Java A perfect binary tree is a complete binary tree with all levels fully filled. Define a new class named BSTWithTestPerfect that extends BST with the following methods: (Hint: The number of nodes in a perfect binary tree is 2^(height+1) - 1.)

/** Returns true if the tree is a perfect binary tree */
public boolean isPerfectBST()

/* Please only use the following template to submit.
PLEASE ONLY USE THE PART BETWEEN BEGIN AND END ONLY

// BEGIN
class BSTWithTestPerfect extends BST {
/** Create a default BST with a natural order comparator */
public BSTWithTestPerfect() {
super();
}

/** Create a BST with a specified comparator */
public BSTWithTestPerfect(java. util. Comparator c) {
super(c);
}

/** Create a binary tree from an array of objects */
public BSTWithTestPerfect(E[] objects) {
super(objects);
}

/**
* Returns the height of this binary tree.
*/
public int height() {
return height(root);
}

private int height(TreeNode root) {
// WRITE YOUR CODE HERE
}

/** Returns true if the tree is a perfect binary tree */
public boolean isPerfectBST() {
// WRITE YOUR CODE HERE
}
}
// END