Balanced Binary Tree 93

Question

Given a binary tree, determine if it is height-balanced.

For this problem, a height-balanced binary tree is defined as a binary tree in which the depth of the two subtrees of every node never differ by more than 1.

Example

Given binary tree A = {3,9,20,#,#,15,7}, B = {3,#,20,15,7}

A) 3 B) 3 / \ \ 9 20 20 / \ / \ 15 7 15 7

The binary tree A is a height-balanced binary tree, but B is not.

Solution

看到binary tree就想用二分和DC。。。咳咳。。。控制一下自己。。。

很简单，首先判断左右子树是否是balanced，然后判断左右子树的max depth是不是相差1以内。寻找左右子树的max depth又是一次DC的过程，即寻找当前子树的左右子树的max depth选较大的那个再＋1即可。

代码如下：

/**
 * Definition of TreeNode:
 * public class TreeNode {
 *     public int val;
 *     public TreeNode left, right;
 *     public TreeNode(int val) {
 *         this.val = val;
 *         this.left = this.right = null;
 *     }
 * }
 */
public class Solution {
    /**
     * @param root: The root of binary tree.
     * @return: True if this Binary tree is Balanced, or false.
     */
    public boolean isBalanced(TreeNode root) {
        // write your code here
        if(root == null){
            return true;
        }

        if(!isBalanced(root.left) || !isBalanced(root.right)){
            return false;
        }

        if(Math.abs(maxDepth(root.left)-maxDepth(root.right)) > 1){
            return false;
        }

        return true;
    }

    public int maxDepth(TreeNode root){
        if(root == null){
            return 0;
        }

        int left = maxDepth(root.left);
        int right = maxDepth(root.right);

        return Math.max(left, right) + 1;
    }
}