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).”

Given the following binary tree: root = [3,5,1,6,2,0,8,null,null,7,4]

        _______3______
       /              \
    ___5__          ___1__
   /      \        /      \
   6      _2       0       8
         /  \
         7   4

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 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.

Note:

  • All of the nodes' values will be unique.
  • p and q are different and both values will exist in the binary tree.

Solution

(1) Java



(2) Python

# 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, p, q):
        """
        :type root: TreeNode
        :type p: TreeNode
        :type q: TreeNode
        :rtype: TreeNode
        """
        if not root:
            return root
        if root == p or root == q:
            return root
        lnode = self.lowestCommonAncestor(root.left, p, q)
        rnode = self.lowestCommonAncestor(root.right, p, q)
        if lnode and rnode:
            return root
        return lnode if lnode else rnode

More concise code

def lowestCommonAncestor(self, root, p, q):
    if root in (None, p, q): return root
    left, right = (self.lowestCommonAncestor(kid, p, q)
                   for kid in (root.left, root.right))
    return root if left and right else left or right

(3) Scala



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