MERGE-SORT: INTRODUCTION TO ALGORITHMS

Merge sort:归并排序

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Animation

An example of merge sort. First divide the list into the smallest unit (1 element), then compare each element with the adjacent list to sort and merge the two adjacent lists. Finally all the elements are sorted and merged.

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Merge sort animation. The sorted elements are represented by dots.

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A recursive merge sort algorithm used to sort an array of 7 integer values. These are the steps a human would take to emulate merge sort (top-down).

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Complexity

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	$О(n)$ total, $O(n)$ auxiliary

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Pseudo code

MERGE-SORT(A,p,r)
 1  if p<r
 2      q = floor((p+r)/2)
 3      MERGE-SORT(A,p,q)
 4      MERGE-SORT(A,q+1,r)
 5      MERGE(A,p,q,r)

MERGE(A,p,q,r)
 1  n1 = q-p+1
 2  n2 = r-q
 3  let L[1..n1+1] and R[1..n2+1] be new arrays
 4  for i=1 to n1
 5      L[i] = A[p+i-1]
 6  for j=1 to n2
 7      R[j] = A[q+j]
 8  L[n1+1] = Infinite
 9  R[n2+1] = Infinite
10  i = 1
11  j = 1
12  for k=p to r
13      if L[i] <= R[j]
14          A[k] = L[i]
15          i = i+1
16      else
17          A[k] = R[j]
18          j = j+1

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Figure

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Reference

<< Introduction to Algorithms >> Third Edition, THOMAS H. CORMEN, CHARLES E. LEISERSON, RONALD L. RIVEST, CLIFFORD STEIN.
https://en.wikipedia.org/wiki/Merge_sort