Checking if a Binary Tree is Balanced

Question

I saw the question in a book (Cracking the Coding Interview). The suggested code is:

public boolean isBalanced(Node root) {

    if(root == null)
        return true;

    int leftHeight = getHeight(root.left);
    System.out.println("left height: " + leftHeight);
    int rightHeight = getHeight(root.right);
    System.out.println("right height: " + rightHeight);
    int diff = Math.abs(leftHeight - rightHeight);

    // check if difference in height is more than 1
    if (diff > 1)
        return false;

    // check if left and right subtrees are balanced
    else 
        return isBalanced(root.left) && isBalanced(root.right);

The part I don't understand is why do we need return isBalanced(root.left) && isBalanced(root.right). Isn't it enough just to check the height and return false if the hight is more than 1, and true otherwise?

Answer 1

No, it is not enough to just to check the height and return false if the height is more than 1, and true otherwise . Simply checking the root's height would result in false positives like the following:

        A
       / \
      B   F
     /   /
    C   G
   /   /
  D   H
 /   /
E   I