Leetcode 236 Lowest Common Ancestor of a Binary Tree

Lowest Common Ancestor of a Binary Tree"/>

Leetcode 236 Lowest Common Ancestor of a Binary Tree

Leetcode 236 Lowest Common Ancestor of a Binary Tree

题目描述

Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Given the following binary tree: root = [3,5,1,6,2,0,8,null,null,7,4]

Example 1:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of nodes 5 and 1 is 3.

Example 2:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

Note:

• All of the nodes’ values will be unique.
• p and q are different and both values will exist in the binary tree.

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思路解析

• 思路一（递归

  root结点有三种可能：

  1. root is None
  2. root is p
  3. root is q

  遇到这三种，直接返回root即可；但如果root不是上述三种情况，则有三种情况：

  1. p、q、LCA均在当前root的左子树上
  2. p、q、LCA均在当前root的右子树上
  3. p、q分别在当前root的左右子树上，LCA为当前root

  代码如下：

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = Noneclass Solution(object):def lowestCommonAncestor(self, root, p, q):        """:type root: TreeNode:type p: TreeNode:type q: TreeNode:rtype: TreeNode"""if root is None or root is p or root is q:return rootleft = self.lowestCommonAncestor(root.left, p, q)right = self.lowestCommonAncestor(root.right, p, q)if not left:return rightif not right:return leftreturn root

时间复杂度最坏为 O ( N ) O(N) O(N)，空间复杂度最坏为 O ( N ) O(N) O(N)