Make rounded values add up to desired product - php

Question

This is a programming question that will require some thinking, and could really be applied to any programming language.
Suppose you have the array:
$arr=array(10,7,4,4,3,2,1,1,1,1,1,1);
This array is dynamic and could be any set of numbers.
You also have a multiplier, lets say 0.6.
The goal is to display each number, one by one, in such a manner that they add as close to the total*multiplier as possible. In this case, the numbers add to 36, *0.6 gives you 21.6
Here's the catch:
You have to round each value (whole numbers only), so your real goal is to make the numbers add as close to 22 as possible.
You cannot use any functions to solve for the sum of the array. You can only loop through it once.
The most basic attempt would be
$multiplier = 0.6;
$sum=0;
foreach($arr AS $value){
$sum+=round($multiplier * $value);
}
But this will not work since 1*0.6 will always round to 1.
I think it is possible with something like this:
$multiplier = 0.6;
$sum=0;
foreach($arr AS $value){
$real=$multiplier * $value;
$rounded=round($multiplier * $value);
$sum_rounded += $rounded;
$sum_real += $real;
//Somehow compare the two sums and break the foreach
}
I don't know where to go from here. What do you guys think?
Tried this:
$sum_real=0;
$sum_round=0;
$count=0;
foreach($rows AS $arr){
$count+=1;
$real_val=$arr*$multiplier;
$sum_round+=round($real_val);
$sum_real+=$real_val;
$avg_round=$sum_round/$count;
$avg_real = $sum_real/$count;
$val = ($avg_round>$avg_real) ? floor($real_val) : round($real_val);
}
But did not work...I think it is getting close though.

Answer 1

Calculate the average for both $sum_rounded and $sum_real at the beginning of each iteration of the foreach loop. If the average for $sum_rounded is larger, use floor() instead of round().
EDIT: You don't actually need to calculate the average at all, since the numbers will both be divided by the same number and that doesn't affect which one is larger. Also, add the $value that is about to be incremented to the comparisons.
foreach($arr AS $value){
$real=$multiplier * $value;
$rounded=round($multiplier * $value);
if($sum_rounded + $rounded > $sum_real + $real) {
$sum_rounded += floor($multiplier * $value);
}
else {
$sum_rounded += $rounded;
}
$sum_real += $real;
}

Answer 2

I think I can talk you into looping twice.
$arr = array(10,7,4,4,3,2,1,1,1,1,1,1);
$out = [];
$multiplier = 0.6;
$sum = round(array_sum($arr) * $multiplier); // that's a loop!
foreach ($arr as $value) {
$value = round($multiplier * $value);
array_push($out, $value);
$sum -= $value;
}
while ($sum > 0) {
$sum --;
$out[$sum] --;
}
while ($sum < 0) {
$sum ++;
$out[-$sum] ++;
}

Answer 3

Here's a 1-pass method:
$orig_sum = 0;
$rounded_sum = 0;
$new_arr = array();
for ($i = 0; $i < count($arr)-1; $i++) {
$orig_sum += $arr[$i];
$new_elt = round($arr[$i] * $multiplier);
$rounded_sum += $new_elt;
$new_arr[] = $new_elt;
}
$orig_sum += $arr[$i];
$expected_rounded_sum = round($orig_sum * $multiplier);
$new_arr[] = $expected_rounded_sum - $rounded_sum;
CODEPAD