Question

Take a look at the file GenericMethods.java.

There are three methods you must implement:

·public static <T extends Comparable<T>> int findMin(T[] arr): Iterate through the array to find the index of the smallest element in the array. If there are two elements with the smallest value, the method should return the index of the first one. The method should run in O(n).

·public static <T extends
Comparable<T>> int findMinRecursive(T[] arr): Should
behave just like findMin, but should be implemented
**recursively**. Your method may not contain any while
or for loops. Hint: the public findMinRecursive method should not,
itself, be recursive. Instead, write an additional private helper
method with additional parameters. This private helper method
should be called from findMinRecursive. This must run in O(n)
time.

·public static <T extends
Comparable<T>> int binarySearch(T[] arr, T x): Implement a
**recursive** binary search to find a value equal to
x. Hint: The public binarySearch method, itself, should not be
recursive. Instead, write an additional private helper method with
additional parameters. This private helper method should be called
from the public binarySearch method. This must run in O(log n)
time. If the value is not found in the array, return -1. Else,
return the index in the array where the value was found.

To test your code, you may compile and run
GenericMethodTester.java. This tester class uses the types defined
in the package shapes, which includes an interface Shape and
concrete classes Rectangle, Square, and Circle. The Shape interface
extends the Comparable interface, which means that the concrete
classes all need to have a compareTo method. In this case, the
differnt shapes are compared according to their
**area**. Take a look at the code for these classes to
make sure you understand how everything works. There is nothing you
need to change in this package – it’s only here to test the
GenericMethods.

Answer #1

public class GenericMethods {

/*

* method that iterate through the array to find the
index of the smallest element in the array.

* If there are two elements with the smallest value,
the method should return the index of the first one

* Input array is not null

*/

public static <T extends Comparable<T>>
int findMin(T[] arr)

{

int minIdx = 0; // set minIdx to
-1

// loop over the array

for(int
i=0;i<arr.length;i++)

{

// if minIdx is
not set or ith element of array < minIdx element of array, set
minIdx to i

if(minIdx == -1
|| (arr[i].compareTo(arr[minIdx]) < 0))

minIdx = i;

}

return minIdx; // return the
minimum index

}

/*

* method that recursively finds the index of the
smallest element in the array.

* Input array is not null

*/

public static <T extends Comparable<T>>
int findMinRecursive(T[] arr)

{

return findMinRecursive(arr,
0);

}

/*

* helper method that recursively returns the index of
the smallest element of the array

* It takes as input the array and the start index of
the array

*/

private static <T extends Comparable<T>>
int findMinRecursive(T[] arr, int startIndex)

{

if(startIndex == arr.length-1) //
if we reach the last index of the array, return the index

return
startIndex;

else

{

// get the index
of minimum element of the array starting with startIndex+1

int index =
findMinRecursive(arr, startIndex+1);

if(arr[index].compareTo(arr[startIndex]) < 0) // if element at
index < element at startIndex, return index

return index;

else

return startIndex; // else return
startIndex

}

}

/*

* method to return the index of x in the array using
recursion.

* return index if x is present in arr else return
-1

* the input array arr, is sorted is ascending
order

*/

public static <T extends Comparable<T>>
int binarySearch(T[] arr, T x)

{

return binarySearch(arr, x, 0,
arr.length-1);

}

/*

* helper method to return the index of x if found else
return -1

*/

private static <T extends Comparable<T>>
int binarySearch(T[] arr, T x, int low, int high)

{

if(low <= high) // if low <=
high

{

int mid =
(low+high)/2; // get the mid index

// if element at
mid = x, return mid

if(arr[mid].compareTo(x) == 0)

return mid;

else
if(arr[mid].compareTo(x) > 0) // element at mid > x then x if
present must be in the left subarray

return binarySearch(arr, x, low, mid-1);

else
// element at mid < x then x if present must
be in the right subarray

return binarySearch(arr, x, mid+1,high);

}

return -1; // x not found in the
array

}

}

//end of GenericMethods.java

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