Lowest Common Ancestor of Deepest Leaves

Given a rooted binary tree, return the lowest common ancestor of its deepest leaves.

Recall that:

• The node of a binary tree is a leaf if and only if it has no children
• The depth of the root of the tree is 0, and if the depth of a node is d, the depth of each of its children is d+1.
• The lowest common ancestor of a set S of nodes is the node A with the largest depth such that every node in S is in the subtree with root A.

Example 1:

Input: root = [1,2,3]
Output: [1,2,3]
Explanation: 
The deepest leaves are the nodes with values 2 and 3.
The lowest common ancestor of these leaves is the node with value 1.
The answer returned is a TreeNode object (not an array) with serialization "[1,2,3]".

Example 2:

Input: root = [1,2,3,4]
Output: [4]

Example 3:

Input: root = [1,2,3,4,5]
Output: [2,4,5]

思路：題目要求求deepest leaf的LCA，我們首先需要depth的信息，然後跟LCA一樣，需要返回node信息，那麼我們就需要resultType作爲返回值；findLCA 表示當前枝，找到的LCA和它所能找到的deepest leaf 的depth；如果左右depth相等，證明當前node就是LCA；並返回leftnode的depth也就是deepest node的depth；

注意這裏有兩個表示：一個是method的depth代表node的depth，另外一個returnType裏面的depth代表找到的node的 deepest depth；

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
class Solution {
    private class ReturnType {
        public TreeNode node;
        public int depth;
        public ReturnType(TreeNode node, int depth) {
            this.node = node;
            this.depth = depth;
        }
    }
    
    public TreeNode lcaDeepestLeaves(TreeNode root) {
        if(root == null) {
            return null;
        }
        ReturnType n = findLCA(root, 0);
        return n.node;
    }
    
    private ReturnType findLCA(TreeNode root, int depth) {
        if(root == null) {
            return new ReturnType(null, depth);
        }
        ReturnType leftnode = findLCA(root.left, depth + 1);
        ReturnType rightnode = findLCA(root.right, depth + 1);
        if(leftnode.depth == rightnode.depth) {
            return new ReturnType(root, leftnode.depth);
        }
        if(leftnode.depth > rightnode.depth) {
            return leftnode;
        } else {
            return rightnode;
        }
    }
}