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Programming Assignment An army battalion has n soldiers and the commander of the battalion would like to arrange a boxing tournament. There will be two categories, lightweight and heavyweight. The commander also wants to have a somewhat equal number of contestants in each category. Therefore, he needs to nd the soldier with the median weight,…

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  • Programming Assignment

An army battalion has n soldiers and the commander of the battalion would like to arrange a boxing tournament. There will be two categories, lightweight and heavyweight. The commander also wants to have a somewhat equal number of contestants in each category. Therefore, he needs to nd the soldier with the median weight, then everyone below or equal to that weight will fall into the lightweight category and the remaining soldiers will be in the heavyweight category. Your job is to nd an algorithm that will help him select the median weight soldier in the shortest possible time, because e ciency is very important in the army. We can assume that the weight of the soldiers are rounded up to the nearest integer.

Input: An array A of n non-negative integers.

Output: The n2 th integer.

A Java template has been provided containing an empty function LinearSelect, which takes an integer array A and an integer k as argument, and returns the kth integer in A when sorted in an ascending order. Your task is to write the body of the LinearSelect function. You may assume that the input array A will always conform to the speci cation above (containing no negative values). Your code is not required to check for incorrectly formed input data.

You must use the provided Java template as the basis of your submission, and put your im-plementation inside the LinearSelect function in the template. You may not change the name, return type or parameters of the LinearSelect function. The main function in the template con-tains code to help you test your implementation by entering test data or reading it from a le. You may modify the main function, because your submission will be tested using a di erent main function. Only the contents of the LinearSelect function and associated helper functions (if any) will be marked.

  • Examples

The table below shows the correct output of the LinearSelect function on various test inputs.

Input Array

Median

3, 75, 12, 20

12

1,2,4,5,3

3

75

75

null

-1

  • Evaluation Criteria

The programming assignment will be marked out of 40, based on a combination of automated testing (using large test arrays) and human inspection.

There are several possible implementations for LinearSelect. For an input array containing n values, the optimal implementation is O(n). The mark for each submission will be based on both the asymptotic worst case running time and the ability of the algorithm to handle inputs of di erent sizes. The table below shows the expectations associated with di erent scores.

Score

Description

0-15

Submission does not compile or does not conform to the provided

template.

15-30

The implemented algorithm is not O(n) or is substantially inac-

curate on the tested inputs.

30-40

The implemented algorithm is O(n) and gives the correct answer

on all tested inputs.

To be properly tested, every submission must compile correctly as submitted, and must be based on the provided template. If your submission does not compile for any reason (even trivial mistakes like typos), or was not based on the template, it will receive at most 15 out of 40. The best way to make sure your submission is correct is to download it from conneX after submitting and test it. You are not permitted to revise your submission after the due date, and late submissions will not be accepted, so you should ensure that you have submitted the correct version of your code before the due date. conneX will allow you to change your submission before the due date if you notice a mistake. After submitting your assignment, conneX will automatically send you a con rmation email. If you do not receive such an email, your submission was not received. If you have problems with the submission process, send an email to the instructor before the due date.

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