MaxCounters

You are given N counters, initially set to 0, and you have two possible operations on them:

increase(X) − counter X is increased by 1,
max counter − all counters are set to the maximum value of any counter.
A non-empty array A of M integers is given. This array represents consecutive operations:

if A[K] = X, such that 1 ≤ X ≤ N, then operation K is increase(X),
if A[K] = N + 1 then operation K is max counter.
For example, given integer N = 5 and array A such that:

    A[0] = 3
    A[1] = 4
    A[2] = 4
    A[3] = 6
    A[4] = 1
    A[5] = 4
    A[6] = 4
the values of the counters after each consecutive operation will be:

    (0, 0, 1, 0, 0)
    (0, 0, 1, 1, 0)
    (0, 0, 1, 2, 0)
    (2, 2, 2, 2, 2)
    (3, 2, 2, 2, 2)
    (3, 2, 2, 3, 2)
    (3, 2, 2, 4, 2)
The goal is to calculate the value of every counter after all operations.

Write a function:

function solution($N, $A);

that, given an integer N and a non-empty array A consisting of M integers, returns a sequence of integers representing the values of the counters.

Result array should be returned as an array of integers.

For example, given:

    A[0] = 3
    A[1] = 4
    A[2] = 4
    A[3] = 6
    A[4] = 1
    A[5] = 4
    A[6] = 4
the function should return [3, 2, 2, 4, 2], as explained above.

Write an efficient algorithm for the following assumptions:

N and M are integers within the range [1..100,000];
each element of array A is an integer within the range [1..N + 1].


************************************** SOLUTION **********************************************

function solution($N, $A) {
    
    if (empty($A)) {
        return 0; 
    }
    
    $arrayASize = sizeof($A);
    
    if ((is_integer($N) && ($N >= 1 && $N <= 100000)) && 
       ($arrayASize >= 1 && $arrayASize <= 100000)) {
        
        $counters = array_fill(0, $N, 0);
            
        foreach ($A as $key => $value) {

            if (is_integer($value) && ($value >= 1 && $value <= $N + 1)) {


                if ($value >= 1 && $value <= $N) {
                    $counters[$value - 1] += 1;
                } 

                if ($value == $N + 1) {

                    $counters = array_fill(0, sizeof($counters), max($counters));            
                }
                
            }
        }
        
    }
    
    return $counters;
}