A function to calculate minimum steps required to make sure there are equal amount of coin in each bag

CoinBags.php

<?php

$c = [0,6,0];
$n = count($c);
$k = array_sum($c) / $n;

/*
 * Consider having "n" bags in which there are ci coins (i=1 to n)
 * as such that total count of coins are dividable by n and equal to "k".
 * 
 * If we define a step as picking one coin from one bag and dropping it
 * in one of the adjacent bags (either left-side or right-side), how can we
 * calculate minimum steps required to make sure there are "k" coins
 * in each and every bag?
 *
 * Minumum Steps = |c1-k| + |c1+c2-2k| + |c1+c2+c3-3k| + ... + |c1+c2+...+cn-nk|
 *
 * c = Bags
 * n = Bags Count
 * k = Expected Coin Per Bag
 *
 * Sum of ci (for i=1 to n)=nk
 */
function calculateOptimumSteps(array $bags, int $bagsCount, int $expectedCoinPerBag)
{
	$cumulativeCoinCount = 0;
	$optimumStepsCount = 0;

	for ($index = 0; $index < $bagsCount; $index++) {
		$cumulativeCoinCount += $bags[$index];
		
		$optimumStepsCount += abs($cumulativeCoinCount - ($index + 1) * $expectedCoinPerBag);
	}
	
	return $optimumStepsCount;
}

print(json_encode($c) . " will be processed in " . calculateOptimumSteps($c, $n, $k) . " steps.");