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