Lowest Common Ancestor of a Binary Search Tree

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.

Tags

• Tree

Thought

Reference: https://discuss.leetcode.com/topic/18387/3-lines-with-o-1-space-1-liners-alternatives

Search along the tree for both of the node q and q, then return the result until the subtree is difference.

Code

class Solution(object):
    def lowestCommonAncestor(self, root, p, q):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
        while (root.val - p.val) * (root.val - q.val) > 0:
            root = (root.left, root.right)[p.val > root.val]
        return root