in python
The program is the same as shown at the end of the Merge sort section, with the following changes:
Numbers are entered by a user in a separate helper function, read_nums(), instead of defining a specific list.
Output of the list has been moved to the function print_nums().
An output has been added to merge_sort(), showing the indices that will be passed to the recursive function calls.
Add code to the merge sort algorithm to count the number of comparisons performed.
Add code at the end of the program that outputs "comparisons: " followed by the number of comparisons performed (Ex: "comparisons: 12")
Hint: Use a global variable to count the comparisons.
Note: Take special care to look at the output of each test to better understand the merge sort algorithm.
Ex: When the input is:
3 2 1 5 9 8
the output is:
unsorted: 3 2 1 5 9 8
0 2 | 3 5
0 1 | 2 2
0 0 | 1 1
3 4 | 5 5
3 3 | 4 4
sorted: 1 2 3 5 8 9
comparisons: 8
main.py
# Read integers into a list and return the list.
def read_nums():
nums = input().split()
return [int(num) for num in nums]
# Output the content of a list, separated by spaces.
def print_nums(numbers):
for num in numbers:
print (num, end=' ')
print()
def merge(numbers, i, j, k):
merged_size = k - i + 1
merged_numbers = []
for l in range(merged_size):
merged_numbers.append(0)
merge_pos = 0
left_pos = i
right_pos = j + 1
while left_pos <= j and right_pos <= k:
if numbers[left_pos] < numbers[right_pos]:
merged_numbers[merge_pos] = numbers[left_pos]
left_pos = left_pos + 1
else:
merged_numbers[merge_pos] = numbers[right_pos]
right_pos = right_pos + 1
merge_pos = merge_pos + 1
while left_pos <= j:
merged_numbers[merge_pos] = numbers[left_pos]
left_pos = left_pos + 1
merge_pos = merge_pos + 1
while right_pos <= k:
merged_numbers[merge_pos] = numbers[right_pos]
right_pos = right_pos + 1
merge_pos = merge_pos + 1
merge_pos = 0
while merge_pos < merged_size:
numbers[i + merge_pos] = merged_numbers[merge_pos]
merge_pos = merge_pos + 1
def merge_sort(numbers, i, k):
j = 0
if i < k:
j = (i + k) // 2
# Trace output added to code in book
print(i, j, "|", j + 1, k)
merge_sort(numbers, i, j)
merge_sort(numbers, j + 1, k)
merge(numbers, i, j, k)
if __name__ == '__main__':
numbers = read_nums()
print ('unsorted:', end=' ')
print_nums(numbers)
print()
merge_sort(numbers, 0, len(numbers) - 1)
print ('\nsorted:', end=' ')
print_nums(numbers)

To add code to the merge sort algorithm to count the number of comparisons performed and  at the end of the program that outputs "comparisons: " followed by the number of comparisons performed check the code given below.

A sorting algorithm is a set of instructions that takes an input array, applies certain operations to the array (also known as a list), and outputs a sorted array.

Sorting algorithms are frequently covered early on in computer science courses because they offer a simple way to introduce other important concepts like Big-O notation, divide-and-conquer strategies, and data structures like binary trees and heaps.

When selecting a sorting algorithm, many factors need to be taken into account.

"""

Python version: 3.6

Python program to sort a list of numbers in ascending order using merge sort

"""

# add a global variable to count number of key comparisons in merge sort and initialize it to 0

comparisons = 0

def read_nums():

"""

Function that takes no inputs and returns a list of integers entered by the user

"""

# read a string of integers and split it into list of strings using default delimiter whitespace

nums = input().split()

# convert the list of strings to list of integers and return it

return [int(num) for num in nums]

def print_nums(numbers):

"""

Function that takes as input a list of numbers and display the

numbers on screen in one line separated by space ending with a newline

"""

for num in numbers:

 print (num, end=' ')

print()

def merge(numbers, i, j, k):

"""

Function that takes as input a list of numbers and 3 integers

representing the start and ends of the sorted left[i, j] and sorted right[j+1, k] sublists

"""

global comparisons # use the global variable comparisons

# calculate the total size of the list after merging the sublists

merged_size = k - i + 1

# create a list of size merged_size and initialize all elements to 0

merged_numbers = []    

for l in range(merged_size):

 merged_numbers.append(0)

# set merge_pos to start index of merged_numbers, left_pos to start index of left sublist and right_pos to start index of right sublist

merge_pos = 0  

left_pos = i

right_pos = j + 1  

# loop until end of a sublist is reached

while left_pos <= j and right_pos <= k:

 comparisons += 1 # increment comparisons by 1

 # current element of left sublist is less than current element of right sublist

 if numbers[left_pos] < numbers[right_pos]:

  # insert current element of left sublist into merged_numbers and increment left_pos by 1

  merged_numbers[merge_pos] = numbers[left_pos]

  left_pos = left_pos + 1

 else:

  # else insert current element of right sublist into merged_numbers and increment right_pos by 1

  merged_numbers[merge_pos] = numbers[right_pos]

  right_pos = right_pos + 1

 merge_pos = merge_pos + 1 # increment merge_pos by 1

# loop to copy the remaining elements of left sublist to merged_numbers

while left_pos <= j:

 merged_numbers[merge_pos] = numbers[left_pos]

 left_pos = left_pos + 1

 merge_pos = merge_pos + 1

# loop to copy the remaining elements of right sublist to merged_numbers

while right_pos <= k:

 merged_numbers[merge_pos] = numbers[right_pos]

 right_pos = right_pos + 1

 merge_pos = merge_pos + 1

# loop to copy the sorted list from merged_numbers to numbers in the range [i, k]

merge_pos = 0

while merge_pos < merged_size:

 numbers[i + merge_pos] = merged_numbers[merge_pos]

 merge_pos = merge_pos + 1

def merge_sort(numbers, i, k):

"""

Function that takes as input an unsorted list of numbers and start and end index

of the list to sort and sorts the list in ascending order using merge sort

"""

j = 0

# current list range contains at least 1 element

if i < k:

 # get the index of middle element of the current range

 j = (i + k) // 2

 # output the range for the left and right sublists to sort

 print(i, j, "|", j + 1, k)

 # recursively sort the numbers in the range [i,j] and [j+1, k]

 merge_sort(numbers, i, j)

 merge_sort(numbers, j + 1, k)

 # merge the sorted lists [i,j] and [j+1,k] to get the sorted list in the range [i,k]

 merge(numbers, i, j, k)

if __name__ == '__main__':

# get the list of numbers entered by the user

numbers = read_nums()

# display the unsorted list

print ('unsorted:', end=' ')

print_nums(numbers)

print()

# sort the list in ascending order using merge sort passing the numbers list and 0 and 1 less than size of list as i and k

merge_sort(numbers, 0, len(numbers) - 1)

# display the sorted list

print ('\nsorted:', end=' ')

print_nums(numbers)

# display the number of comparisons using the global variable

print("comparisons:",comparisons)

# end of program

Learn more about sorting algorithm

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The is context sensitive, meaning it will display options that relate to an active tool.

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