重做104. Maximum Depth of Binary Tree

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.

思路：知道有recursion的方法。但是想应用一下dfs和backtracking，啊哈哈终于做出来了。

Solution1:

/**
 * Definition for a binary tree node.
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int maxDepth(TreeNode root) {
        if(root==null)
        {
            return 0;
        }
        List<Integer> res=new ArrayList<Integer>();
        dfs(root,res,1);
        Collections.sort(res);
        return res.get(res.size()-1);
    }
    public void dfs(TreeNode root,List<Integer> res, int max)
    {
        if(root==null)
        {
            return;
        }
        if(root.left==null&&root.right==null)
        {
            res.add(max);
            return;
        }
        dfs(root.left,res,++max);
        max--;
        dfs(root.right,res,++max);
        max--;
    }

}

Solution2:

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

Recursion的定义. ref:http://www.cs.princeton.edu/courses/archive/fall10/cos126/lectures/07-23Recursion-2x2.pdf

Recursive Program Recursive Program. Implement a function having integer arguments by

• base case: Implementing it for some specific values of the arguments.

• reduction step: Assume the function works for smaller values of its arguments and use it to implement it for the given values