Question

(Duplicate Elimination) Use a one-dimensional array to solve the following problem: Write an application that inputs five numbers, each between 10 and 100 , inclusive. As each number is read, display it only if it's not a duplicate of a number already read. Provide for the "worst case," in which all five numbers are different. Use the smallest possible array to solve this problem. Display the complete set of unique values input after the user enters each new value.

Short answer

Initialize a 5-element array, input numbers checking for the range and duplicates, and store only unique numbers. Display the set of unique numbers after each input and provide the final list after all five numbers are entered.

Step-by-step solution

Initialize the Array

Initialize a one-dimensional array with a size of 5 to store the unique numbers. Since we only need to store unique values and we expect at most five unique numbers, this is the smallest array that can be used.

Input Numbers

Prompt the user to input five numbers, one at a time. After each number is entered, check if it falls within the range of 10 to 100, inclusive. If it doesn't, prompt the user to enter a valid number.

Check for Duplicates

After receiving a number, iterate through the array to check if the number has already been entered. If the number is found in the array, it's a duplicate and should not be added again.

Store Unique Numbers

If the current number is not a duplicate, find the first 'empty' position (which can be initialized with a value outside the acceptable range or null) in the array and store the new number there.

Display Unique Numbers

After each input, display the current set of unique numbers. This helps the user know which numbers have been recorded so far.

Repeat the Process

Repeat steps 2 to 5 until all five numbers have been processed. If the user inputs a duplicate, they should be prompted to enter a different number until a unique one is given.

Final Output

Once all five unique numbers have been entered, display the final set of unique values to the user.

Key concepts

One-Dimensional Array

Imagine a row of mailboxes along a street; each can hold a piece of mail, similar to how a one-dimensional array in Java stores a sequence of elements. This type of array is a fundamental data structure used to store a collection of items, where each item, referred to as an element, is identified by a unique index number.

In the context of eliminating duplicates, think of an array with five slots, each capable of holding a unique number. If we visualize our array as $\text{Double subscripts: use braces to clarify}$, at the start, all five slots are empty. As numbers are entered, we fill these slots, ensuring no two slots contain the same number, which represents our unique values. The simplicity of a one-dimensional array is its strength, offering easy accessibility and manipulation of stored data, which makes it perfect for scenarios where a straightforward list of elements is needed.

Unique Values

Uniqueness is the spice that brings variety to a set, just as unique values in an array ensure no repetition. When tasked with accepting five numbers and displaying only those that aren't duplicates, our goal is to maintain an array that reflects diversity. It's analogous to holding a hand of playing cards where no two cards are the same.

To ensure uniqueness in our array after a number is entered, we sweep through the array, comparing the new number to each stored number. If there's a match, it's a signal that our number is not unique, akin to discovering you have two queens of hearts in your playing card deck. Only when we confirm a number is absent from our array do we allocate it a spot, preserving the sanctity of unique values.

Input Validation

The act of policing the entry of information is akin to a bouncer at a club checking IDs, a process known as input validation. In Java, this critical operation ensures that user input meets specific criteria before being processed. For our unique number collector, we set boundaries: every number must be between 10 and 100, both inclusive.

Every time a user attempts to add a number, input validation kicks in. Just like a math teacher checking a homework problem, if the number doesn't meet the requirements, we ask the user to 'try again'. This gatekeeping not only keeps our data clean but also simplifies the subsequent steps of our program because we can trust that, if a number is in the array, it's already been vetted for validity.