Task 1

Lafore exercise 6.1. Write a java program to perform multiplication by recursively calling a method that uses addition. Include a main() method that demonstrates how it works with several different values.

public long multiply(long x, long y) {...}

Task 2

Lafore exercise 6.3. Implement exponentiation using a recursive approach. Include a main() method that demonstrates how it works with several different values.

public long power(long base, int exponent) {...}

Task 3

Write a java program using recursion to check a string to see if it is a palindrome. Ignore punctuation, capitalization, spaces, and any other non-alphabetic characters -- in other words, remove them from the string before checking. (thus a phrase like "Madam, I'm Adam" should be ruled a palindrome, even though it's precise reverse would be the nonsensical "madA m'I ,madaM") Then use the following logic to check for palindromicity: the empty string is a palindrome; any single alphabetic character is a palindrome; a string a$b is a palindrome if a=b and $ is a palindrome. Note: use recursion rather than iteration.

Write a main method that repeatedly prompts the user for input, checks whether the input is a palindrome, and informs the user of the result. Terminate if the user enters a single period '.' as the input. The user prompt should notify the user of this special termination char.

public boolean isPalindrome(String phrase) {...}