Merge sort algorithm

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Merge sort is a sorting algorithm based on the divide and conquer technique, with a worst-case time complexity of O(n log n). It works by recursively splitting the array into halves, sorting each half, and then merging them back together in a sorted order. Developed by John von Neumann for EDVAC in 1945, it efficiently handles sorting tasks through its systematic approach.

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 Merge sort is a sorting technique based on
divide and conquer technique. With worst-
case time complexity being Ο(n log n), it is
one of the most respected algorithms.
 Merge sort first divides the array into equal
halves and then combines them in a sorted
manner.

Invented by
John von Neumann
(1903-1957)
 Follows divide and
conquer paradigm.
 Developed merge
sort for EDVAC in
1945

1.Divide: Divide the unsorted list into two sub lists
of about half the size.
2.Conquer: Sort each of the two sub lists
recursively until we have list sizes of length 1,in
which case the list itself is returned.
3.Combine: Merge the two-sorted sub lists back
into one sorted list.

 MERGE SORT (A,p,r) //divide
if p < r
then q= [ (p + r) / 2 ]
MERGE SORT(A,p,q)
MERGER SORT(A,q + 1,r)
MERGE(A,p,q,r)

Merge(array A, int p, int q, int r)
{
array B[p..r] //temp array taken
i = k = p // initialize pointers
j = q+1
while (i <= q and j <= r)
{
if (A[i] <= A[j]) B[k++] = A[i++]
else B[k++] = A[j++]
}
while (i <= q)
B[k++] = A[i++] // copy any leftover to B
while (j <= r)
B[k++] = A[j++]
for i = p to r
A[i] = B[i] // copy B back to A
}

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Merge

Merge sort is a divide and conquer algorithm that divides an array into halves, recursively sorts the halves, and then merges the sorted halves back together. The key steps are: 1. Divide the array into equal halves until reaching base cases of arrays with one element. 2. Recursively sort the left and right halves by repeating the divide step. 3. Merge the sorted halves back into a single sorted array by comparing elements pairwise and copying the smaller element into the output array. Merge sort has several advantages including running in O(n log n) time in all cases, accessing data sequentially with low random access needs, and being suitable for external sorting of large data sets that do not fit in memory

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John von Neumann invented the merge sort algorithm in 1945. Merge sort follows the divide and conquer paradigm by dividing the unsorted list into halves, recursively sorting each half through merging, and then merging the sorted halves back into a single sorted list. The time complexity of merge sort is O(n log n) in all cases (best, average, worst) due to its divide and conquer approach, while its space complexity is O(n) to store the temporary merged list.

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Merge sort algorithm

1. Shubham Dwivedi

2.  Merge sort is a sorting technique based on divide and conquer technique. With worst- case time complexity being Ο(n log n), it is one of the most respected algorithms.  Merge sort first divides the array into equal halves and then combines them in a sorted manner.

3. Invented by John von Neumann (1903-1957)  Follows divide and conquer paradigm.  Developed merge sort for EDVAC in 1945

4. 1.Divide: Divide the unsorted list into two sub lists of about half the size. 2.Conquer: Sort each of the two sub lists recursively until we have list sizes of length 1,in which case the list itself is returned. 3.Combine: Merge the two-sorted sub lists back into one sorted list.

5.  MERGE SORT (A,p,r) //divide if p < r then q= [ (p + r) / 2 ] MERGE SORT(A,p,q) MERGER SORT(A,q + 1,r) MERGE(A,p,q,r)

6. Merge(array A, int p, int q, int r) { array B[p..r] //temp array taken i = k = p // initialize pointers j = q+1 while (i <= q and j <= r) { if (A[i] <= A[j]) B[k++] = A[i++] else B[k++] = A[j++] } while (i <= q) B[k++] = A[i++] // copy any leftover to B while (j <= r) B[k++] = A[j++] for i = p to r A[i] = B[i] // copy B back to A }

7. 99 6 86 15 58 35 86 4 0

8. 99 6 86 15 58 35 86 4 0 99 6 86 15 58 35 86 4 0

9. 99 6 86 15 58 35 86 4 0 99 6 86 15 58 35 86 4 0 86 1599 6 58 35 86 4 0

10. 99 6 86 15 58 35 86 4 0 99 6 86 15 58 35 86 4 0 86 1599 6 58 35 86 4 0 99 6 86 15 58 35 86 4 0

11. 99 6 86 15 58 35 86 4 0 99 6 86 15 58 35 86 4 0 86 1599 6 58 35 86 4 0 99 6 86 15 58 35 86 4 0 4 0

12. 99 6 86 15 58 35 86 0 4 4 0Merge

13. 15 866 99 58 35 0 4 86 99 6 86 15 58 35 86 0 4 Merge

14. 6 15 86 99 0 4 35 58 86 15 866 99 58 35 0 4 86 Merge

15. 0 4 6 15 35 58 86 86 99 6 15 86 99 0 4 35 58 86 Merge

Merge sort algorithm

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