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
console.log("O(n)");

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Hack 2: Your Turn!

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

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

// O(n^2) example — nested loops
for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
        console.log(i, j);
    }
}

console.log("Time complexity: O(n^2)");

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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
    // Instead of looping j < i, add i directly
    count += i;
}

console.log(count);
console.log("Time complexity: O(n)");

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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.)

%%javascript
import itertools

n = int(input())
nums = list(range(n))

perms = list(itertools.permutations(nums))
print(len(perms))
print("Time complexity: O(n!)")

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