(20 points) Merge sort involves recursively splitting the array into 2 parts, so

Question

(20 points) Merge sort involves recursively splitting the array into 2 parts, sorting and finally merging them. A variant of merge sort is called 3-way merge sort where instead of splitting the array into 2 parts we split it into 3 parts. As shown in the MergeSort code, it recursively breaks down the arrays to subarrays of size half. Similarly, 3-way Merge sort breaks down the arrays to subarrays of size one third In this question, you need to implement the 3-way Merge sort algorithm (in function mergeSort 3_way) in a descending order. During the sorting, count the number of comparisons in each merge stage.

Explanation / Answer

// Java program to perform 3 way Merge Sort
public class MergeSort3Way
{
// Function for 3-way merge sort process
public static void mergeSort3Way(Integer[] gArray)
{
// if array of size is zero returns null
if (gArray == null)
return;

// creating duplicate of given array
Integer[] fArray = new Integer[gArray.length];

// copying alements of given array into
// duplicate array
for (int i = 0; i < fArray.length; i++)
fArray[i] = gArray[i];

// sort function
mergeSort3WayRec(fArray, 0, gArray.length, gArray);

// copy back elements of duplicate array
// to given array
for (int i = 0; i < fArray.length; i++)
gArray[i] = fArray[i];
}

/* Performing the merge sort algorithm on the
given array of values in the rangeof indices
[low, high). low is minimum index, high is
maximum index (exclusive) */
public static void mergeSort3WayRec(Integer[] gArray,
int low, int high, Integer[] destArray)
{
// If array size is 1 then do nothing
if (high - low < 2)
return;

// Splitting array into 3 parts
int mid1 = low + ((high - low) / 3);
int mid2 = low + 2 * ((high - low) / 3) + 1;

// Sorting 3 arrays recursively
mergeSort3WayRec(destArray, low, mid1, gArray);
mergeSort3WayRec(destArray, mid1, mid2, gArray);
mergeSort3WayRec(destArray, mid2, high, gArray);

// Merging the sorted arrays
merge(destArray, low, mid1, mid2, high, gArray);
}

/* Merge the sorted ranges [low, mid1), [mid1,
mid2) and [mid2, high) mid1 is first midpoint
index in overall range to merge mid2 is second
midpoint index in overall range to merge*/
public static void merge(Integer[] gArray, int low,
int mid1, int mid2, int high,
Integer[] destArray)
{
int i = low, j = mid1, k = mid2, l = low;

// choose smaller of the smallest in the three ranges
while ((i < mid1) && (j < mid2) && (k < high))
{
if (gArray[i].compareTo(gArray[j]) < 0)
{
if (gArray[i].compareTo(gArray[k]) < 0)
destArray[l++] = gArray[i++];

else
destArray[l++] = gArray[k++];
}
else
{
if (gArray[j].compareTo(gArray[k]) < 0)
destArray[l++] = gArray[j++];
else
destArray[l++] = gArray[k++];
}
}

// case where first and second ranges have
// remaining values
while ((i < mid1) && (j < mid2))
{
if (gArray[i].compareTo(gArray[j]) < 0)
destArray[l++] = gArray[i++];
else
destArray[l++] = gArray[j++];
}

// case where second and third ranges have
// remaining values
while ((j < mid2) && (k < high))
{
if (gArray[j].compareTo(gArray[k]) < 0)
destArray[l++] = gArray[j++];

else
destArray[l++] = gArray[k++];
}

// case where first and third ranges have
// remaining values
while ((i < mid1) && (k < high))
{
if (gArray[i].compareTo(gArray[k]) < 0)
destArray[l++] = gArray[i++];
else
destArray[l++] = gArray[k++];
}

// copy remaining values from the first range
while (i < mid1)
destArray[l++] = gArray[i++];

// copy remaining values from the second range
while (j < mid2)
destArray[l++] = gArray[j++];

// copy remaining values from the third range
while (k < high)
destArray[l++] = gArray[k++];
}

// Driver function
public static void main(String args[])
{
// test case of values
Integer[] data = new Integer[] {45, -2, -45, 78,
30, -42, 10, 19, 73, 93};
mergeSort3Way(data);

System.out.println("After 3 way merge sort: ");
for (int i = 0; i < data.length; i++)
System.out.print(data[i] + " ");
}
}

Output:-

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