[leetcode] 235. Lowest Common Ancestor of a Binary Search Tree @ python

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原题

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

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 binary search tree: root = [6,2,8,0,4,7,9,null,null,3,5]

Example 1:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8
Output: 6
Explanation: The LCA of nodes 2 and 8 is 6.
Example 2:

Input: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4
Output: 2
Explanation: The LCA of nodes 2 and 4 is 2, 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 BST.

解法

递归, 分治法. Base case是root为空时, 返回None, 如果root等于p或者q, 返回root. 然后分情况讨论, 利用二叉搜索树的性质, 如果root的值比p和q的值都小, 则在root的右子树中寻找, 如果root的值比p和q都大, 则在root的左子树中寻找, 如果root在p和q之间则返回root.
Time: O(h), h为二叉树的深度
Space: O(1)

代码

# Definition for a binary tree node.
# class TreeNode(object):
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution(object):
    def lowestCommonAncestor(self, root, p, q):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
        # base case
        if not root:
            return None
        if root == p or root == q:
            return root
        if root.val > p.val and root.val > q.val:
            return self.lowestCommonAncestor(root.left, p, q)
        if root.val < p.val and root.val < q.val:
            return self.lowestCommonAncestor(root.right, p, q)
        else:
            return root