Problem Explanation:

Given an array of integers, you can perform the following operations any number of times: - Subtract 1 from any element. - Subtract 2 from any element. - Subtract 5 from any element.

The goal is to determine the minimum number of operations required to make all the elements in the array equal.

Solution Approach:

1. Find the Minimum Element: Identify the smallest element in the array since this will guide us on how much we need to reduce the other elements.
2. Consider Different Targets: To minimize operations, consider making all elements equal to min_element, min_element-1, min_element-2, min_element-3, and min_element-4. This is because these slight variations might help avoid some larger reductions.
3. Calculate Operations: For each of these target values, calculate the total number of operations required to reduce all elements in the array to that target.
4. Choose the Best Option: The answer will be the minimum number of operations required among all these target values.

PHP Implementation:

Here is the implementation in PHP:

<?php

function minOperations($arr, $target) {
    $operations = 0;
    foreach ($arr as $value) {
        $diff = $value - $target;
        $operations += intdiv($diff, 5);
        $diff %= 5;
        $operations += intdiv($diff, 2);
        $diff %= 2;
        $operations += $diff;
    }
    return $operations;
}

function equal($arr) {
    $min_value = min($arr);
    $min_operations = PHP_INT_MAX;

    // Check reducing to min_value, min_value-1, ..., min_value-4
    for ($i = 0; $i < 5; $i++) {
        $target = $min_value - $i;
        $operations = minOperations($arr, $target);
        if ($operations < $min_operations) {
            $min_operations = $operations;
        }
    }

    return $min_operations;
}

// Test cases
$arr1 = [2, 2, 3, 7];
$arr2 = [10, 7, 12];
$arr3 = [1, 1, 1, 1];

echo equal($arr1) . "\n"; // Output: 2
echo equal($arr2) . "\n"; // Output: 3
echo equal($arr3) . "\n"; // Output: 0
?>

Explanation of the Code:

1. minOperations Function: This function calculates the number of operations needed to reduce all elements in the array to a specified target.
   • It uses integer division and modulo operations to determine how many steps of 5, 2, and 1 are needed.
2. equal Function: This function iterates over possible target values (from min_value to min_value-4) and uses the minOperations function to determine the minimum number of operations required.
3. Test Cases: The test cases check for various scenarios to ensure the solution works correctly.

This implementation ensures that all possible target reductions are considered, and the minimum number of operations required to make all elements in the array equal is found.

Hello, If I do this in Scala, I'm getting a timeout on several testcases -

def equal(arr: Array[Int]): Int = Array(0, 1, 2).map(x => (arr.map(y => {val dist = y - (arr.min-x); dist/5 + (dist%5)/2 + (dist%5)%2}).sum)).min`

What am I doing wrong?

To make things difficult, she must equalize the number of chocolates in a series of operations. For each operation, she can give pieces to all but one colleague, creating a challenging scenario for fair distribution. This problem requires strategic thinking and careful planning to ensure that every colleague ends up with the same number of chocolates. Meanwhile, checking her Fab Bank balance check online provides her with a momentary distraction, offering insights into her financial status while she contemplates the next move. Balancing the chocolates becomes a test of patience and logic, mirroring the precision needed to manage her finances effectively.

For those generating solution values < than the test cases provided. This is because you are evaluting a convergence towards MAX and not MIN (or some other convergence value in the array). This isn't allowed because the problem states she has to ADD chocolates on each move -> she is not allowed to TAKE away chocolates from all but one in order to equalise.