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1. (50 points) Let a[0..n-1] be an array of n distinct integers. A pair (a[i], a[j]) is said to be an inversion if these numbers are out of order, i.e., i < j but a[i] > a[j]. For example: if array a

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1. (50 points) Let a[0..n-1] be an array of n distinct integers. A pair (a[i], a[j]) is said to be an inversion if these numbers are out of order, i.e., i < j but a[i] > a[j].

For example: if array a contains the following numbers:
              &nbs...

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Question Preview:

1. (50 points) Let a[0..n-1] be an array of n distinct integers. A pair (a[i], a[j]) is said to be an inversion if these numbers are out of order, i.e., i < j but a[i] > a[j].

For example: if array a contains the following numbers:
                     9, 8, 4, 5
then the number of inversions is 5. 
(inversions are 9 > 8, 9 > 4, 9 > 5, 8 > 4, 8 > 5)

Write a program that uses the divide-and-conquer technique to count the number of inversion in the array.

 

2. (50 points) Given two sets of n unique integers A and B, determine if A is equal to B, i.e., all the elements of A are in B. Write a program that uses a transform-and-conquer algorithm with efficiency class Θ(nlogn) to solve this problem. 

Example #1:    Enter the number of integers in the sets:  4

Enter the first set:  9 5 3 2

Enter the second set: 3 2 9 5

These two sets are equal.

 

Example #2:    Enter the number of integers in the sets:  6

Enter the first set:  1 4 3 2 8 6

Enter the second set: 1 3 9 4 6 8

These two sets are not equal.

Please note that a program using a brute-force algorithm with efficiency class Θ(n2) will NOT be marked.

 

 

 

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Solution preview

Solution:
CountingInversion.java
import java.util.Scanner;
public class CountingInversion
{
/*
* This function continuously divides the array into two equal halves.
* Determine the number of inversions in each small sub array
* and then determine the total inversion count in the array
* This algorithm is similar to merge sort algorithm which uses divide and conquer
methodology

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