created 01/01/03
Chapter 73 Programming Exercises
Exercise 1
Write a program that implements this definition of
cube numbers:
cube(1) = 1 cube(N) = cube(N-1) + 3(square(N)) - 3N + 1
Implement the square() method using this definition
(also given in the exercises for chapter 71):
square(1) = 1 square(N) = square(N-1) + 2N - 1
Make a complete program similar to PyramidTester.java given in
the chapter.
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Exercise 2
Consider this definition of the sum of the elements
in an integer array:
sum( array, index ) = 0, if index == array.length sum( array, index ) = array[index] + sum( array, index+1), if index < array.length
Write a Java method that implements this definition
and a program to test it.
The method should look something like:
int sum ( int[] array, int index )
{
. . .
}
The testing program will call sum( testArray, 0 )
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Exercise 3
Improve the previous program by extending the definition of sum:
sum( array ) = sum( array, 0 ) sum( array, index ) = 0, if index == array.length sum( array, index ) = array[index] + sum( array, index+1), if index < array.length
To implement this, write a second method sum( int[] array)
that overloads the method of exercise 1.
The testing program will call sum( testArray )
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Exercise 4
Write your own recursive definition of the maximum element in
an array of integers.
Then, implement your definition in Java and test it with a testing
program.
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Exercise 5
A palindrome is a string that is the same when reversed.
For example, “abba” is a palindrome.
Here is a math-like definition:
palindrome( "" ) = true
palindrome( x ) = true
palindrome( x+X+y ) = false, if x != y
= palindrome( X ), if x == y
The symbol x stands for a single character,
as does y.
The symbol X stands for a string of characters.
The symbol + stands for concatenation.
Implement palindrome() and a program that tests it.
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End of Exercises