Homework 4, Five Recursive Pieces.

Short Description:

Recursive Programs. This assignment is worth 100 points.

Goals

When you finish this homework, you should:

Design and implement simple recursive algorithms.
Work with static 2 dimensional arrays.

Formal Description

Implement the following programs.

multiply
palindrome
binaryConversion
numberReverse
maze

Multiply

Write a program which will display a multiplication table for up to 12×12.

Input

None

Output

The table.

Discussion

All multiplications for the table must be done using a recursive function.

Mult(m,n)
if (n =1) 
   Mult(m,n) = m
else
   Mult(m,n) = m + Mult(m,n-1)

Palindrome

Write a program which will determine if a string is a palindrome. For this program, we will ignore non letter characters, as well as punctuation, space and capitalization.

Able was I ere I saw elba. is a palindrome. 
Live devil, lived evil!  is a palindrome. 
race car #4 is a palindrome.

This program should be interactive, and continue until the user types in the string QUIT

Input/Output

Example Session: (Computer output in bold)

Enter a string or QUIT: Able was I ere I saw elba.
Able was I ere I saw elba. is a palindrome 

Enter a string or QUIT: Mad dame!
Mad dame! is not a palindrome.

Enter a stbing or QUIT: QUIT 
Good By!

Discussion

The code should include a recursive routine which takes a string and returns true if the string is a palindrome and false if it is not. This routine must include a call to a recursive routine. However the routine in's self might just preprocess the string.

BinaryConversion

Write a program that implements problem 2 page 1008 of your book.

Discussion

You should have a recursive function that takes in integer and returns a string containing the binary representation of the input integer.

Number Reverse

Write an interactive program which reads in a number, and prints out the corresponding number with reversed digits.

Input/Output

The program should be interactive, and should continue until a -1 is entered.

Enter a number: 1234
The reverse of 1234 is 4321

Enter a number: -1
Good By

Discussion

This program should employ a recursive routine to reverse the digits of the number.

Maze

Implement a solution to program 6, page 1009 of the book.

Input

Your program should prompt the user for the name of a file containing a maze.

Output

Your program should output two lists, one that indicates all points from which one can escape the maze and the other indicating points from which one can not escape the maze.

Discussion

This program is not trivial, but it is not impossible either. You should not start on it until we discuss two dimensional arrays.

Required Files

The source code, ReadMe, and Makefile for all programs should be submitted in a single tar file.

Submission

Email the tar file to dbennett@edinboro.edu no later than class time November 5.