Print all array elements having frequencies equal to powers of K in ascending order

Given an array arr[] consisting of N integers and a positive integer K, the task is to find the array elements having frequencies in the power of K i.e., K¹, K², K³, and so on.

Examples:

Input: arr[] = {1, 3, 2, 1, 2, 2, 2, 3, 3, 4}, K = 2
Output: 1 2
Explanation:
The frequency of 1 is 2, that can be represented as the power of K( = 2), i.e., 2¹.
The frequency of 2 is 4, that can be represented as the power of K( = 2), i.e., 2².

Input: arr[] = {6, 1, 3, 1, 2, 2, 1}, K = 2
Output: 2 3 6

Naive Approach: The simplest approach is to count the frequencies of each array element and if the frequency of any element is a perfect power of K, then print that element. Otherwise, check for the next element.

Time Complexity: O(N²)
Auxiliary Space: O(1)

Efficient Approach: The above approach can also be optimized by using Hashing for storing the frequency of arrays elements in a HashMap and then check for the required conditions. Follow the steps below to solve the given problem:

• Traverse the given array arr[] and store the frequency of each array element in a Map, say M.
• Now, traverse the map and perform the following steps:
  • Store the frequency of each value in the map in a variable, say F.
  • If the value of (log F)/(log K) and K^{(log F)/(log K)} are the same, then the current element has the frequency as the perfect power of K. Therefore, print the current element.

Below is the implementation of the above approach:

3 2 1 4

Time Complexity: O(N)
Auxiliary Space: O(N)