Best Approach to Getting Adjustment from Raw Number - php

Question

I would like advice on the best/most efficient way to get an adjusted score for a team based on a raw score. Let me explain.
The teams are contract bridge teams and the raw score for the winner is from 0 (tie) to any number, but greater than 100 would be rare. The raw score is called IMPS and the adjusted score is called VPs, but that is just for clarity.
The adjustment table is:
IMPs VPs
1 thru 2 16 to 14
3 thru 4 17 to 13
5 thru 7 18 to 12
8 thru 11 19 to 11
12 thru 15 20 to 10
16 thru 20 21 to 9
21 thru 26 22 to 8
27 thru 33 23 to 7
34 thru 41 24 to 6
42 thru 50 25 to 5
51 thru 60 26 to 4
61 thru 71 27 to 3
72 thru 83 8 to 2
84 thru 95 29 to 1
96+ 30 to 0
Here is my code. It works fine:
PHP
$teamArawScore = 20; //Actual result will come from form input
if ($teamArawScore >95 )
{
$teamAadjScore = 30;
$teamBadjScore = 0;
}
else
{
$adjustmentArray = array
(15,
16,16,
17,17,
18,18,18,
19,19,19,19,
20,20,20,20,
21,21,21,21,21,
22,22,22,22,22,22,
23,23,23,23,23,23,23,
24,24,24,24,24,24,24,24,
25,25,25,25,25,25,25,25,25,
26,26,26,26,26,26,26,26,26,26,
27,27,27,27,27,27,27,27,27,27,27,
28,28,29,29,28,28,28,28,28,28,28,28,
29,29,29,29,29,29,29,29,29,29,29,29);
$teamAadjScore = $adjustmentArray[$teamArawScore];
$teamBadjScore = 30 - $teamAadjScore;
}
echo "TeamA won by $teamArawScore so it won $teamAadjScore VPs and TeamB won $teamBadjScore VPs.";
My approach just seems inefficient. Since the array is small, I doubt there is any performance issues, but I would like to do the conversion as efficiently as possible.
What do you suggest?

Answer 1

Since there's no consistency in the table you described you will always be populating a lookup array containing the actual logic. You could also structure this differently, with a shorter array containing the sequential amount of points leading to a given score etc., but in the end those would all result in having to loop over the array to see where you end up - swapping memory for CPU cycles.
Effectively, you need a lookup table anyway because there appears to be no algorithm that can reliably map the contents of the lookup table, and your implementation is now O(1) in big-O notation. As such it can by definition not be made more efficient.
For reference on lookup tables (emphasis added in quote):
In computer science, a lookup table is an array that replaces runtime
computation with a simpler array indexing operation. The savings in
terms of processing time can be significant, since retrieving a value
from memory is often faster than undergoing an 'expensive' computation
or input/output operation. The tables may be precalculated and
stored in static program storage, calculated (or "pre-fetched") as
part of a program's initialization phase (memoization), or even stored
in hardware in application-specific platforms.
There's nothing 'bad practice' about using them. Back in the days when CPUs didn't have floating point units on board we'd have entire sine and sqrt tables embedded in programs to circumvent computationally expensive calculations at runtime.

Answer 2

I got a little something for you.Even though I'm not sure it would actualy optimize the execution speed.
Looping through an array, knowing the base value being 16 if we have a positive score (higher than one) from the A team.
This is not optimized at all (mainly because of the $a == 0 condition), but here it is:
<?php
$teamArawScore = 30;
$a = $teamArawScore;
$teamAfinalScore = 16;
$scoreArray = array(3,5,8,12,16,21,27,34,42,51,61,72,84,10000000000);
$count = 0;
foreach($scoreArray as $elem)
{
if($a < $elem)
{
$teamAfinalScore += $count;
break;
}
$count++;
}
if($a ==0)
{
$teamAfinalScore = 15;
$teamBfinalScore = 30 - $teamAfinalScore;
}
echo "Team A: ".$teamAfinalScore. "<br />Team B:".$teamBfinalScore;
?>

Answer 3

<?php
$teamArawScore = 1000; //Actual result will come from form input
if ($teamArawScore >95 )
{
$teamAadjScore = 30;
$teamBadjScore = 0;
}
else
{
$adjustmentArray = array('1'=>16,'3'=>17,'5'=>18,'8'=>19,'12'=>20,'16'=>21,'21'=>22,'27'=>23,'34'=>24,'42'=>50,'51'=>60,'61'=>27,'72'=>83,'84'=>95);
$base_score=array(1,3,5,8,12,16,21,27,34,42,51,61,72,84);
$count=count($base_score);
$adjustment_value=$adjustmentArray['1'];
for($i=1; $i<$count-1; $i++){
if($teamArawScore < $base_score[$i+1]){
$adjustment_value=$adjustmentArray[$base_score[$i]];
break;
}
else{
$adjustment_value=$adjustmentArray[$base_score[$i]]; // for values greater than 84
}
}
$teamAadjScore = $adjustment_value;
$teamBadjScore = 30 - $teamAadjScore;
}
echo "TeamA won by $teamArawScore so it won $teamAadjScore VPs and TeamB won $teamBadjScore VPs." ;