Question

I have been programming in PHP for a long time now, and as I don’t come from a computer science / math background I only have a basic understanding of the Big O notation, so I have taken a function and tried to improve it and express them both in Big O:

Example 1

function foo($j) {
    $ids = array();
    while (count($ids) < $j) {
        $id = gen_id();  // assume this function will return you an integer
        if (!in_array($id, $ids)) {
            $ids[] = $id;
        }
    }
    return $ids;
}

I would improve this function by removing the while loop for count($ids) and replace with forloop So that count($ids) doesn’t have to be evaluated every time in the loop, and also replace is_array with isset and move the values to keys (isset is quicker than in_array)

Example 2 – Improved

function foo($j) {
    $ids = array();
    for($i = 1; $i<= $j; ++$j) {
        $id = gen_id();  // assume this function will return you an integer
        if (!isset($ids[$id])) {
            $ids[$id] = true;
        }
        else {
            --$i;
        }
    }
    return $ids;
}

I would express the above functions with the following Big O Notation:

Example 1: O(n^2), Example 2: O(n)

Am I correct with my notations? Is there a better way still to do the same function?

Thanks in advance!

Answer 1

Here is how I would write that function in a more straightforward approach: The inner for loop is the perfect scenario for a do ... while loop.

function foo( $j)
{
    $ids = array();
    for( $i = 0; $i < $j; $i++)
    {
        do
        {
            $id = gen_id();
        } while( isset( $ids[$id]));
        $ids[$id] = true;
    }
    return $ids;
}

Edit: Actually, this function is O($j) / O(n), since gen_id() and isset() are both constant O(1) (isset() is a hash table lookup). So, the inner efficiency of the for loop is constant time O(1), making the whole function O(n).