Question 1 This question considers binary trees using the following node class. You may not assume that the tree has any method or additional fields. class Node \{ String key; Node left, right; \} Node root; // the root of the tree Recall that the height of a node x is the maximum of the number nodes between x and a null link. By definition, the height of a leaf is 0 , and therefore the height of the empty tree is 1. (a) Implement a method height which returns the height of the t ee, starting from the root. public int height ()\{ (b) If you assume that the tree is balanced, what is the order of growth for height ()? Circle the best answer, where N is the number of keys in the tree. 1logNNlogNN2N2logNN32N