1. A code for merge sort is provided in this document. We are going to experimentally check the runtime for these algorithms for varying input sizes.

Input size n (size of the list):

We are going to experiment with the following list sizes

1. 10,000

2. 100,000

3. 1000,000

For each of these sizes we are going to have two types of input:

a. Sorted list (ascending order) of elements from range (1:n)

b. Sorted list (descending order) of elements from range (n:1)

#PYTHON CODE

def mergeSort(mylist):

if len(mylist)>1:

mid = len(mylist)//2

lefthalf = mylist[:mid]

righthalf = mylist[mid:]

mergeSort(lefthalf)

mergeSort(righthalf)

# Merging the lists occurs here

i=j=k=0

while i < len(lefthalf) and j < len(righthalf):

if lefthalf[i] <= righthalf[j]:

mylist[k]=lefthalf[i]

i=i+1

else:

mylist[k]=righthalf[j]

j=j+1

k=k+1

while i < len(lefthalf):

mylist[k]=lefthalf[i]

i=i+1

k=k+1

while j < len(righthalf):

mylist[k]=righthalf[j]

j=j+1

k=k+1

return mylist