Big O - O(log(n)) code example

Question

Like the Big O notation \"O(1)\" can describe following code:

O(1):

    for (int i = 0; i < 10; i++) {
        // do stuff 
        a[i] = INT;
    }

O         


        

Answer 1

Simplest code with a for loop that you would use to represent:

O(1):

function O_1(i) {
    // console.log(i);
    return 1
}

O(n):

function O_N(n) {
    count = 0;
    for (i = 0; i < n; i++) {
        // console.log(i);
        count++;
    }
    return count
}

O(n²):

function O_N2(n) {
    count = 0;
    for (i = 0; i < n; i++) {
        for (j = 0; j < n; j++) {
            // console.log(i, j);
            count++;
        }
    }
    return count
}

O(Log_2(n)):

function O_LOG_2(n) {
    count = 0;
    for (var i = 1; i < n; i = i * 2) {

        count++;
    }
    return count
}

O(Sqrt(n)):

function O_SQRT(n) {
    count = 0;
    for (var i = 1; i * i < n; i++) {
        // console.log(i);
        count++;
    }
    return count
}