Lowest Common Ancestor of a Binary Tree（二叉树公共祖先）

Posted 2020-10-06 人总闲

来源：https://leetcode.com/problems/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 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.

递归搜索，当root非空时，对其左右两子数分别进行搜索。若搜索结果都为非空，则两个节点分别位于左右两个子树中，LCA为root节点；若其中一个结果为空，则另一个不为空的为LCA；若两个结果都为空，则返回null

 1 /**
 2  * Definition for a binary tree node.
 3  * public class TreeNode {
 4  *     int val;
 5  *     TreeNode left;
 6  *     TreeNode right;
 7  *     TreeNode(int x) { val = x; }
 8  * }
 9  */
10 class Solution {
11     public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
12         if(root == null || (p == null && q == null)) {
13             return null;
14         }
15         if(root == p || root == q) {
16             return root;
17         }
18         TreeNode left = lowestCommonAncestor(root.left, p, q);
19         TreeNode right = lowestCommonAncestor(root.right, p, q);
20         if(left != null && right != null) {
21             return root;
22         } else if(left != null && right == null) {
23             return left;
24         } else if(left == null && right != null) {
25             return right;
26         } else {
27             return null;
28         }
29     }
30 }