Homework 11: Recursion

Introduction
- This homework is intended to reinforce your recursion programming skills...

Preparatiion

Make directory and copy files:

mkdir ~/cs170/hw11 cp ~cs170002/share/hw11/*.java ~/cs170/hw11 cd ~/cs170/hw11

Part 1: palindromes

We have written a isPalindrome(s) method is an earlier homework.
The isPalindrome(s) receives a String typed input parameter s and returns true if s is a palindrome and returns false otherwise.
In this homework, we will write a recursive algorithm to test if a string is a palindrome

NOTE:

Your algorithm must use recursion to get any credits
BTW, it is easy to detect program that does not use recursion; so please do not try to turn in your previous program as answer.

How to solve the "palindrome" problem using the solution of a smaller palindrome problem:

Example 1: Input: "abccbx" Check the first and the last letters: "abccbx" Not equal ===> not a palindrome (done)
Example 2: Input: "abccxa" Check the first and the last letters: "abccxa" Equal ===> my answer depends on the solution of this smaller Palindrome problem: bccx Solve this smaller problem with recursion

Base case:

As discussed in class, every recursive method contains one or more if-statements to determine the bases cases of the problem.
A base case is a problem where the solution to the problem can be easily determined

The base cases in the Palindrome problem

When the input string is "" the input is a palindrome
- How do you determine this base case ? (i.e., what if-statement do you use to check ?)
- And what should you return ?
When the input string is a single character "?" the input is also a palindrome
- How do you determine this base case ? (i.e., what if-statement do you use to check ?)
- And what should you return ?
Another base case (shown in Example 1 above) is:
- How do you determine this base case ? (i.e., what if-statement do you use to check ?)
- And what should you return ?

Assignment for Part 1:

Write the class method isPalindrome in the program file hw11.java
You can test your isPalindrome method with the test program Palindrome.java as follows:
The Palindrome.java program will invoke the isPalindrome() method as hw11.isPalindrome(), so you don't need to make any changes to the Palindrome.java file.

Note: don't just use my test program blindly.... you should look inside my test programs also. They should you how your methods are invoked. Very informative....

Part 2: fold String with a recursive algorithm

We have also written a foldString(s) method in lab 8. The foldString(s) receives a String typed input parameter s and returns a String consisting of alternately the first and last characters of the input string.

In lab 8, the fold operation on a string was defined as follows:

Original string: "c₀c₁c₂.....c_n-3c_n-2c_n-1" Folded string: "c₀c_n-1c₁c_n-2c₂c_n-3....."

In this homework, we will write a recursive foldString algorithm

How to fold a string using the solution of a smaller fold string problem:

Suppose you want to fold this string: "c₀c₁c₂.....c_n-3c_n-2c_n-1" You can solve it as follows: 1. have someone solve this smaller problem: "c₁c₂.....c_n-3c_n-2" 2. using the solution of the above problem, your problem is solved by pre-pending c₀c_n-1 in front of the solution of the above problem.

There are 2 base cases that you need to take care of:

The empty string (an input string with an even number of character will reduce to an empty string)
The string with 1 character (an input string with an odd number of character will reduce to a singleton string)

Assignment for Part 1:

Write the class method foldString in the program file hw11.java
You can test your foldString method with the test program FoldString.java as follows:
The FoldString.java program will invoke the foldString() method as hw11.foldString(), so you don't need to make any changes to the FoldString.java tes program file.

Turnin
- Turn in your hw11.java program file (containing the methods isPalindrome() and foldString()) as follows: