Algorithmic Efficiency Hacks: Javascript

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).

%%javascript
let n = 10; // change this value to test different outputs!

for (let i = 0; i < n * 2; i++) {
    console.log(i);
}

//TODO: print the above algorithm's time complexity
//BE CAREFUL - This one might trick some people. Remember that Big-O notation shows how much an algorithm's time complexity GROWS, so coefficients don't matter...

<IPython.core.display.Javascript object>

Hack 2: Your Turn!

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

%%javascript
const n = 10; // change this if you want.

//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

%%javascript
const n = 10; // change this
let count = 0;

for(let i = 0; i < n; i++){ //Outer loop, DO NOT MODIFY
    for(let j = 0; j < i; j++){
        count ++;
    }
}
console.log(count);

//TODO: Modify the algorithm so that it has a lower time complexity but same output, and keep the outer loop the same
//Hint: This algorithm has a time complexity of O(n^2).

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).