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### Merge Sort

Mergesort is another comparison-based algorithm also known as a "divide and conquer" algorithm and its main focus is on how to merge together two pre-sorted arrays such that the resulting array is also sorted. You may be interested to know that it was invented by the marvellous John von Neumann in 1945.

The key word of course is 'merge', so we are referring to bringing two lists together. Conceptually, a merge sort works as follows : First, divide the unsorted list into n sublists, each containing 1 element (a list of 1 element is considered sorted). Then, repeatedly merge sub lists to produce new sorted sublists until there is only 1 sublist remaining. This will be the sorted list.

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### Challenge

#1 Write a Python program to sort a list of elements using the Merge sort algorithm

#2 Comment each line of the python solution below to show your understanding of the algorithm

### Solution

```def mergeSort(nlist):
print("Splitting ",nlist)
if len(nlist)>1:
mid = len(nlist)//2
lefthalf = nlist[:mid]
righthalf = nlist[mid:]

mergeSort(lefthalf)
mergeSort(righthalf)
i=j=k=0
while i < len(lefthalf) and j < len(righthalf):
if lefthalf[i] < righthalf[j]:
nlist[k]=lefthalf[i]
i=i+1
else:
nlist[k]=righthalf[j]
j=j+1
k=k+1

while i < len(lefthalf):
nlist[k]=lefthalf[i]
i=i+1
k=k+1

while j < len(righthalf):
nlist[k]=righthalf[j]
j=j+1
k=k+1
print("Merging ",nlist)

nlist = [14,46,43,27,57,41,45,21,70]
mergeSort(nlist)
print(nlist)```

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