## LCA of Binary Tree

### 描述

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.

### 分析

• 如果两边都能找到，说明当前节点就是最近公共祖先
• 如果左边没找到，则说明pq都在右子树
• 如果右边没找到，则说明pq都在左子树

### 代码

// Lowest Common Ancestor of a Binary Tree
// Time complexity: O(n), Space complexity: O(h)
public class Solution {
public TreeNode lowestCommonAncestor(TreeNode root, TreeNode p, TreeNode q) {
// if root is null or found p or q
if (root == null || root == p || root == q) return root;
// find p or q in the left subtree
final TreeNode left = lowestCommonAncestor(root.left, p, q);
// find p or q in the right subtree
final TreeNode right = lowestCommonAncestor(root.right, p, q);
if (left != null && right != null) return root;
else return left == null ? right : left;
}
}