[Leetcode 10] 111 Minimum Depth of Binary Tree

Problem:

Given a binary tree, find its minimum depth.

The minimum depth is the number of nodes along the shortest path from the root node down to the nearest leaf node.

 

Analysis:

This problem is quite easy. When we compute the height of a binary tree, we use 1 + max(left_height, right_height) recursivly. So the height of a binary tree is actually the maximum depth of this tree. So to get minimum depth, we change max to min to have the following formular 1 + min (left_height, right_height) computed recursively.

One problem here is that height must be the distance from root to leaf. This implies that the following two trees :[1 2] and [1 # 2] has the height of 2 rather than one. We need to omit those null leaf nodes while computing

 

Code:

/**
 * Definition for binary tree
 * public class TreeNode {
 *     int val;
 *     TreeNode left;
 *     TreeNode right;
 *     TreeNode(int x) { val = x; }
 * }
 */
public class Solution {
    public int minDepth(TreeNode root) {
        // Start typing your Java solution below
        // DO NOT write main() function
        if (root == null)
            return 0;
        else if (root.left==null && root.right==null)
            return 1;
        else if (root.left==null && root.right!=null)
            return 1 + minDepth(root.right);
        else if (root.left!=null && root.right==null)
            return 1 + minDepth(root.left);
        else
            return 1 + min(minDepth(root.left), minDepth(root.right));
    }
    
    private int min(int a, int b) {
        return (a>b) ? b : a;
    }
}

 

Attention:

The minimum depth of a binary tree must from root to some not-null leaf nodes. See the definition clearly.!