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2 Way Merge Sort Program In C

Like QuickSort, Merge Sort is a Divide and Conquer algorithm. It divides input array in two halves, calls itself for the two halves and then merges the two sorted halves.The merge() function is used for merging two halves. The merge(arr, l, m, r) is key process that assumes that arr[l.m] and arr[m+1.r] are sorted and merges the two sorted sub-arrays into one. See following C implementation for details.

Two2 Way Merge Sort Program In C

The following diagram from wikipedia shows the complete merge sort process for an example array {38, 27, 43, 3, 9, 82, 10}. If we take a closer look at the diagram, we can see that the array is recursively divided in two halves till the size becomes 1. Once the size becomes 1, the merge processes comes into action and starts merging arrays back till the complete array is merged.

  • Figure: 2-way.merge sort. Mergesort is the greatest method for sorting linked lists into random order. The total computing time is of the 0(n log 2 n ). The drawback of using mergesort is that it needs two arrays of the similar size and space for the merge phase. That is, to sort a list of size n, it requires space for 2n elements.
  • The Merge Sort¶ We now turn our attention to using a divide and conquer strategy as a way to improve the performance of sorting algorithms. The first algorithm we will study is the merge sort. Merge sort is a recursive algorithm that continually splits a list in half.

Implement a d-way merging algorithm that given d sorted input streams of 32-bit integers creates an output stream containing the elements from the input streams in sorted order. The merging should be based on the priority queue structure Heap. Implement external Merge-sort for sorting 32-bit integers. The program should take param.

C/C++

#include<stdlib.h>
// First subarray is arr[l.m]
voidmerge(intarr[], intl, intm, intr)
inti, j, k;
intn2 = r - m;
/* create temp arrays */
for(i = 0; i < n1; i++)
for(j = 0; j < n2; j++)
i = 0; // Initial index of first subarray
k = l; // Initial index of merged subarray
{
{
i++;
else
arr[k] = R[j];
}
}
/* Copy the remaining elements of L[], if there
while(i < n1)
arr[k] = L[i];
k++;
are any */
{
j++;
}
/* l is for left index and r is right index of the
voidmergeSort(intarr[], intl, intr)
if(l < r)
// Same as (l+r)/2, but avoids overflow for
intm = l+(r-l)/2;
// Sort first and second halves
mergeSort(arr, m+1, r);
merge(arr, l, m, r);
}
/* UTILITY FUNCTIONS */
voidprintArray(intA[], intsize)
inti;
printf('%d ', A[i]);
}
/* Driver program to test above functions */
{
intarr_size = sizeof(arr)/sizeof(arr[0]);
printf('Given array is n');
printArray(arr, arr_size);
}

Java

classMergeSort
// Merges two subarrays of arr[].
// Second subarray is arr[m+1.r]
{
intn1 = m - l + 1;
intL[] = newint[n1];
for(inti=0; i<n1; ++i)
for(intj=0; j<n2; ++j)
/* Merge the temp arrays */
// Initial indexes of first and second subarrays
intk = l;
{
{
i++;
else
arr[k] = R[j];
}
}
/* Copy remaining elements of L[] if any */
{
i++;
}
/* Copy remaining elements of R[] if any */
{
j++;
}
// merge()
{
{
intm = (l+r)/2;
// Sort first and second halves
sort(arr , m+1, r);
// Merge the sorted halves
}
staticvoidprintArray(intarr[])
intn = arr.length;
System.out.print(arr[i] + ' ');
}
// Driver method
{
printArray(arr);
MergeSort ob = newMergeSort();
printArray(arr);
}

Python3

defmergeSort(arr):
mid =len(arr)//2#Finding the mid of the array
R =arr[mid:] # into 2 halves
mergeSort(L) # Sorting the first half
whilei < len(L) andj < len(R):
arr[k] =L[i]
else:
j+=1
whilei < len(L):
i+=1
arr[k] =R[j]
k+=1
# Code to print the list
fori inrange(len(arr)):
print()
# driver code to test the above code
arr =[12, 11, 13, 5, 6, 7]
printList(arr)
print('Sorted array is: ', end='n')

Output:

Time Complexity: Sorting arrays on different machines. Merge Sort is a recursive algorithm and time complexity can be expressed as following recurrence relation.
T(n) = 2T(n/2) +
The above recurrence can be solved either using Recurrence Tree method or Master method. It falls in case II of Master Method and solution of the recurrence is .
Time complexity of Merge Sort is in all 3 cases (worst, average and best) as merge sort always divides the array into two halves and take linear time to merge two halves.

Quick Sort Program

Auxiliary Space: O(n)

Algorithmic Paradigm: Divide and Conquer

Sorting In Place: No in a typical implementation

Stable: Yes

Merge Sort Program In Java

Applications of Merge Sort Caldera sky islands s.

  1. Merge Sort is useful for sorting linked lists in O(nLogn) time.In the case of linked lists, the case is different mainly due to the difference in memory allocation of arrays and linked lists. Unlike arrays, linked list nodes may not be adjacent in memory. Unlike an array, in the linked list, we can insert items in the middle in O(1) extra space and O(1) time. Therefore merge operation of merge sort can be implemented without extra space for linked lists.

    Sandra nasic the signal rar. In arrays, we can do random access as elements are contiguous in memory. Let us say we have an integer (4-byte) array A and let the address of A[0] be x then to access A[i], we can directly access the memory at (x + i*4). Unlike arrays, we can not do random access in the linked list. Quick Sort requires a lot of this kind of access. In linked list to access i’th index, we have to travel each and every node from the head to i’th node as we don’t have a continuous block of memory. Therefore, the overhead increases for quicksort. Merge sort accesses data sequentially and the need of random access is low.

  2. Used in External Sorting


Snapshots:

Way

Other Sorting Algorithms on GeeksforGeeks:
3-way Merge Sort, Selection Sort, Bubble Sort, Insertion Sort, Merge Sort, Heap Sort, QuickSort, Radix Sort, Counting Sort, Bucket Sort, ShellSort, Comb Sort

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