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题目地址

https://leetcode.com/problems/maximum-depth-of-binary-tree/description/

题目描述

Given a binary tree, find its maximum depth.

The maximum depth is the number of nodes along the longest path from the root node down to the farthest leaf node.

Note: A leaf is a node with no children.

Example:

Given binary tree [3,9,20,null,null,15,7],

    3
   / \
  9  20
    /  \
   15   7
return its depth = 3.

思路

由于树是一种递归的数据结构,因此用递归去解决的时候往往非常容易,这道题恰巧也是如此, 用递归实现的代码如下:

var maxDepth = function(root) {
  if (!root) return 0;
  if (!root.left && !root.right) return 1;
  return 1 + Math.max(maxDepth(root.left), maxDepth(root.right));
};

如果使用迭代呢? 我们首先应该想到的是树的各种遍历,由于我们求的是深度,因此 使用层次遍历(BFS)是非常合适的。 我们只需要记录有多少层即可。相关思路请查看binary-tree-traversal

关键点解析

  • 队列

  • 队列中用 Null(一个特殊元素)来划分每层,或者在对每层进行迭代之前保存当前队列元素的个数(即当前层所含元素个数)

  • 树的基本操作- 遍历 - 层次遍历(BFS)

代码

  • 语言支持:JS,C++,Python

JavaScript Code:

/*
 * @lc app=leetcode id=104 lang=javascript
 *
 * [104] Maximum Depth of Binary Tree
 */
/**
 * Definition for a binary tree node.
 * function TreeNode(val) {
 *     this.val = val;
 *     this.left = this.right = null;
 * }
 */
/**
 * @param {TreeNode} root
 * @return {number}
 */
var maxDepth = function(root) {
  if (!root) return 0;
  if (!root.left && !root.right) return 1;

  // 层次遍历 BFS
  let cur = root;
  const queue = [root, null];
  let depth = 1;

  while ((cur = queue.shift()) !== undefined) {
    if (cur === null) {
      // 注意⚠️: 不处理会无限循环,进而堆栈溢出
      if (queue.length === 0) return depth;
      depth++;
      queue.push(null);
      continue;
    }
    const l = cur.left;
    const r = cur.right;

    if (l) queue.push(l);
    if (r) queue.push(r);
  }

  return depth;
};

C++ Code:

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     TreeNode *left;
 *     TreeNode *right;
 *     TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int maxDepth(TreeNode* root) {
        if (root == nullptr) return 0;
        auto q = vector<TreeNode*>();
        auto d = 0;
        q.push_back(root);
        while (!q.empty())
        {
            ++d;
            auto sz = q.size();
            for (auto i = 0; i < sz; ++i)
            {
                auto t = q.front();
                q.erase(q.begin());
                if (t->left != nullptr) q.push_back(t->left);
                if (t->right != nullptr) q.push_back(t->right);
            }
        }
        return d;
    }
};

Python Code:

class Solution:
    def maxDepth(self, root: TreeNode) -> int:
        if not root: return 0
        q, depth = [root, None], 1
        while q:
            node = q.pop(0)
            if node:
                if node.left: q.append(node.left)
                if node.right: q.append(node.right)
            elif q:
                q.append(None)
                depth += 1
        return depth

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