# 3-way Merge Sort

Prerequisite – Merge Sort

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.
Merge sort 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.

Examples:

Input  : 45, -2, -45, 78, 30, -42, 10, 19 , 73, 93
Output : -45 -42 -2 10 19 30 45 73 78 93

Input  : 23, -19
Output : -19  23

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

// 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:

After 3 way merge sort:
-45 -42 -2 10 19 30 45 73 78 93

Here, we first copy the contents of data array to another array called fArray. Then, sort the array by finding midpoints that divide the array into 3 parts and called sort function on each array respectively. The base case of recursion is when size of array is 1 and it returns from the function. Then merging of arrays starts and finally the sorted array will be in fArray which is copied back to gArray.

Time Complexity: In case of 2-way Merge sort we get the equation: T(n) = 2T(n/2) + O(n)
Similarly, in case of 3-way Merge sort we get the equation: T(n) = 3T(n/3) + O(n)
By solving it using Master method, we get its complexity as O(n log 3n).. Although time complexity looks less compared to 2 way merge sort, the time taken actually may become higher because number of comparisons in merge function go higher. Please refer Why is Binary Search preferred over Ternary Search? for details.

Similar article :
3 way Quick Sort

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