104. Maximum Depth of Binary Tree

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本文介绍两种求解二叉树最大深度的方法：深度优先搜索（DFS）递归及层序遍历。通过DFS递归，自顶向下计算最远叶节点路径；层序遍历则逐层遍历树结构，确定总层数即为最大深度。

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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.

算法1：dfs递归求解

/**
 * Definition for binary tree
 * struct TreeNode {
 * int val;
 * TreeNode *left;
 * TreeNode *right;
 * TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int maxDepth(TreeNode *root) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        if(root == NULL)return 0;
        int res = INT_MIN;
        dfs(root, 1, res);
        return res;
    }
    void dfs(TreeNode *root, int depth, int &res)
    {
        if(root->left == NULL && root->right == NULL && res < depth)
            {res = depth; return;}
        if(root->left)
            dfs(root->left, depth+1, res);
        if(root->right)
            dfs(root->right, depth+1, res);
    }
};

算法2：层序遍历，树的总层数就是树的最大高度

/**
 * Definition for binary tree
 * struct TreeNode {
 * int val;
 * TreeNode *left;
 * TreeNode *right;
 * TreeNode(int x) : val(x), left(NULL), right(NULL) {}
 * };
 */
class Solution {
public:
    int maxDepth(TreeNode *root) {
        // IMPORTANT: Please reset any member data you declared, as
        // the same Solution instance will be reused for each test case.
        //层序遍历计算树的层数即可,NULL作为每一层节点的分割标志
        if(root == NULL)return 0;
        int res = 0;
        queue<TreeNode*> Q;
        Q.push(root);
        Q.push(NULL);
        while(Q.empty() == false)
        {
            TreeNode *p = Q.front();
            Q.pop();
            if(p != NULL)
            {
                if(p->left)Q.push(p->left);
                if(p->right)Q.push(p->right);
            }
            else 
            {
                res++;
                if(Q.empty() == false)Q.push(NULL);
            }
        }
        return res;
    }
};