recursion experiments carrying out these experiments will help to provide insights into the topics covered in the no programming is involved in the triangle java program (listing )remove the code for the base case (the if( == )the return ;and the elsethen run the program and see what happens use the towers workshop applet in manual mode to solve the puzzle with seven or more disks rewrite the main(part of mergesort java (listing so you can fill the array with hundreds of thousands of random numbers run the program to sort these numbers and compare its speed with the sorts in "simple sorting programming projects writing programs that solve the programming projects helps to solidify your understanding of the material and demonstrates how the concepts are applied (as noted in the introductionqualified instructors may obtain completed solutions to the programming projects on the publisher' web site suppose you buy budget-priced pocket pc and discover that the chip inside can' do multiplicationonly addition you program your way out of this quandary by writing recursive methodmult()that performs multiplication of and by adding to itself times its arguments are and and its return value is the product of and write such method and main(program to call it does the addition take place when the method calls itself or when it returns in "binary trees,we'll look at binary treeswhere every branch has (potentiallyexactly two sub-branches if we draw binary tree on the screen using characterswe might have branch on the top row on the next rowthen and so on here' what that looks like for tree characters widexxx---- --- --- --- - - - - - - - - xxxxxxxxxxxxxxxx