Objective

$$ Demonstrate knowledge of recursion by describing common applications and by effectively

using it to solve problems.

$$ Use of appropriate algorithms to solve common computing problems.

Problem

In this assignment, you will write a guessing game. In this program, you will create an array of $20$

elements and write a method that randomly generates integer values between $1$ and $100$

$($inclusive$).$ The method then uses the Java built$-$in sort function Arrays.sort$($myArray$)$ to sort

the array in ascending order and returns the sorted array. The program then asks the user to think

of an integer between $1$ and $100.$ The program then uses a modified binary search algorithm to

guess the value.

The program may ask the user a question such as $$Is your number greater than $61?$ See below for

example sample runs. Your program should have a worst$-$case time of O$($log n$),$ where n is the size

of the collection object.

Sample run #$1$: Value NOT FOUND in the collection $($target $=63)$

Choose a random number between $1$ and $100.$

For the following questions, enter $"$Y$"$ for Yes or $"$N$"$ for No$.$

$============$

Is your number greater than $56?$ y

Is your number $76?$ n

$============$

Is your number greater than $76?$ n

Is your number $68?$ n

$============$

Is your number greater than $68?$ n

Is your number $66?$ n

$============$

Is your number greater than $66?$ n

Is your number $58?$ n

$============$

Is your number greater than $58?$ y

Is your number $66?$ n

$=============================================================================$

SORRY! Your number is not in the collection.

$=============================================================================$

Here is the Collection:

$8,8,23,28,31,37,38,49,54,56,58,66,68,73,76,82,84,87,98,98,$