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numIslands.py
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numIslands.py
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"""
https://leetcode-cn.com/problems/number-of-islands
https://leetcode-cn.com/problems/number-of-islands/solution/dfs-bfs-bing-cha-ji-python-dai-ma-java-dai-ma-by-l/
https://www.liwei.party/2019/01/18/algorithms-and-data-structures/union-find-set/
https://www.jb51.net/article/136687.htm
给定一个由 '1'(陆地)和 '0'(水)组成的的二维网格,计算岛屿的数量。
一个岛被水包围,并且它是通过水平方向或垂直方向上相邻的陆地连接而成的。
你可以假设网格的四个边均被水包围。
示例 1:
输入:
11110
11010
11000
00000
输出: 1
示例 2:
输入:
11000
11000
00100
00011
输出: 3
"""
from typing import List
from collections import deque
class Solution:
def __init__(self):
"""
x-1, y
x, y-1 x, y x, y+1
x+1, y
方向数组,它表示了相对于当前位置的 4 个方向的横、纵坐标的偏移量,这是一个常见的技巧
"""
self.directions = [(-1, 0), (0, 1), (1, 0), (0, -1)]
def numIslands(self, grid: List[List[str]]) -> int:
"""
提示:
法一:深度优先搜索
"""
m = len(grid)
# 特判
if m == 0:
return 0
n = len(grid[0])
# marked 尺寸与 grid 一样,主要是用来标记哪一块已经处理过,处理过且是陆地的格子被标记为 True。
marked = [[False for _ in range(n)] for _ in range(m)]
count = 0
# 从第 1 行、第 1 格开始,对每一格尝试进行一次 DFS 操作
for i in range(m):
for j in range(n):
# 只要是陆地,且没有被访问过的,就可以使用 DFS 发现与之相连的陆地,并进行标记
if not marked[i][j] and grid[i][j] == '1':
# count 可以理解为连通分量,你可以在深度优先遍历完成以后,再计数,
# 即这行代码放在【位置 1】也是可以的
count += 1
self.__dfs(grid, i, j, m, n, marked)
# 【位置 1】
return count
def __dfs(self, grid, i, j, m, n, marked):
marked[i][j] = True
for direction in self.directions:
new_i = i + direction[0]
new_j = j + direction[1]
if 0 <= new_i < m and 0 <= new_j < n and not marked[new_i][new_j] and grid[new_i][new_j] == '1':
self.__dfs(grid, new_i, new_j, m, n, marked)
def numIslands2(self, grid: List[List[str]]) -> int:
"""
提示:
法二:广度优先搜索
"""
m = len(grid)
# 特判
if m == 0:
return 0
n = len(grid[0])
marked = [[False for _ in range(n)] for _ in range(m)]
count = 0
# 从第 1 行、第 1 格开始,对每一格尝试进行一次 BFS 操作
for i in range(m):
for j in range(n):
# 只要是陆地,且没有被访问过的,就可以使用 BFS 发现与之相连的陆地,并进行标记
if not marked[i][j] and grid[i][j] == '1':
# count 可以理解为连通分量,你可以在广度优先遍历完成以后,再计数,
# 即这行代码放在【位置 1】也是可以的
count += 1
queue = deque()
queue.append((i, j))
# 注意:这里要标记上已经访问过
marked[i][j] = True
while queue:
cur_x, cur_y = queue.popleft()
# 得到 4 个方向的坐标
for direction in self.directions:
new_i = cur_x + direction[0]
new_j = cur_y + direction[1]
# 如果不越界、没有被访问过、并且还要是陆地,我就继续放入队列,放入队列的同时,要记得标记已经访问过。
if 0 <= new_i < m and 0 <= new_j < n and \
not marked[new_i][new_j] and grid[new_i][new_j] == '1':
queue.append((new_i, new_j))
# 【特别注意】在放入队列以后,要马上标记成已经访问过,语义也是十分清楚的:
# 反正只要进入了队列,你迟早都会遍历到它,而不是在出队列的时候再标记
# 【特别注意】如果是出队列的时候再标记,会造成很多重复的结点进入队列,
# 造成重复的操作,这句话如果你没有写对地方,代码会严重超时。
marked[new_i][new_j] = True
# 【位置 1】
return count
def numIslands3(self, grid: List[List[str]]) -> int:
"""
提示:
法三:并查集
"""
class UnionFind:
"""
定义简单的并查集
这个并查集没有任何的优化,是最简单的版本。
优化的版本可以看 leetcode 547 朋友圈 里写的并查集:
"""
def __init__(self, n):
self.count = n
self.parent = [i for i in range(n)]
def find(self, p):
while p != self.parent[p]:
p = self.parent[p]
return p
def is_connected(self, p, q):
return self.find(p) == self.find(q)
def union(self, p, q):
p_root = self.find(p)
q_root = self.find(q)
if p_root == q_root:
return
self.parent[q_root] = p_root
self.count -= 1
row = len(grid)
# 特判
if row == 0:
return 0
col = len(grid[0])
def get_index(x, y):
# 把二维的地图从左往右,从上往下,编号为 0 ~ row * col,
# 依次判断相邻的成员所属阵营(是否都是陆地)
return x * col + y
# 注意:我们不用像 DFS 和 BFS 一样,4 个方向都要尝试,只要看一看右边和下面就可以了
directions = [(1, 0), (0, 1)]
# 多开一个空间,把水域 "0" 都归到这个虚拟的老大上
dummy_node = row * col
# 多开的一个空间就是那个虚拟的空间
uf = UnionFind(dummy_node + 1)
for i in range(row):
for j in range(col):
# 如果是水域,都连到那个虚拟的空间去
if grid[i][j] == '0':
uf.union(get_index(i, j), dummy_node)
if grid[i][j] == '1':
# 向下、向右如果都是陆地,即 "1",就要合并一下
for direction in directions:
new_x = i + direction[0]
new_y = j + direction[1]
if new_x < row and new_y < col and grid[new_x][new_y] == '1':
uf.union(get_index(i, j), get_index(new_x, new_y))
# 不要忘记把那个虚拟结点减掉
return uf.count - 1
if __name__ == '__main__':
grid = [['1', '1', '0', '1', '0'],
['1', '0', '0', '1', '0'],
['0', '1', '0', '1', '1'],
['0', '1', '1', '0', '1']]
grid2 = 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solution = Solution()
result = solution.numIslands(grid)
print(result)
result2 = solution.numIslands2(grid)
print(result2)
result3 = solution.numIslands3(grid)
print(result3)