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

• Last Updated : 31 May, 2022

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 ans;```

## Python3

 `# Program to find pairs count``import` `math` `# function to count the required pairs``def` `countPairs(A, n, k):``    ``ans ``=` `0` `    ``# sort the given array``    ``A.sort()``    ` `    ``# for each A[i] traverse rest array``    ``for` `i ``in` `range``(``0``,n):` `        ``for` `j ``in` `range``(i ``+` `1``, n):` `            ``# count Aj such that Ai*k^x = Aj``            ``x ``=` `0` `            ``# increase x till Ai * k^x <= largest element``            ``while` `((A[i] ``*` `math.``pow``(k, x)) <``=` `A[j]) :``                ``if` `((A[i] ``*` `math.``pow``(k, x)) ``=``=` `A[j]) :``                    ``ans``+``=``1``                    ``break``                ``x``+``=``1``    ``return` `ans`  `# driver program``A ``=` `[``3``, ``8``, ``9``, ``12``, ``18``, ``4``, ``24``, ``2``, ``6``]``n ``=` `len``(A)``k ``=` `3` `print``(countPairs(A, n, k))` `# This code is contributed by``# Smitha Dinesh Semwal`

Output :

`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!

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