算法：树的最大深度 深度优先和广度优先两种解法104. Maximum Depth of Binary Tree

Posted 2021-10-15 架构师易筋

104. Maximum Depth of Binary Tree

Given the root of a binary tree, return its maximum depth.

A binary tree’s maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Example 1:

Input: root = [3,9,20,null,null,15,7]
Output: 3

Example 2:

Input: root = [1,null,2]
Output: 2

Example 3:

Input: root = []
Output: 0

Example 4:

Input: root = [0]
Output: 1

Constraints:

The number of nodes in the tree is in the range [0, 104].
-100 <= Node.val <= 100

1. 深度优先遍历

每往下一层，回溯的时候+1

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public int maxDepth(TreeNode root) {
        if (root == null) return 0;
        return Math.max(maxDepth(root.left), maxDepth(root.right)) + 1;
    }
}

2. 广度优先遍历

这里要先进后出 first in last out, 要用到queue队列的特性。

1. 初始化队列 Queue<TreeNode> queue = new LinkedList<>();
2. 从头部入队列 queue.offer(node);
3. 从尾部出队列queue.poll();

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode() {}
 *     TreeNode(int val) { this.val = val; }
 *     TreeNode(int val, TreeNode left, TreeNode right) {
 *         this.val = val;
 *         this.left = left;
 *         this.right = right;
 *     }
 * }
 */
class Solution {
    public int maxDepth(TreeNode root) {
        if (root == null) return 0;
        int depth = 0;
        Queue<TreeNode> queue = new LinkedList<>();
        queue.offer(root);
        while (!queue.isEmpty()) {
            int size = queue.size();
            while (size-- > 0) {
                TreeNode node = queue.poll();
                if (node.left != null) 
                    queue.offer(node.left);
                if (node.right != null)
                    queue.offer(node.right);
            }
            depth++;
        }
        
        return depth;
    }
}