Question

A 'array palindrome' is an array which, when its elements are reversed, remains the same (i.e., the elements of the array are same when scanned forward or backward) Write a recursive, boolean-valued method, isPalindrome, that accepts an integer-valued array, and a pair of integers representing the starting and ending indexes of the portion of the array to be tested for being a palindrome. The function returns whether that portion of the array is a palindrome. An array is a palindrome if: the array is empty (0 elements) or contains only one element (which therefore is the same when reversed), or the first and last elements of the array are the same, and the rest of the array (i.e., the second through next-to-last elements) form a palindrome.

Answer 1

Answer:

Here is the JAVA program:

class Main {    

static boolean isPalindrome(int array[], int starting, int ending) {  /*a boolean method that takes an integer-valued array, and a pair of integers representing the starting and ending indexes of the portion of the array to be tested for being a palindrome */

   if (starting >= ending) {  //base case

       return true;     }  //returns true

   if (array[starting] == array[ending]) {  //recursive case

       return isPalindrome(array, starting + 1, ending - 1);     }  //calls isPalindrome recursively to find out palindrome

   else {  

       return false;    }  }  //returns false if array is not palindrome

 

   public static void main (String[] args) {  //start of main function

   int array[] = { 1,2,3,2,1};  //creates an array

   int size = array.length;   //computes the size of array

 System.out.print(isPalindrome(array, 0, size - 1));    } } //calls method to test array for being  a palindrome

Explanation:

The program works as follows:

array = { 1,2,3,2,1}

starting = 0

ending = size-1 = 5-1 = 4

if (starting >= ending) condition evaluates to false because starting i.e. 0 is not greater or equal to ending i.e. 4. So the program moves to the next if part

if (array[starting] == array[ending])

This becomes:

if (array[0] == array[4])

The element at 0th index is the first element of the array i.e. 1 and the element at 4th index of array is the last element of array i.e. 1. So both these elements are equal so the following statement executes:

return isPalindrome(array, starting + 1, ending - 1);

Now the starting and ending become:

starting+1 = 0+1 = 1

ending-1 = 3

if (starting >= ending) base condition evaluates to false because starting  is not greater or equal to ending. So the program moves to the next if part

if (array[starting] == array[ending])

This becomes:

if (array[1] == array[3])

The element at 1st index is 2 and the element at 3rd index of array is 2. So both these elements are equal so the following statement executes:

return isPalindrome(array, starting + 1, ending - 1);

Now the starting and ending become:

starting+1 = 1+1 = 2

ending-1 = 2

if (starting >= ending) base condition evaluates to true because starting  is  equal to ending. So the following statement executes:

       return true;    

This means the function returns true and this shows that array is a palindrome.

The screenshot of the program and its output is attached.