Question II $(25$ points$)$: Implement in BinaryTree class the following methods:

a$)$ public int longestPathTwoLeaves$()$ to return the length of the longest path between two leaves. $($Hint: use the height method$)$

b$)$ public void maxValueInEachLevel$()$ to print the largest value in each level. $($Hint keep track of nodes$$ level$)$

c$)$ public int sizeRightSubtree$($BTNode v$)$ to find the size of the right subtree of a node v$.$

d$)$ public void deleteNodes$($int x$)$ to delete all nodes whose keys are larger than x$.$

e$)$ public void deleteAllLeaves$()$ to delete all leaves from a binary tree.

Question III $(20$ points$)$: Implement the following Boolean methods in BinaryTree class to test whether a binary tree is

a$)$ a binary search tree. $($Header: public boolean isBinarySearchTree$())$

b$)$ a max heap. $($Header: public boolean isMaxHeapTree$())$