Lowest Common Ancestor of a Binary Search Tree in Python

Suppose we have a binary search tree. we have to find the Lowest common ancestor nodes of two given nodes. The LCA of two nodes p and q is actually as the lowest node in tree that has both p and q as decedent. So if the binary tree is like [6, 2, 8, 0, 4, 7, 9, null, null, 3, 5]. The tree will be like −

Here LCA of 2 and 8 is 6

To solve this, we will follow these steps −

• If the tree is empty, then return null
• if p and q both are same as root, then return root
• left := LCA of left subtree of the root using p and q
• right := LCA of right subtree of the root using p and q
• if left and right both are non-zero, then return root
• return left OR right

Example

Let us see the following implementation to get better understanding −

 Live Demo

class TreeNode:    def __init__(self, data, left = None, right = None):       self.data = data       self.left = left       self.right = right class Solution():    def lowestCommonAncestor(self, root, p, q):       if not root:          return None       if p == root or q==root:          return root       left = self.lowestCommonAncestor(root.left, p, q)       right = self.lowestCommonAncestor(root.right, p, q)       if left and right:          return root       return left or right def insert(temp,data):    que = []    que.append(temp)    while (len(que)):       temp = que[0]       que.pop(0)       if (not temp.left):          temp.left = TreeNode(data)          break       else:          que.append(temp.left)       if (not temp.right):          temp.right = TreeNode(data)          break       else:          que.append(temp.right) def make_tree(elements):    Tree = TreeNode(elements[0])    for element in elements[1:]:       insert(Tree, element)    return Tree def search_node(root, element):    if (root == None):       return None    if (root.data == element):       return root    res1 = search_node(root.left, element)    if res1:       return res1    res2 = search_node(root.right, element)    return res2 root = make_tree([6,2,8,0,4,7,9,None,None,3,5]) ob1 = Solution() op = ob1.lowestCommonAncestor(root, search_node(root, 2), search_node(root, 8)) print(op.data)

Input

[6,2,8,0,4,7,9,null,null,3,5] 2 8

Output

6