Algorithmic Efficiency Hacks: Python

Let’s test your knowledge on algorithmic efficiency!

Hack 1: How Much Time?

Objective: write the time complexity of the algorithm below using Big-O notation.

(don’t worry about special cases such as n = 1 or n = 0).

n = int(input()) # remember what O(n) means? This is a good way of visualizing n.

for i in range(n):
    print(i)

#TODO: print the above algorithm's time complexity

Hack 2: Your Turn!

Objective: write an algorithm with O(n^2) time complexity.

n = int(input())

#TODO: Write an algorithm with O(n^2) time complexity
#Hint: think about nested loops...

Hack 3: Gotta Go Fast!

Objective: Optimize this algorithm so that it has a lower time complexity without modifying the outer loop

import math
n = int(input())
count = 0

for i in range(n):
    for j in range(math.ceil(math.sqrt(n)*2)):
        count += 1

print(count)

#TODO: make this algorithm more efficient, but keep the outer loop and make sure the output is still the same!
#Hint: how does the inner loop affect time complexity?

42

Hack 4: Extra Challenge

Objective: Write an algorithm that does NOT have a time complexity of O(1), O(n), or O(n^x) and identify the time complexity

(I will not accept O(n^3) or some other power, it needs to be more complex.)

n = int(input())

#TODO: Write an algorithm that has a more complicated time complexity than O(n^x).