PHP Program for Pairs such that one is a power multiple of other

You are given an array A[] of n-elements and a positive integer k (k > 1). Now you have find the number of pairs Ai, Aj such that Ai = Aj*(k^x) where x is an integer. 
Note: (Ai, Aj) and (Aj, Ai) must be count once.

Examples : 

Input : A[] = {3, 6, 4, 2},  k = 2
Output : 2
Explanation : We have only two pairs 
(4, 2) and (3, 6)

Input : A[] = {2, 2, 2},   k = 2
Output : 3
Explanation : (2, 2), (2, 2), (2, 2) 
that are (A1, A2), (A2, A3) and (A1, A3) are 
total three pairs where Ai = Aj * (k^0) 

 To solve this problem, we first sort the given array and then for each element Ai, we find number of elements equal to value Ai * k^x for different value of x till Ai * k^x is less than or equal to largest of Ai. 

Algorithm: 

    // sort the given array
    sort(A, A+n);

    // for each A[i] traverse rest array
    for (int i=0; i ? n-1; i++)
    {
        for (int j=i+1; j ? n-1; j++)
        {
            // count Aj such that Ai*k^x = Aj
            int x = 0;

            // increase x till Ai * k^x ? 
            // largest element
            while ((A[i]*pow(k, x)) ? A[j])
            {
                if ((A[i]*pow(k, x)) == A[j])
                {              
                     ans++;
                     break;
                }
                x++;
            }        
        }   
    }
    // return answer
    return ans;

 Below is the implementation of above approach:

<?php
// PHP Program to find pairs count

// function to count
// the required pairs
function countPairs($A, $n, $k) 
{
$ans = 0;

// sort the given array
sort($A);

// for each A[i] 
// traverse rest array
for ($i = 0; $i < $n; $i++) 
{
    for ($j = $i + 1; $j < $n; $j++) 
    {

    // count Aj such that Ai*k^x = Aj
    $x = 0;

    // increase x till Ai * 
    // k^x <= largest element
    while (($A[$i] * pow($k, $x)) <= $A[$j]) 
    {
        if (($A[$i] * pow($k, $x)) == $A[$j]) 
        {
        $ans++;
        break;
        }
        $x++;
    }
    }
}
return $ans;
}

// Driver Code

$A = array(3, 8, 9, 12, 18, 
              4, 24, 2, 6);
$n = count($A);
$k = 3;
echo countPairs($A, $n, $k);

// This code is contributed by anuj_67.
?>

6

Complexity Analysis: 

• Time Complexity: O(n*n), as nested loops are used
• Auxiliary Space: O(1), as no extra space is used

Please refer complete article on Pairs such that one is a power multiple of other for more details!