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);
}
console.log("Time Complexity: O(n)");
//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...

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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.
for (let i = 0; i < n; i++) {          // Outer loop runs n times
    for (let j = 0; j < n; j++) {      // Inner loop runs n times for each outer loop
        console.log(i, j);
    }
}
//TODO: Write an algorithm with O(n^2) time complexity
//Hint: think about nested loops...

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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
        count += 1;
}
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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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
const n = 10; // you can change this number

function fib(x) {
    if (x <= 1) {
        return x;
    }
    return fib(x - 1) + fib(x - 2);
}

console.log(fib(n));
//TODO: Write an algorithm that has a more complicated time complexity than O(n^x).

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