Check if a number can be expressed as x^y (x raised to power y)
Given a positive integer n, find if it can be expressed as x^y where y > 1 and x > 0. x and y both are integers.
Examples :
Input: n = 8 Output: true 8 can be expressed as 2^3 Input: n = 49 Output: true 49 can be expressed as 7^2 Input: n = 48 Output: false 48 can't be expressed as x^y
We have discussed two different approaches in below post.
Check if a number can be expressed as x^y (x raised to power y).
The idea is find Log n in different bases from 2 to square root of n. If Log n for a base becomes integer then result is true, else result is false.
C++
// CPP program to find if a number// can be expressed as x raised to// power y.#include <bits/stdc++.h>using namespace std;bool isPower(unsigned int n){ // Find Log n in different bases // and check if the value is an // integer for (int x=2; x<=sqrt(n); x++) { float f = log(n) / log(x); if ((f - (int)f) == 0.0) return true; } return false;}// Driver codeint main(){ for (int i = 2; i < 100; i++) if (isPower(i)) cout << i << " "; return 0;} |
Java
// Java program to find if a number// can be expressed as x raised to// power y.class GFG { static boolean isPower(int n) { // Find Log n in different // bases and check if the // value is an integer for (int x = 2; x <= (int)Math.sqrt(n); x++) { float f = (float)Math.log(n) / (float) Math.log(x); if ((f - (int)f) == 0.0) return true; } return false; } // Driver code public static void main(String args[]) { for (int i = 2; i < 100; i++) if (isPower(i)) System.out.print( i + " "); }}// This code is contributed by Sam007 |
Python3
# Python3 program to find if a number# can be expressed as x raised to# power y.import mathdef isPower(n): # Find Log n in different # bases and check if the # value is an integer for x in range(2,int(math.sqrt(n)) + 1): f = math.log(n) / math.log(x); if ((f - int(f)) == 0.0): return True; return False;# Driver codefor i in range(2, 100): if (isPower(i)): print(i, end = " ");# This code is contributed by mits |
C#
// C# program to find if a number// can be expressed as x raised to// power y.using System;class GFG { static bool isPower(int n) { // Find Log n in different // bases and check if the // value is an integer for (int x = 2; x <= (int)Math.Sqrt(n); x++) { float f = (float)Math.Log(n) / (float) Math.Log(x); if ((f - (int)f) == 0.0) return true; } return false; } // Driver Code public static void Main() { for (int i = 2; i < 100; i++) if (isPower(i)) Console.Write( i + " "); } }// This code is contributed by Sam007 |
PHP
<?php// PHP program to find if a number// can be expressed as x raised to// power y.function isPower($n){ // Find Log n in different // bases and check if the // value is an integer for ($x = 2; $x <= sqrt($n); $x++) { $f = log($n) / log($x); if (($f - (int)$f) == 0.0) return true; } return false;}// Driver codefor ($i = 2; $i < 100; $i++) if (isPower((int)$i)) echo $i." ";// This code is contributed by Sam007?> |
Javascript
<script>// javascript program to find if a number// can be expressed as x raised to// power y. function isPower(n) { // Find Log n in different // bases and check if the // value is an integer for (x = 2; x <= parseInt( Math.sqrt(n)); x++) { var f = Math.log(n) / Math.log(x); if ((f - parseInt( f)) == 0.0) return true; } return false; } // Driver code for (i = 2; i < 100; i++) if (isPower(i)) document.write(i + " ");// This code contributed by Rajput-Ji</script> |
Output:
4 8 9 16 25 27 32 36 49 64 81
Time Complexity : O(sqrt(N))
Auxiliary Space : O(1) ,as we are not using any extra space
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