Lowest Common Ancestor of a Binary Search Tree

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.

URL: https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/

# 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 __init__(self):
        self.inorder_list = []
        self.postorder_list = []

    def lowestCommonAncestor(self, root, p, q):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
        if root == None:
            return None
        else:
            self.inorder_traversal(root)
            self.postorder_traversal(root)
            #get the positions of node1 and node2 in the inorder traversal of the tree
            index_node1 = self.inorder_list.index(p.val)
            index_node2 = self.inorder_list.index(q.val)

            if index_node1 < index_node2:
                between_elems = self.inorder_list[index_node1 : index_node2 + 1]
            else:
                between_elems = self.inorder_list[index_node2 : index_node1 + 1]


            lca_elem = self.find_elem_max_index(between_elems)

            return lca_elem

    def find_elem_max_index(self, between_elems):
        max_index = -1
        elem = None
        for entries in between_elems:
            elem_index = self.postorder_list.index(entries)
            if elem_index > max_index:
                max_index = elem_index
                elem = entries
        return elem

    def inorder_traversal(self, node):
        if node:
            self.inorder_traversal(node.left)
            self.inorder_list.append(node.val)
            self.inorder_traversal(node.right)

    def postorder_traversal(self, node):
        if node:
            self.postorder_traversal(node.left)
            self.postorder_traversal(node.right)
            self.postorder_list.append(node.val)