LeetCode 236. Lowest Common Ancestor of a Binary Tree



Given a binary tree, find the lowest common ancestor (LCA) of two given nodes in the tree.

According to the definition of LCA on Wikipedia: “The lowest common ancestor is defined between two nodes p and q as the lowest node in T that has both p and q as descendants (where we allow a node to be a descendant of itself).”

Example 1:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 1
Output: 3
Explanation: The LCA of nodes 5 and 1 is 3.

Example 2:

Input: root = [3,5,1,6,2,0,8,null,null,7,4], p = 5, q = 4
Output: 5
Explanation: The LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.

Example 3:

Input: root = [1,2], p = 1, q = 2
Output: 1


  • The number of nodes in the tree is in the range [2, 105].
  • -109 <= Node.val <= 109
  • All Node.val are unique.
  • p != q
  • p and q will exist in the tree.


If p and q in the left and right subtrees, return root.

If in one side of the subtree, find the LCA in that subtree.

If the root is p or q or is null, return root.

# Definition for a binary tree node.
# class TreeNode:
#     def __init__(self, x):
#         self.val = x
#         self.left = None
#         self.right = None

class Solution:
    def lowestCommonAncestor(self, root: 'TreeNode', p: 'TreeNode', q: 'TreeNode') -> 'TreeNode':
        return self.lca_helper(root, p, q)
    def lca_helper(self, root, p, q):
        if not root:
            return None
        if p == root or q == root:
            return root
        left_lca = self.lca_helper(root.left, p, q)
        right_lca = self.lca_helper(root.right, p, q)
        if left_lca and right_lca:
            return root
        if left_lca:
            return left_lca
        if right_lca:
            return right_lca
        return None
  • Time Complexity: O(N).
  • Space Complexity: O(1).

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