Merge Sort

Merge Sort

In computer science, a merge sort (also commonly spelled merge sort) is an O (n log n) comparison-based sorting algorithm. Most implementations produce a stable sort, which means that the implementation preserves the input order of equal elements in the sorted output. Merge sort is a divide and conquer algorithm that was invented by John von Neumann in 1945. A detailed description and analysis of bottom-up merge sort appeared in a report by Goldstone and Neumann as early as 1948.

Merge sort
Class	Sorting algorithm
Data structure	Array
Worst case performance	O(n log n)
Best case performance	O(n log n) typical, O(n) natural variant
Average case performance	O(n log n)
Worst case space complexity	O(n) auxiliary

Example

Algorithm

MERGE (A, p, q, r )

1.      n₁ ← q − p + 1
2.      n₂ ← r − q
3.      Create arrays L[1 . . n₁ + 1] and R[1 . . n₂ + 1]

4.      FOR i ← 1 TO n₁
5.            DO L[i] ← A[p + i − 1]
6.      FOR j ← 1 TO n₂
7.            DO R[j] ← A[q + j ]
8.      L[n₁ + 1] ← ∞
9.      R[n₂ + 1] ← ∞
10.    i ← 1
11.    j ← 1
12.    FOR k ← p TO r
13.         DO IF L[i ] ≤ R[ j]
14.                THEN A[k] ← L[i]
15.                        i ← i + 1
16.                ELSE A[k] ← R[j]
17.                        j ← j + 1