Given a number check whether it is a power of 8 or not.
Examples :
Input : n = 64 Output : Yes Input : 75 Output : No
First solution
We calculate log8(n) of the number if it is an integer, then n is in the power of 8. We use trunc(n) function that finds the closest integer for a double value.
C++
// C++ program to check if a number is power of 8#include <cmath>#include <iostream>using namespace std;/* function to check if power of 8 */bool checkPowerof8(int n){ /* calculate log8(n) */ double i = log(n) / log(8); /* check if i is an integer or not */ return (i - trunc(i) < 0.000001);}/* driver function */int main(){ int n = 65; checkPowerof8(n) ? cout << "Yes" : cout << "No"; return 0;} |
Java
// Java program to check if// a number is power of 8class GFG { // function to check // if power of 8 static boolean checkPowerof8(int n) { /* calculate log8(n) */ double i = Math.log(n) / Math.log(8); /* check if i is an integer or not */ return (i - Math.floor(i) < 0.000001); } // Driver Code public static void main(String args[]) { int n = 65; if (checkPowerof8(n)) System.out.println("Yes"); else System.out.println("No"); }}// This code is contributed by Sam007 |
Python3
# Python3 program to check # if a number is power of 8from math import log,trunc# function to check if power of 8 def checkPowerof8(n): # calculate log8(n) i = log(n, 8) # check if i is an integer or not return (i - trunc(i) < 0.000001);# Driver Coden = 65if checkPowerof8(n): print("Yes")else: print("No")# This code is contributed by Mohit Kumar |
C#
// C# program to check if// a number is power of 8using System;class GFG { // function to check // if power of 8 static bool checkPowerof8(int n) { // calculate log8(n) */ double i = Math.Log(n) / Math.Log(8); // check if i is an integer or not */ return (i - Math.Floor(i) < 0.000001); } // Driver Code static public void Main() { int n = 65; if (checkPowerof8(n)) Console.WriteLine("Yes"); else Console.WriteLine("No"); }}// This code is contributed by akt_mit |
PHP
<?php// PHP program to check if // a number is power of 8 // function to check // if power of 8 function checkPowerof8($n) { /* calculate log8(n) */ $i = log($n) / log(8); /* check if i is an integer or not */ return ($i - floor($i) < 0.000001); } // Driver Code $n = 65; if(checkPowerof8($n)) echo "Yes"; else echo "No"; // This code is contributed // by Sach_Code?> |
Javascript
<script> // Javascript program to check if // a number is power of 8 // function to check // if power of 8 function checkPowerof8(n) { // calculate log8(n) */ let i = Math.log(n) / Math.log(8); // check if i is an integer or not */ return (i - Math.floor(i) < 0.000001); } let n = 65; if (checkPowerof8(n)) document.write("Yes"); else document.write("No"); </script> |
Output :
No
Time Complexity: O(1)
Auxiliary Space: O(1)
Second solution
A number is a power of 8 if the following conditions are satisfied.
- The number is the power of two. A number is the power of two if it has only one set bit, i.e., bitwise and of n and n-1 is 0.
- The number has its only set a bit at position 0 or 3 or 6 or …. 30 [For a 32-bit number]. To check the position of its set bit we can use a mask (0xB6DB6DB6)16 = (10110110110110110110110110110110)2.
Below is the implementation of the above idea.
C++
// C++ program to check if a number is power of 8// using bit mask.#include <bits/stdc++.h>using namespace std;/*function to check if power of 8*/bool checkPowerof8(int n){ return (n && !(n & (n - 1)) && !(n & 0xB6DB6DB6));}/*driver function*/int main(){ int n = 65; checkPowerof8(n) ? cout << "Yes" : cout << "No"; return 0;} |
Java
// Java program to check if a// number is power of 8 using // bit mask.import java.util.*;class GFG{// function to check if // power of 8static boolean checkPowerof8(int n){ return (n > 0 && (n & (n - 1)) > 0 && (n & 0xB6DB6DB6) > 0);}// Driver codepublic static void main(String[] args){ int n = 65; if (checkPowerof8(n) == true) System.out.print("Yes" ); else System.out.print("No");}}// This code is contributed by 29AjayKumar |
Python3
# Python3 program to check if a number # is power of 8# function to check if power of 8def checkPowerof8(n): return (n and not (n & (n - 1)) and not (n & 0xB6DB6DB6))# Driver Codeif __name__ == "__main__": n = 65 if checkPowerof8(n): print ("Yes") else: print ("No")# This code is contributed by ita_c |
C#
// C# program to check if a// number is power of 8 using // bit mask.using System;class GFG{ // Function to check if // power of 8static bool checkPowerof8(int n){ return (n > 0 && (n & (n - 1)) > 0 && (n & 0xB6DB6DB6) > 0);}// Driver codestatic public void Main(){ int n = 65; if (checkPowerof8(n) == true) { Console.WriteLine("Yes"); } else { Console.WriteLine("No"); }}}// This code is contributed by avanitrachhadiya2155 |
PHP
<?php// PHP program to check if a number // is power of 8 using bit mask. // function to check if power of 8function checkPowerof8($n) { $t = ($n && !($n & ($n - 1)) && !($n & 0xB6DB6DB6)); return $t; } // Driver Code$n = 65; if(checkPowerof8($n)) echo "Yes" ;else echo "No"; // This code is contributed by Sach ?> |
Javascript
<script>/*function to check if power of 8*/function checkPowerof8( n){ return (n && !(n & (n - 1)) && !(n & 0xB6DB6DB6));}var n = 65; if(checkPowerof8(n)) document.write("Yes" ); else document.write("No");</script> |
Output :
No
Time Complexity: O(1)
Auxiliary Space: O(1)
One simple observation that can be made here is that if a number is the power of 8 then it has only a one-bit set and that bit is at positions 1, 4, 7, 10, …
Thus, we can just check if the only bit set in the number is at one of these positions then it is a power of 8 otherwise not.
Below is the implementation of the above approach:
C++
// C++ implementation of the approach#include <bits/stdc++.h>using namespace std;// Function to check if n is power of 8bool checkPowerof8(int n){ // Variable i will denote the bit // that we are currently at int i = 0; unsigned long long l = 1; while (i <= 63) { l <<= i; // If only set bit in n // is at position i if (l == n) return true; // Get to next valid bit position i += 3; l = 1; } return false;}// Driver codeint main(){ int n = 65; if (checkPowerof8(n)) cout << "Yes"; else cout << "No"; return 0;} |
Java
// Java implementation of the approachimport java.io.*;class GFG { // Function to check if n is power of 8static boolean checkPowerof8(int n){ // Variable i will denote the bit // that we are currently at int i = 0; long l = 1; while (i <= 63) { l <<= i; // If only set bit in n // is at position i if (l == n) return true; // Get to next valid bit position i += 3; l = 1; } return false;}// Driver codepublic static void main (String[] args){ int n = 65; if (checkPowerof8(n)) System.out.println ("Yes"); else System.out.println( "No");}}// This code is contributed by Tushil. |
Python3
# Python3 implementation of the approach# Function to check if n is power of 8def checkPowerof8(n): # Variable i will denote the bit # that we are currently at i = 0 l = 1 while (i <= 63): l <<= i # If only set bit in n # is at position i if (l == n): return True # Get to next valid bit position i += 3 l = 1 return False # Driver codeif __name__ == '__main__': n = 65 if (checkPowerof8(n)): print("Yes") else: print("No")# This code is contributed by math_lover |
C#
// C# implementation of the approachusing System;class GFG{ // Function to check if n is power of 8static bool checkPowerof8(int n){ // Variable i will denote the bit // that we are currently at int i = 0; long l = 1; while (i <= 63) { l <<= i; // If only set bit in n // is at position i if (l == n) return true; // Get to next valid bit position i += 3; l = 1; } return false;}// Driver codestatic public void Main (){ int n = 65; if (checkPowerof8(n)) Console.WriteLine("Yes"); else Console.WriteLine( "No");}}// This code is contributed by ajit. |
Javascript
<script>// Function to check if n is power of 8function checkPowerof8( n){ // Variable i will denote the bit // that we are currently at var i = 0; var l= 1; while (i <= 63) { l<<=i; // If only set bit in n // is at position i if (l == n) return 1; // Get to next valid bit position i += 3; l = 1; } return 0;}var n = 65; if (checkPowerof8(n)) document.write( "Yes"); else document.write("No");</script> |
Output :
No
Time Complexity: O(1)
Auxiliary Space: O(1)
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