二叉树的最大深度

Essential：Recursive

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
    /  \
   15   7

return its depth = 3.

Mine

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

Discussion

第一种方法：BFS广度优先搜索，使用双端队列deque（因为性能比另外两种Queue好得多），在大循环内对二叉树的每个层做一次遍历，

使只遍历当前的层，每次大循环

ans

加1。由于每个节点仅访问一次，所以时间复杂度

O(n)

import collections
class Solution:
    def maxDepth(self, root: TreeNode) -> int:
        if not root:
            return 0
        queue = collections.deque()
        queue.append(root)
        ans = 0
        while queue:
            ans += 1
            for _ in range(len(queue)):
                node = queue.popleft()
                if node.left:
                    queue.append(node.left)
                if node.right:
                    queue.append(node.right)
        return ans

第二种方法：DFS深度优先搜索，利用递归的栈，借助

标记当前层，由于每个节点仅访问一次，所以时间复杂度

O(n)

class Solution:
    def maxDepth(self, root: TreeNode) -> int:
        if not root:
            return 0
        self.ans = 0
        self._dfs(root, 0)
        return self.ans
        
    def _dfs(self, node, level):
        if not node:
            return
        if self.ans < level + 1:
            self.ans = level + 1
        self._dfs(node.left, level + 1)
        self._dfs(node.right, level + 1)

第三种方法：DFS+分治，虽然代码简洁但耗时比上面两种方法都久

class Solution:
    def maxDepth(self, root: TreeNode) -> int:
        if not root:
            return 0
        return 1 + max(self.maxDepth(root.left), self.maxDepth(root.right))

C语言，经典算法了

/**
 * Definition for a binary tree node.
 * struct TreeNode {
 *     int val;
 *     struct TreeNode *left;
 *     struct TreeNode *right;
 * };
 */


int maxDepth(struct TreeNode* root){
    if(root == NULL)
        return 0;
    int left = maxDepth(root->left);
    int right = maxDepth(root->right);
    return left>right?left+1:right+1;
}