
            for ii1 in range(ss2):
                rr = []
                for ii2 in range(ss1):
                    rr.append(source[ii2][ii1])
                result.append("".join(rr))
            return " ".join(result)

        # 水平翻转
        def reverse_horizontal(source):
            source = source.split(" ")
            ss1, ss2 = len(source), len(source[0])
            result = []
            for ii1 in range(ss1):
                rr = []
                for ii2 in range(ss2):
                    rr.append(source[ii1][ss2 - 1 - ii2])
                result.append("".join(rr))
            return " ".join(result)

        # 垂直翻转
        def reverse_perpendicular(source):
            source = source.split(" ")
            ss1, ss2 = len(source), len(source[0])
            result = [[] for _ in range(ss1)]
            for ii2 in range(ss2):
                for ii1 in range(ss1):
                    result[ii1].append(source[ss1 - 1 - ii1][ii2])
            str_result = []
            for ii1 in range(ss1):
                str_result.append("".join(result[ii1]))
            return " ".join(str_result)

        # 所有可能
        def all_change(source):
            yield source
            yield reverse_horizontal(source)
            yield reverse_perpendicular(source)
            yield reverse_horizontal(reverse_perpendicular(source))
            yield reverse_diagonal(source)
            yield reverse_diagonal(reverse_horizontal(source))
            yield reverse_diagonal(reverse_perpendicular(source))
            yield reverse_diagonal(reverse_horizontal(reverse_perpendicular(source)))

        # 生成所有岛屿
        islands = self.numDistinctIslands(grid)

        # 岛屿去重
        islands_set = set()

        for island in islands:
            unique = True
            for change in all_change(island):
                if change in islands_set:
                    unique = False
                    break
            if unique:
                islands_set.add(island)

        return len(islands_set)