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*(kx) 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;
<?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
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!