# Summary of algorithm for merge sort (recursive, non-recursive, and natural merge sort)

Source: Internet
Author: User

Note: The merge sort referred to in this article refers to the two-way merge sort.

Merge sort is a stable sorting algorithm with average, worst-case and best-case time complexity O (nlog2n). Recently, the recursive, non-recursive, and natural merge sorting algorithms of the merge sort were combed.

The basis of the merge sort: Merging two ordered arrays into an ordered array requires an O (n) of auxiliary space.

Photo from: https://www.cnblogs.com/chengxiao/p/6194356.html

Array: arrays to be sorted

Temparray: Temporary Array

startindex: Starting subscript

Middleindex: Intermediate value subscript

Endindex: Terminating subscript

void merge (int sourcearray[], int temparray[], int startindex, int middleindex, int endindex)
{
int left = startindex, index = startindex;
int right = Middleindex + 1;
if (left >= right)
Return

Merging two ordered arrays
while (left! = middleindex + 1 && Right! = endindex + 1)
{
if (Sourcearray[left] <= sourcearray[right])
{
temparray[index++] = sourcearray[left++];
}
Else
{
temparray[index++] = sourcearray[right++];
}
}

The left array is not merged and is directly joined
while (left!= middleindex+ 1)
{
temparray[index++] = sourcearray[left++];
}

The right array is not merged, directly into
while (right! = Endindex + 1)
{
temparray[index++] = sourcearray[right++];
}

Assigns an ordered array to a sorted array in a temporary array

for (int i = 0; i < endindex+ 1; ++i)
{
Sourcearray[i] = Temparray[i];
}

}

Merge sort recursive algorithm:

void mergesort (int sourcearray[],int temparray[], int low, int. high)

{

if (Low>=high)

Return

Divided

int middle = (Low+high)/2;

Left half recursive

MergeSort (Sourcearray, Temparray, Low,middle);

Right half recursion

MergeSort (Sourcearray, Temparray, Middle+1,high);

Merge the left and right halves

Merge (Sourcearray,temparray,low,middle,high);

}

Non-recursive merge sorting algorithm:

Instead of recursive ordering, an ordered array of elements and adjacent elements is formed, and an ordered array is formed with the next array until the entire array is ordered.

void merge_noncursive (int sourcearray[], int temparray[],int endindex)

{

Step, in the I+step array order, will sourcearray[i]...sourcearray[step-1] and Sourcearray[i+step]...sourcearray[min (endindex,i+2* STEP-1)] Two ordered arrays are merged together.

int step = 1;

int index;

while (step <= endindex)

{

index = 0;

while (index <= endindex-2*step + 1)

{

Merge (sourcearray,temparray,index,index+step-1,index+2*step-1);

Index + = 2*step;

}

Merge ordered left half and less than one step in the right half

if (index + step <= endindex)

{

Merge (Sourcearray,temparray,index,index+step-1,endindex);

}

Step *= 2;

}

}

Natural Merge Sort:

Since merge sorting is the merging of multiple ordered arrays into an array, in addition to the fully inverted array, there is always a part of the array that is ordered, and we can get the tag of an ordered array, merging multiple ordered arrays into an ordered array.

This is the key to understanding the nature merge sort

int getindex (int array[], int flag[],int index)

{

int next = 0;

The first is subscript 0

Flag[next] = 0;

next++;

for (int i = 0;i<index;i++)

{

Finding array elements is not an orderly place

if (Array[i] > Array[i+1])

{

flag[next++] = i;

}

}

The last one is the maximum subscript

Flag[next] = index;

return next;

}

void merge_naturally (int sourcearray[],int temparray[],int index)

{

int * flag = new Int[index];

int num = GetIndex (sourcearray,flag,index);

A value greater than or equal to 2 indicates that the array is not fully ordered except for 0 with the other number

while (Num >= 2)

{

for (int i = 0; i<=num;i+=2)

{

Merge (sourcearray,temparray,flag[i],flag[i+1],flag[i+2]);

}

Continue to get unordered sequence numbers

num = GetIndex (sourcearray,flag,index);

}

}

Summary of algorithm for merge sort (recursive, non-recursive, and natural merge sort)

Related Keywords:

The content source of this page is from Internet, which doesn't represent Alibaba Cloud's opinion; products and services mentioned on that page don't have any relationship with Alibaba Cloud. If the content of the page makes you feel confusing, please write us an email, we will handle the problem within 5 days after receiving your email.

If you find any instances of plagiarism from the community, please send an email to: info-contact@alibabacloud.com and provide relevant evidence. A staff member will contact you within 5 working days.

## A Free Trial That Lets You Build Big!

Start building with 50+ products and up to 12 months usage for Elastic Compute Service

• #### Sales Support

1 on 1 presale consultation

• #### After-Sales Support

24/7 Technical Support 6 Free Tickets per Quarter Faster Response

• Alibaba Cloud offers highly flexible support services tailored to meet your exact needs.