# Merge Sort

Nishant Kumar
·Jan 27, 2022·

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Merge Sort is a sorting algorithm which is based on divide and conquer approach. The list is divided into two halves until each sub list has a single element, and the sub lists are merged in a sorted manner that the sorted list is obtained. It is a very efficient algorithm for sorting. The technique simply involves: Divide the list into two sub slists, Make recursion call for the sub lists, and then Merge the sub lists.

### Illustration

``````if length(list)>1
find point of divide,mid=length(list)//2
left sublist L,index 0 to mid
right sublist R, index mid+1 to length(list)-1
recursion,calling function itself for L
recursion,calling function itself for R
i=j=k=0
while i<length(L) and j<length(R)
if L[i] < R[j],then list[k]=L[i] and i=i+1
else, list[k]=R[j] and j=j+1
k=k+1
while i<length(L)
list[k]=L[i]
update i=i+1 and k=k+1
while i<length(R)
list[k]=R[j]
update j=j+1 and k=k+1
``````

Time Complexity: Worst Case: O(nlogn) Average Case: O(nlogn) Best Case: O(nlogn) Space Complexity: O(n)

### Program for Merge Sort:

``````def mergeSort(data):
if len(data) > 1:

mid = len(data)//2 #point where the list is divided into two sublists
L = data[:mid]
R = data[mid:]

mergeSort(L) #sorting first half
mergeSort(R) #sorting second half

i = j = k = 0

while i < len(L) and j < len(R):
if L[i] < R[j]:
data[k] = L[i]
i += 1
else:
data[k] = R[j]
j += 1
k += 1

while i < len(L):
data[k] = L[i]
i += 1
k += 1

while j < len(R):
data[k] = R[j]
j += 1
k += 1

inp=input("Enter the data: ").split()
data=[]
for i in inp:
data.append(int(i))

mergeSort(data)

print("Sorted List is: ")
print(data)
``````