LeetCode#235 Lowest Common Ancestor of a Binary Search Tree

Problem Definition:

　　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 v and w as the lowest node in T that has both v and w as descendants (where we allow a node to be a descendant of itself).”

思路：由根节点开始：

　　1) 如果根节点的值等于其中一个节点，则根节点就是要找的最低公共祖先，返回它；

　　2) 排序，确保p<=q;

　　3) 如果根节点值大于p而小于q，则p和q分别在根节点的左右子树，根节点就是要找的最低公共祖先，返回它；

　　4) 如果根节点值大于较大的q，则p和q都在根节点的左子树，令根节点左子节点为新的根节点；如果根节点值小于较小的p，则p和q都在根节点的右子树

　　　　另根节点右子节点为新的根节点；

　　5)递归地进行1)-->4).

代码：

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

class Solution:
    # @param {TreeNode} root
    # @param {TreeNode} p
    # @param {TreeNode} q
    # @return {TreeNode}
    def lowestCommonAncestor(self, root, p, q):
        if (root.val==p.val) or (root.val==q.val):
            return root
        if p.val>q.val:
            p,q=q,p
        if p.val<root.val and root.val<q.val:
            return root
        if root.val>q.val:
            root=root.left
        if root.val<p.val:
            root=root.right
        if root!=None:
            return self.lowestCommonAncestor(root, p, q)