# Elements of Array which can be expressed as power of some integer to given exponent K

Given an array arr[] of size N, and an integer K, the task is to print all the elements of the Array which can be expressed as a power of some integer (X) to the exponent K, i.e. XK.

Examples:

Input: arr[] = {46656, 64, 256, 729, 16, 1000}, K = 6
Output: 46656 64 729
Explanation:
Only numbers 46656, 64, 729 can be expressed as a power of 6.
46656 = 66,
64 = 26,
729 = 36

Input: arr[] = {23, 81, 256, 125, 16, 1000}, K = 4
Output: 81 256 16
Explanation:
The number 81, 256, 16 can be expressed as a power of 4.

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

Approach: To solve the problem mentioned above the main idea is to for each number in the Array, find the N-th root of a number. Then check whether this number is an integer or not. If yes, then print it, else skip to the next number.

Below is the implementation of the above approach:

## CPP

 `// C++ implementation to print elements of ` `// the Array which can be expressed as ` `// power of some integer to given exponent K ` ` `  `#include ` `using` `namespace` `std; ` `#define ll long long ` ` `  `// Method returns Nth power of A ` `double` `nthRoot(ll A, ll N) ` `{ ` ` `  `    ``double` `xPre = 7; ` ` `  `    ``// Smaller eps, denotes more accuracy ` `    ``double` `eps = 1e-3; ` ` `  `    ``// Initializing difference between two ` `    ``// roots by INT_MAX ` `    ``double` `delX = INT_MAX; ` ` `  `    ``// x^K denotes current value of x ` `    ``double` `xK; ` ` `  `    ``// loop untill we reach desired accuracy ` `    ``while` `(delX > eps) { ` ` `  `        ``// calculating current value from previous ` `        ``// value by newton's method ` `        ``xK = ((N - 1.0) * xPre ` `              ``+ (``double``)A / ``pow``(xPre, N - 1)) ` `             ``/ (``double``)N; ` ` `  `        ``delX = ``abs``(xK - xPre); ` `        ``xPre = xK; ` `    ``} ` ` `  `    ``return` `xK; ` `} ` ` `  `// Function to check ` `// whether its k root ` `// is an integer or not ` `bool` `check(ll no, ``int` `k) ` `{ ` `    ``double` `kth_root = nthRoot(no, k); ` `    ``ll num = kth_root; ` ` `  `    ``if` `(``abs``(num - kth_root) < 1e-4) ` `        ``return` `true``; ` ` `  `    ``return` `false``; ` `} ` ` `  `// Function to find the numbers ` `void` `printExpo(ll arr[], ``int` `n, ``int` `k) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(check(arr[i], k)) ` `            ``cout << arr[i] << ``" "``; ` `    ``} ` `} ` ` `  `// Driver code ` `int` `main() ` `{ ` ` `  `    ``int` `K = 6; ` ` `  `    ``ll arr[] = { 46656, 64, 256, ` `                 ``729, 16, 1000 }; ` `    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]); ` ` `  `    ``printExpo(arr, n, K); ` ` `  `    ``return` `0; ` `} `

## Java

 `// Java implementation to print elements of ` `// the Array which can be expressed as ` `// power of some integer to given exponent K ` ` `  `class` `GFG{ ` `  `  `// Method returns Nth power of A ` `static` `double` `nthRoot(``long` `A, ``long` `N) ` `{ ` `  `  `    ``double` `xPre = ``7``; ` `  `  `    ``// Smaller eps, denotes more accuracy ` `    ``double` `eps = 1e-``3``; ` `  `  `    ``// Initializing difference between two ` `    ``// roots by Integer.MAX_VALUE ` `    ``double` `delX = Integer.MAX_VALUE; ` `  `  `    ``// x^K denotes current value of x ` `    ``double` `xK = ``0``; ` `  `  `    ``// loop untill we reach desired accuracy ` `    ``while` `(delX > eps) { ` `  `  `        ``// calculating current value from previous ` `        ``// value by newton's method ` `        ``xK = ((N - ``1.0``) * xPre ` `              ``+ (``double``)A / Math.pow(xPre, N - ``1``)) ` `             ``/ (``double``)N; ` `  `  `        ``delX = Math.abs(xK - xPre); ` `        ``xPre = xK; ` `    ``} ` `  `  `    ``return` `xK; ` `} ` `  `  `// Function to check ` `// whether its k root ` `// is an integer or not ` `static` `boolean` `check(``long` `no, ``int` `k) ` `{ ` `    ``double` `kth_root = nthRoot(no, k); ` `    ``long` `num = (``long``) kth_root; ` `  `  `    ``if` `(Math.abs(num - kth_root) < 1e-``4``) ` `        ``return` `true``; ` `  `  `    ``return` `false``; ` `} ` `  `  `// Function to find the numbers ` `static` `void` `printExpo(``long` `arr[], ``int` `n, ``int` `k) ` `{ ` `    ``for` `(``int` `i = ``0``; i < n; i++) { ` `        ``if` `(check(arr[i], k)) ` `            ``System.out.print(arr[i]+ ``" "``); ` `    ``} ` `} ` `  `  `// Driver code ` `public` `static` `void` `main(String[] args) ` `{ ` `  `  `    ``int` `K = ``6``; ` `  `  `    ``long` `arr[] = { ``46656``, ``64``, ``256``, ` `                 ``729``, ``16``, ``1000` `}; ` `    ``int` `n = arr.length; ` `  `  `    ``printExpo(arr, n, K); ` `  `  `} ` `} ` ` `  `// This code is contributed by sapnasingh4991 `

## Python3

 `# Python3 implementation to prelements of ` `# the Array which can be expressed as ` `# power of some integer to given exponent K ` ` `  `# Method returns Nth power of A ` `def` `nthRoot(A, N): ` ` `  `    ``xPre ``=` `7` ` `  `    ``# Smaller eps, denotes more accuracy ` `    ``eps ``=` `1e``-``3` ` `  `    ``# Initializing difference between two ` `    ``# roots by INT_MAX ` `    ``delX ``=` `10``*``*``9` ` `  `    ``# x^K denotes current value of x ` `    ``xK ``=` `0` ` `  `    ``# loop untiwe reach desired accuracy ` `    ``while` `(delX > eps): ` ` `  `        ``# calculating current value from previous ` `        ``# value by newton's method ` `        ``xK ``=` `((N ``-` `1.0``) ``*` `xPre``+` `A ``/``pow``(xPre, N ``-` `1``))``/` `N ` ` `  `        ``delX ``=` `abs``(xK ``-` `xPre) ` `        ``xPre ``=` `xK ` ` `  `    ``return` `xK ` ` `  `# Function to check ` `# whether its k root ` `# is an integer or not ` `def` `check(no, k): ` `    ``kth_root ``=` `nthRoot(no, k) ` `    ``num ``=` `int``(kth_root) ` ` `  `    ``if` `(``abs``(num ``-` `kth_root) < ``1e``-``4``): ` `        ``return` `True` ` `  `    ``return` `False` ` `  `# Function to find the numbers ` `def` `printExpo(arr, n, k): ` `    ``for` `i ``in` `range``(n): ` `        ``if` `(check(arr[i], k)): ` `            ``print``(arr[i],end``=``" "``) ` ` `  `# Driver code ` `if` `__name__ ``=``=` `'__main__'``: ` ` `  `    ``K ``=` `6` ` `  `    ``arr ``=` `[``46656``, ``64``, ``256``,``729``, ``16``, ``1000``] ` `    ``n ``=` `len``(arr) ` ` `  `    ``printExpo(arr, n, K) ` ` `  `# This code is contributed by mohit kumar 29 `

## C#

 `// C# implementation to print elements of ` `// the Array which can be expressed as ` `// power of some integer to given exponent K ` `using` `System; ` ` `  `class` `GFG{ ` `   `  `// Method returns Nth power of A ` `static` `double` `nthRoot(``long` `A, ``long` `N) ` `{ ` `   `  `    ``double` `xPre = 7; ` `   `  `    ``// Smaller eps, denotes more accuracy ` `    ``double` `eps = 1e-3; ` `   `  `    ``// Initializing difference between two ` `    ``// roots by int.MaxValue ` `    ``double` `delX = ``int``.MaxValue; ` `   `  `    ``// x^K denotes current value of x ` `    ``double` `xK = 0; ` `   `  `    ``// loop untill we reach desired accuracy ` `    ``while` `(delX > eps) { ` `   `  `        ``// calculating current value from previous ` `        ``// value by newton's method ` `        ``xK = ((N - 1.0) * xPre ` `              ``+ (``double``)A / Math.Pow(xPre, N - 1)) ` `             ``/ (``double``)N; ` `   `  `        ``delX = Math.Abs(xK - xPre); ` `        ``xPre = xK; ` `    ``} ` `   `  `    ``return` `xK; ` `} ` `   `  `// Function to check ` `// whether its k root ` `// is an integer or not ` `static` `bool` `check(``long` `no, ``int` `k) ` `{ ` `    ``double` `kth_root = nthRoot(no, k); ` `    ``long` `num = (``long``) kth_root; ` `   `  `    ``if` `(Math.Abs(num - kth_root) < 1e-4) ` `        ``return` `true``; ` `   `  `    ``return` `false``; ` `} ` `   `  `// Function to find the numbers ` `static` `void` `printExpo(``long` `[]arr, ``int` `n, ``int` `k) ` `{ ` `    ``for` `(``int` `i = 0; i < n; i++) { ` `        ``if` `(check(arr[i], k)) ` `            ``Console.Write(arr[i]+ ``" "``); ` `    ``} ` `} ` `   `  `// Driver code ` `public` `static` `void` `Main(String[] args) ` `{ ` `   `  `    ``int` `K = 6; ` `   `  `    ``long` `[]arr = { 46656, 64, 256, ` `                 ``729, 16, 1000 }; ` `    ``int` `n = arr.Length; ` `   `  `    ``printExpo(arr, n, K); ` `   `  `} ` `} ` ` `  `// This code is contributed by Princi Singh `

Output:

```46656 64 729
```

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