Lowest Common Ancestor of a Binary Search Tree 解答

Question

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).”

        _______6______
       /              \
    ___2__          ___8__
   /      \        /      \
   0      _4       7       9
         /  \
         3   5

For example, the lowest common ancestor (LCA) of nodes 2 and 8 is 6. Another example is LCA of nodes 2 and 4 is 2, since a node can be a descendant of itself according to the LCA definition.

Solution

Use property of BST.

 # 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
         """
         if root is None:
             return root
         if p.val > q.val:
             return self.lowestCommonAncestor(root, q, p)
         if p.val < root.val and q.val > root.val:
             return root
         elif p.val < root.val and q.val < root.val:
             return self.lowestCommonAncestor(root.left, p, q)
         elif p.val > root.val and q.val > root.val:
             return self.lowestCommonAncestor(root.right, p, q)
         return root