Check if a number is power of 8 or not

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 8

class 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 8
from 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 Code
n = 65
if 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 8
using 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. 

1. 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.
2. 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 8
static boolean checkPowerof8(int n)
{
  return (n > 0 && (n & (n - 1)) > 0 &&
         (n & 0xB6DB6DB6) > 0);
}

// Driver code
public 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 8
def checkPowerof8(n):

    return (n and not (n & (n - 1)) and
                  not (n & 0xB6DB6DB6))

# Driver Code
if __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 8
static bool checkPowerof8(int n)
{
    return (n > 0 && (n & (n - 1)) > 0 &&
           (n & 0xB6DB6DB6) > 0);
}

// Driver code
static 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 8
function 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 8
bool 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 code
int main()
{
    int n = 65;
    if (checkPowerof8(n))
        cout << "Yes";
    else
        cout << "No";

    return 0;
}

Java

// Java implementation of the approach
import java.io.*;

class GFG
{

// Function to check if n is power of 8
static 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 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 Tushil.

Python3

# Python3 implementation of the approach

# Function to check if n is power of 8
def 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 code
if __name__ == '__main__':

    n = 65
    if (checkPowerof8(n)):
        print("Yes")
    else:
        print("No")

# This code is contributed by math_lover

C#

// C# implementation of the approach
using System;

class GFG
{

// Function to check if n is power of 8
static 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 code
static 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 8
function 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)