面试150 建立四叉树

思路

采用递归分治的思路构建四叉树。首先判断当前区域内的值是否全部相同，若是，则构建一个叶子节点；若否，则将区域划分为四个子区域（左上、右上、左下、右下），对每个子区域递归构建对应的子节点，并将其作为当前非叶子节点的四个子树。通过不断划分和合并，实现将二维网格压缩为一棵结构紧凑的四叉树。

"""
# Definition for a QuadTree node.
class Node:
    def __init__(self, val, isLeaf, topLeft, topRight, bottomLeft, bottomRight):
        self.val = val
        self.isLeaf = isLeaf
        self.topLeft = topLeft
        self.topRight = topRight
        self.bottomLeft = bottomLeft
        self.bottomRight = bottomRight
"""

class Solution:
    def construct(self, grid: List[List[int]]) -> 'Node':
        n=len(grid)
        def isSame(x,y,size):
            val=grid[x][y]
            for i in range(x,x+size):
                for j in range(y,y+size):
                    if grid[i][j]!=val:
                        return False,val
            return True,val
        
        def build(x,y,size):
            same,val=isSame(x,y,size)
            if same:
                return Node(val==1,True)
            else:
                half=size//2
                return Node(
                    val=True,
                    isLeaf=False,
                    topLeft=build(x,y,half),
                    topRight=build(x,y+half,half),
                    bottomLeft=build(x+half,y,half),
                    bottomRight=build(x+half,y+half,half)
                )
        return build(0,0,n)