Math 121: Introduction to Computing Handout #3Assignment #1: Karel the RobotDue: Tuesday, September 5Solve four Karel problems. You have a starter program for each problem in theAssignment1 folder that this course has provided. Edit the program files so that theassignment actually does what it’s supposed to do. This will involve a cycle of coding,testing, and debugging until everything works. The final step is to submit yourassignment. We will discuss how to submit an assignment electronically.Problem 1. Your first task is to solve a simple story-problem in Karel’s world. Suppose that Karel has settled cozily into its house the square area in the center of the following diagram:1 2 3 4 5 6 712345Karel starts off in the northwest corner of its house as shown in the diagram. The problemyou need to get Karel to solve is to collect the newspaper—represented (as all objects inKarel’s world are) by a beeper—from outside the doorway and then to return to its initialposition.This purpose of this simple exercise only to get you started. You can assume that everyaspect of the world looks just as it does in the diagram. The house is exactly this size, thedoor is always in the position shown, and the beeper is just outside the door. Thus, allyou have to do is write the sequence of commands necessary to have Karel1. Move to the newspaper,2. Pick it up, and3. Return to its starting point.– 2 –Even though the program is only a few lines, it is still worth getting at least a littlepractice in decomposition. In your solution, include a private method for each of thesteps shown in the outline.Problem 2. Karel has been hired to repair the damage done to the Stanford UniversityQuad in the 1989 earthquake. In particular, Karel is to repair a set of arches where someof the stones (represented by beepers, of course) are missing from the columnssupporting the arches, as follows:1 2 3 4 5 6 7 8 9 10 11 12 1312345678Your program should work on the world shown above, but it should be general enough tohandle any world that meets certain basic conditions as outlined at the end of thisproblem. There are several example worlds in the starter folder, and your program shouldwork correctly with all of them.When Karel is done, the missing stones in the columns should be replaced by beepers, sothat the final picture resulting from the world shown above would look like this:– 3 –1 2 3 4 5 6 7 8 9 10 11 12 1312345678Karel may count on the following facts about the world:• Karel starts at 1st Avenue and 1st Street, facing east, with an infinite number ofbeepers.• The columns are exactly four units apart, on 1st, 5th, 9th Avenue, and so forth.• The end of the columns is marked by a wall immediately after the final column. Thiswall section appears after 13th Avenue in the example, but your program should workfor any number of columns.• The top of the column is marked by a wall, but Karel cannot assume that columns arealways five units high, or even that all columns are the same height.• Some of the corners in the column may already contain beepers representing stonesthat are still in place. Your program should not put a second beeper on these corners.Problem 3. In this exercise, your job is to get Karel to create a checkerboard pattern of beepers inside an empty rectangular world, as illustrated in the following before-and-afterdiagram:– 4 –1 2 3 4 5 6 7 812345678Before1 2 3 4 5 6 7 8AfterThis problem has a nice decomposition structure along with some interesting algorithmicissues. As you think about how you will solve the problem, you should make sure thatyour solution works with checkerboards that are different in size from the standard 8x 8checkerboard shown in the example. Odd-sized checkerboards are tricky, and you shouldmake sure that your program generates the following pattern in a 5x3 world:1231 2 3 4 5Another special case you need to consider is that of a world which is only one columnwide or one row high. The starter folder contains several sample worlds that test thesespecial cases, and you should make sure that your program works for each of them.Problem 4: As an exercise in solving algorithmic problems, program Karel to place asingle beeper at the center of 1st Street. For example, if Karel starts in the world– 5 –1 2 3 4 512345it should end with Karel standing on a beeper in the following position:1 2 3 4 512345Note that the final configuration of the world should have only a single beeper at themidpoint of 1st Street. Along the way, Karel is allowed to place additional beeperswherever it wants to, but must pick them all up again before it finishes.In solving this problem, you may count on the following facts about the world:• Karel starts at 1st Avenue and 1st Street, facing east, with an infinite number ofbeepers in its bag.• The initial state of the world includes no interior walls or beepers.• The world need not be square, but you may assume that it is at least as tall as it is wide.Your program, moreover, can assume the following simplifications:• If the width of the world is odd, Karel must put the beeper in the center square. If thewidth is even, Karel may drop the beeper on either of the two center squares.• It does not matter which direction Karel is facing at the end of the run.There are many different algorithms you can use to solve this problem. The interestingpart of this assignment is to come up with a strategy that