[LintCode] 93 Balanced Binary Tree

Description
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.


思路
分治的思想。
如果一个二叉树是平衡的。那么root的左子树和右子树一定是平衡的。
并且左子树和右子树高度差是小于等于1的。


Code

/**
 * 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;
        }
        
        int leftHeight = getHeight(root.left);
        int rightHeight = getHeight(root.right);
        
        return isBalanced(root.left) && isBalanced(root.right) 
                && Math.abs(leftHeight - rightHeight) <= 1;
    }
    
    public int getHeight(TreeNode root) {
        if (root == null) {
            return 0;
        }
        return Math.max(getHeight(root.left), getHeight(root.right)) + 1;
    }
}