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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 −

Lowest Common Ancestor of a Binary Search Tree in Python

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 −

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