【leetcode】Balanced Binary Tree

题目：

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.

分析：该题要判断一棵二叉树是高度平衡的，平衡的条件是”对于任何一个节点，它的左右子树高度直插不超过1"。解法很显然是递归地判断每个节点是否满足高度平衡的要求，对于某个节点是否满足高度平衡，与三个因素有关：它的左子树是否高度平衡，它的右子树是否高度平衡，它的左右子树高度之差是否小于等于1。因此在递归的过程要传入两个参数：ifBalanced，该节点是否高度平衡，height，该节点的高度，可以定义内部类Node，包含以上变量。注意对于null节点，ifBalanced=true。

Java AC代码如下：

public boolean isBalanced(TreeNode root) {
		return cal(root).ifBalanced;
	}

	public Node cal(TreeNode root) {
		Node node = new Node();
		if (root == null) {
			node.height = 0;
			node.ifBalanced = true;
			return node;
		}
		node.left = cal(root.left);
		node.right = cal(root.right);
		node.height = Math.max(node.left.height, node.right.height) + 1;
		node.ifBalanced = (Math.abs(node.left.height - node.right.height) <= 1)
				&& node.left.ifBalanced && node.right.ifBalanced;
		return node;
	}

	class Node {
		boolean ifBalanced;
		int height;
		Node left;
		Node right;
	}