110. Balanced Binary Tree

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.

Solution：递归post-order dfs来upwards累积height

思路： 利用递归post-order dfs来upwards累积height，并在过程中判断是否Math.abs(left_height - right_height) > 1 for early stop
Note:
Time Complexity: O(N) Space Complexity: O(N) 递归缓存

Solution Code：

class Solution {
    public boolean isBalanced(TreeNode root) {
        return dfsHeight(root) != -1;
    }
    
    private int dfsHeight(TreeNode root) {
        // post-order dfsly check from left-bottom and accumulate max_height upwards
        // meanwhile, check if |left_height - right_height)| > 1 for early stop
        
        if(root == null) return 0;
        
        int left_height = dfsHeight(root.left);
        if(left_height == -1) return -1;
        
        int right_height = dfsHeight(root.right);
        if(right_height == -1) return -1;
        
        if(Math.abs(left_height - right_height) > 1) return -1;
        
        return Math.max(left_height, right_height) + 1;
    }
}

Solution2：

Solution2是O(NlogN)的方法，避免使用，因为每个结点都要去求depth(重复计算）
不是O(N^2)因为是balanced，否则就return。

time complexity for depth:T(n) = 2T(n/2) + O(1) => O(N) ，
只对当前点看，每个当前点一下都当成N，因为是一次depth总。要遍历每个结点的depth是在下面考虑的，有n/2二分。

Time complexity for isBalanced: T(n) = 2T(n/2) + O(n) => O(NlogN)
O(n)是求depth的；n/2是因为是balanced的否则return

class Solution2 {
    public boolean isBalanced(TreeNode root) {
        if(root == null) return true;
        int left_height = getMaxDepth(root.left);
        int right_height = getMaxDepth(root.right);
        return Math.abs(left_height - right_height) <= 1 && isBalanced(root.left) && isBalanced(root.right);
    }
    
    private int getMaxDepth(TreeNode root) {
        if(root == null) return 0;
            return 1 + Math.max(getMaxDepth(root.left), getMaxDepth(root.right));
    }
}