https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/
Lowest Common Ancestor of a Binary Tree
Total Accepted: 17453 Total Submissions: 63885 Difficulty: Medium
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 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).”
_______3______
/ \
___5__ ___1__
/ \ / \
6 _2 0 8
/ \
7 4
For example, the lowest common ancestor (LCA) of nodes 5 and 1 is 3. Another example is LCA of nodes 5 and 4 is 5, since a node can be a descendant of itself according to the LCA definition.
Code:
# 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 lowestCommonAncestor(self, root, p, q):
if root is None:
return None
if root == p or root == q:
return root
left = self.lowestCommonAncestor(root.left, p, q)
right = self.lowestCommonAncestor(root.right, p, q)
if left and right:
return root
elif left:
return left
elif right:
return right
else:
None
Idea:
lowestCommonAncestor will do the following judgement:
- if applying lowestCommonAncestor on root.left returns non-None value, it means at least p or q is in its left subtree.
- if appling lowestCommonAncestor on root.right returns non-None value, it means at least p or q is in its right subtree.
- if both root’s left and root’s right return non-None values, then p and q are in its left subtree and right subtree. So the common ancestor should be root.
- if only one of root’s left and root’s right returns non-None value, that means both p and q is in that subtree. In this case, just return whichever non-None value you get.
- If lowestCommonAncestor returns none, that means neither p or q is in root and its subtrees.