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 = 5; // change this value to test different outputs!

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

console.log("O(n)")


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Console Output

Hack 2: Your Turn!

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

%%javascript
const n = 5;

for (let i = 0; i < n; i++) {
    for (let j = 0; j < n; j++) {
        console.log(`i=${i}, j=${j}`);
    }
}

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Console Output

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;
let count = 0;

for (let i = 0; i < n; i++) {
    count += i; 
}

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).

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Console Output

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.)
%%js 
const n = 10; 

function fibonacci(k) {
    if (k <= 1) return k;
    return fibonacci(k - 1) + fibonacci(k - 2);
}

console.log(`Fibonacci(${n}) = ${fibonacci(n)}`);


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Console Output