Program to find whether a given number is power of 2
Given a positive integer n, write a function to find if it is a power of 2 or not
Examples:
Input : n = 4
Output : Yes
Explanation: 22 = 4Input : n = 42
Output : No
Explanation: 42 is not a power of 2Input : n = 1
Output : Yes
Explanation: 20 = 1
Finding whether a given number is a power of 2 using Log operator:
A simple method for this is to simply take the log of the number on base 2 and if you get an integer then the number is the power of 2
Below is the implementation of the above approach:
// C++ Program to find whether a
// no is a power of two
#include <bits/stdc++.h>
using namespace std;
// Function to check if x is power of 2
bool isPowerOfTwo(int n)
{
if (n == 0)
return false;
return (ceil(log2(n)) == floor(log2(n)));
}
// Driver code
int main()
{
// Function call
isPowerOfTwo(31) ? cout << "Yes" << endl
: cout << "No" << endl;
isPowerOfTwo(64) ? cout << "Yes" << endl
: cout << "No" << endl;
return 0;
}
// This code is contributed by Surendra_Gangwar
// C Program to find whether a
// no is power of two
#include <math.h>
#include <stdbool.h>
#include <stdio.h>
/* Function to check if x is power of 2*/
bool isPowerOfTwo(int n)
{
if (n == 0)
return false;
return (ceil(log2(n)) == floor(log2(n)));
}
// Driver code
int main()
{
// Function call
isPowerOfTwo(31) ? printf("Yes\n") : printf("No\n");
isPowerOfTwo(64) ? printf("Yes\n") : printf("No\n");
return 0;
}
// This code is contributed by bibhudhendra
// Java Program to find whether a
// no is power of two
import java.lang.Math;
class GFG {
/* Function to check if x is power of 2*/
static boolean isPowerOfTwo(int n)
{
if (n == 0)
return false;
return (int)(Math.ceil((Math.log(n) / Math.log(2))))
== (int)(Math.floor(
((Math.log(n) / Math.log(2)))));
}
// Driver Code
public static void main(String[] args)
{
// Function call
if (isPowerOfTwo(31))
System.out.println("Yes");
else
System.out.println("No");
if (isPowerOfTwo(64))
System.out.println("Yes");
else
System.out.println("No");
}
}
// This code is contributed by mits
# Python3 Program to find
# whether a no is
# power of two
import math
# Function to check
# Log base 2
def Log2(x):
if x == 0:
return false
return (math.log10(x) /
math.log10(2))
# Function to check
# if x is power of 2
def isPowerOfTwo(n):
return (math.ceil(Log2(n)) ==
math.floor(Log2(n)))
# Driver Code
if __name__ == "__main__":
# Function call
if(isPowerOfTwo(31)):
print("Yes")
else:
print("No")
if(isPowerOfTwo(64)):
print("Yes")
else:
print("No")
# This code is contributed
# by mits
// C# Program to find whether
// a no is power of two
using System;
class GFG {
/* Function to check if
x is power of 2*/
static bool isPowerOfTwo(int n)
{
if (n == 0)
return false;
return (int)(Math.Ceiling(
(Math.Log(n) / Math.Log(2))))
== (int)(Math.Floor(
((Math.Log(n) / Math.Log(2)))));
}
// Driver Code
public static void Main()
{
// Function call
if (isPowerOfTwo(31))
Console.WriteLine("Yes");
else
Console.WriteLine("No");
if (isPowerOfTwo(64))
Console.WriteLine("Yes");
else
Console.WriteLine("No");
}
}
// This code is contributed
// by Akanksha Rai(Abby_akku)
<script>
// javascript Program to find whether a
// no is power of two
/* Function to check if x is power of 2 */
function isPowerOfTwo(n)
{
if (n == 0)
return false;
return parseInt( (Math.ceil((Math.log(n) / Math.log(2))))) == parseInt( (Math.floor(((Math.log(n) / Math.log(2))))));
}
// Driver Code
if (isPowerOfTwo(31))
document.write("Yes<br/>");
else
document.write("No<br/>");
if (isPowerOfTwo(64))
document.write("Yes<br/>");
else
document.write("No<br/>");
// This code is contributed by shikhasingrajput.
</script>
<?php
// PHP Program to find
// whether a no is
// power of two
// Function to check
// Log base 2
function Log2($x)
{
return (log10($x) /
log10(2));
}
// Function to check
// if x is power of 2
function isPowerOfTwo($n)
{
return (ceil(Log2($n)) ==
floor(Log2($n)));
}
// Driver Code
// Function call
if(isPowerOfTwo(31))
echo "Yes\n";
else
echo "No\n";
if(isPowerOfTwo(64))
echo "Yes\n";
else
echo "No\n";
// This code is contributed
// by Sam007
?>
Output
No Yes
Time Complexity: O(1)
Auxiliary Space: O(1)
Finding whether a given number is a power of 2 using the modulo & division operator:
Keep dividing the number by two, i.e, do n = n/2 iteratively. In any iteration, if n%2 becomes non-zero and n is not 1 then n is not a power of 2. If n becomes 1 then it is a power of 2.
Below is the implementation of the above approach:
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
/* Function to check if x is power of 2*/
bool isPowerOfTwo(int n)
{
if (n == 0)
return 0;
while (n != 1) {
if (n % 2 != 0)
return 0;
n = n / 2;
}
return 1;
}
// Driver code
int main()
{
// Function call
isPowerOfTwo(31) ? cout << "Yes\n" : cout << "No\n";
isPowerOfTwo(64) ? cout << "Yes\n" : cout << "No\n";
return 0;
}
// This code is contributed by rathbhupendra
// C program for the above approach
#include <stdbool.h>
#include <stdio.h>
/* Function to check if x is power of 2*/
bool isPowerOfTwo(int n)
{
if (n == 0)
return 0;
while (n != 1) {
if (n % 2 != 0)
return 0;
n = n / 2;
}
return 1;
}
// Driver code
int main()
{
// Function call
isPowerOfTwo(31) ? printf("Yes\n") : printf("No\n");
isPowerOfTwo(64) ? printf("Yes\n") : printf("No\n");
return 0;
}
// Java program to find whether
// a no is power of two
import java.io.*;
class GFG {
// Function to check if
// x is power of 2
static boolean isPowerOfTwo(int n)
{
if (n == 0)
return false;
while (n != 1) {
if (n % 2 != 0)
return false;
n = n / 2;
}
return true;
}
// Driver code
public static void main(String args[])
{
// Function call
if (isPowerOfTwo(31))
System.out.println("Yes");
else
System.out.println("No");
if (isPowerOfTwo(64))
System.out.println("Yes");
else
System.out.println("No");
}
}
// This code is contributed by Nikita tiwari.
# Python program to check if given
# number is power of 2 or not
# Function to check if x is power of 2
def isPowerOfTwo(n):
if (n == 0):
return False
while (n != 1):
if (n % 2 != 0):
return False
n = n // 2
return True
# Driver code
if __name__ == "__main__":
# Function call
if(isPowerOfTwo(31)):
print('Yes')
else:
print('No')
if(isPowerOfTwo(64)):
print('Yes')
else:
print('No')
# This code is contributed by Danish Raza
// C# program to find whether
// a no is power of two
using System;
class GFG {
// Function to check if
// x is power of 2
static bool isPowerOfTwo(int n)
{
if (n == 0)
return false;
while (n != 1) {
if (n % 2 != 0)
return false;
n = n / 2;
}
return true;
}
// Driver code
public static void Main()
{
// Function call
Console.WriteLine(isPowerOfTwo(31) ? "Yes" : "No");
Console.WriteLine(isPowerOfTwo(64) ? "Yes" : "No");
}
}
// This code is contributed by Sam007
<script>
/* Function to check if x is power of 2*/
function isPowerOfTwo(n)
{
if (n == 0)
return 0;
while (n != 1)
{
if (n%2 != 0)
return 0;
n = n/2;
}
return 1;
}
isPowerOfTwo(31)? document.write("Yes" + "</br>"): document.write("No" + "</br>");
isPowerOfTwo(64)? document.write("Yes"): document.write("No");
</script>
<?php
// php program for the above approach
// Function to check if
// x is power of 2
function isPowerOfTwo($n)
{
if ($n == 0)
return 0;
while ($n != 1)
{
if ($n % 2 != 0)
return 0;
$n = $n / 2;
}
return 1;
}
// Driver Code
// Function call
if(isPowerOfTwo(31))
echo "Yes\n";
else
echo "No\n";
if(isPowerOfTwo(64))
echo "Yes\n";
else
echo "No\n";
// This code is contributed
// by Sam007
?>
Output
No Yes
Time Complexity: O(log N)
Auxiliary Space: O(1)
Finding whether a given number is a power of 2 by checking the count of set bits:
To solve the problem follow the below idea:
All power of two numbers has only a one-bit set. So count the no. of set bits and if you get 1 then the number is a power of 2. Please see Count set bits in an integer for counting set bits.
Below is the implementation of the above approach:
// C++ program of the above approach
#include <bits/stdc++.h>
using namespace std;
/* Function to check if x is power of 2*/
bool isPowerOfTwo(int n)
{
/* First x in the below expression is for the case when
* x is 0 */
int cnt = 0;
while (n > 0) {
if ((n & 1) == 1) {
cnt++;
}
n = n >> 1; // keep dividing n by 2 using right
// shift operator
}
if (cnt == 1) { // if cnt = 1 only then it is power of 2
return true;
}
return false;
}
// Driver code
int main()
{
// Function call
isPowerOfTwo(31) ? cout << "Yes\n" : cout << "No\n";
isPowerOfTwo(64) ? cout << "Yes\n" : cout << "No\n";
return 0;
}
// This code is contributed by devendra salunke
// Java program of the above approach
import java.io.*;
class GFG {
// Function to check if x is power of 2
static boolean isPowerofTwo(int n)
{
int cnt = 0;
while (n > 0) {
if ((n & 1) == 1) {
cnt++; // if n&1 == 1 keep incrementing cnt
// variable
}
n = n >> 1; // keep dividing n by 2 using right
// shift operator
}
if (cnt == 1) {
// if cnt = 1 only then it is power of 2
return true;
}
return false;
}
// Driver code
public static void main(String[] args)
{
// Function call
if (isPowerofTwo(30) == true)
System.out.println("Yes");
else
System.out.println("No");
if (isPowerofTwo(128) == true)
System.out.println("Yes");
else
System.out.println("No");
}
}
// This code is contributed by devendra salunke.
# Python3 program to check if given
# number is power of 2 or not
# Function to check if x is power of 2
def isPowerOfTwo(n):
cnt = 0
while n > 0:
if n & 1 == 1:
cnt = cnt + 1
n = n >> 1
if cnt == 1:
return 1
return 0
# Driver code
if __name__ == "__main__":
# Function call
if(isPowerOfTwo(31)):
print('Yes')
else:
print('No')
if(isPowerOfTwo(64)):
print('Yes')
else:
print('No')
# This code is contributed by devendra salunke
// C# program to check for power for 2
using System;
class GFG {
// Method to check if x is power of 2
static bool isPowerOfTwo(int n)
{
int cnt = 0; // initialize count to 0
while (n > 0) {
// run loop till n > 0
if ((n & 1) == 1) {
// if n&1 == 1 keep incrementing cnt
// variable
cnt++;
}
n = n >> 1; // keep dividing n by 2 using right
// shift operator
}
if (cnt
== 1) // if cnt = 1 only then it is power of 2
return true;
return false;
}
// Driver code
public static void Main()
{
// Function call
Console.WriteLine(isPowerOfTwo(31) ? "Yes" : "No");
Console.WriteLine(isPowerOfTwo(64) ? "Yes" : "No");
}
}
// This code is contributed by devendra salunke
<script>
// JavaScript code for the above approach
// Function to check if x is power of 2
function isPowerofTwo(n)
{
let cnt = 0;
while (n > 0) {
if ((n & 1) == 1) {
cnt++; // if n&1 == 1 keep incrementing cnt
// variable
}
n = n >> 1; // keep dividing n by 2 using right
// shift operator
}
if (cnt == 1) {
// if cnt = 1 only then it is power of 2
return true;
}
return false;
}
// Driver code
if (isPowerofTwo(30) == true)
document.write("Yes" + "<br/>");
else
document.write("No" + "<br/>");
if (isPowerofTwo(128) == true)
document.write("Yes" + "<br/>");
else
document.write("No" + "<br/>");
// This code is contributed by sanjoy_62.
</script>
Output
No Yes
Time complexity: O(log N)
Auxiliary Space: O(1)
Finding whether a given number is a power of 2 using the AND(&) operator:
To solve the problem follow the below idea:
If we subtract a power of 2 numbers by 1 then all unset bits after the only set bit become set; and the set bit becomes unset.
For example for 4 ( 100) and 16(10000), we get the following after subtracting 1
3 –> 011
15 –> 01111So, if a number n is a power of 2 then bitwise & of n and n-1 will be zero. We can say n is a power of 2 or not based on the value of n&(n-1). The expression n&(n-1) will not work when n is 0. To handle this case also, our expression will become n& (!n&(n-1)) (thanks to https://www.w3wiki.net/program-to-find-whether-a-no-is-power-of-two/Mohammad for adding this case).
Note: With any method which involves subtraction by 1 (just as below, ‘n-1’), some online platforms may give an error if n is given the minimum value of integer or -2147483648. Subtraction by 1 gives integer overflow error in C++.
Below is the implementation of the above approach:
// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;
/* Function to check if x is power of 2*/
bool isPowerOfTwo(int x)
{
if(x<0) return false;
/* First x in the below expression is for the case when
* x is 0 */
return x && (!(x & (x - 1)));
}
// Driver code
int main()
{
// Function call
isPowerOfTwo(31) ? cout << "Yes\n" : cout << "No\n";
isPowerOfTwo(64) ? cout << "Yes\n" : cout << "No\n";
return 0;
}
// This code is contributed by rathbhupendra
// C program for the above approach
#include <stdio.h>
#define bool int
/* Function to check if x is power of 2*/
bool isPowerOfTwo(int x)
{
/* First x in the below expression is for the case when
* x is 0 */
return x && (!(x & (x - 1)));
}
// Driver code
int main()
{
// Function call
isPowerOfTwo(31) ? printf("Yes\n") : printf("No\n");
isPowerOfTwo(64) ? printf("Yes\n") : printf("No\n");
return 0;
}
// Java program for the above approach
class Test {
/* Method to check if x is power of 2*/
static boolean isPowerOfTwo(int x)
{
/* First x in the below expression is
for the case when x is 0 */
return x != 0 && ((x & (x - 1)) == 0);
}
// Driver code
public static void main(String[] args)
{
// Function call
System.out.println(isPowerOfTwo(31) ? "Yes" : "No");
System.out.println(isPowerOfTwo(64) ? "Yes" : "No");
}
}
// This program is contributed by Gaurav Miglani
# Python3 program for the above approach
# Function to check if x is power of 2
def isPowerOfTwo(x):
# First x in the below expression
# is for the case when x is 0
return (x and (not(x & (x - 1))))
# Driver code
if __name__ == "__main__":
# Function call
if(isPowerOfTwo(31)):
print('Yes')
else:
print('No')
if(isPowerOfTwo(64)):
print('Yes')
else:
print('No')
# This code is contributed by Danish Raza
// C# program for the above approach
using System;
class GFG {
// Method to check if x is power of 2
static bool isPowerOfTwo(int x)
{
// First x in the below expression
// is for the case when x is 0
return x != 0 && ((x & (x - 1)) == 0);
}
// Driver code
public static void Main()
{
// Function call
Console.WriteLine(isPowerOfTwo(31) ? "Yes" : "No");
Console.WriteLine(isPowerOfTwo(64) ? "Yes" : "No");
}
}
// This code is contributed by Sam007
<script>
// JavaScript program to efficiently
// check for power for 2
/* Method to check if x is power of 2*/
function isPowerOfTwo (x)
{
/* First x in the below expression is
for the case when x is 0 */
return x!=0 && ((x&(x-1)) == 0);
}
// Driver method
document.write(isPowerOfTwo(31) ? "Yes" : "No");
document.write("<br>"+(isPowerOfTwo(64) ? "Yes" : "No"));
// This code is contributed by 29AjayKumar
</script>
<?php
// php program for the above approach
// Function to check if
// x is power of 2
function isPowerOfTwo ($x)
{
// First x in the below expression
// is for the case when x is 0
return $x && (!($x & ($x - 1)));
}
// Driver Code
// Function call
if(isPowerOfTwo(31))
echo "Yes\n" ;
else
echo "No\n";
if(isPowerOfTwo(64))
echo "Yes\n" ;
else
echo "No\n";
// This code is contributed by Sam007
?>
Output
No Yes
Time Complexity: O(1)
Auxiliary Space: O(1)
Finding whether a given number is a power of 2 using the AND(&) and NOT(~) operator:
To solve the problem follow the below idea:
Another way is to use the logic to find the rightmost bit set of a given number and then check if (n & (~(n-1))) is equal to n or not
Note: With any method which involves subtraction by 1 (just as below, ‘n-1’), some online platforms may give an error if n is given the minimum value of integer or -2147483648. Subtraction by 1 gives integer overflow error in C++.
Below is the implementation of the above approach:
// C++ program of the above approach
#include <bits/stdc++.h>
using namespace std;
/* Function to check if x is power of 2*/
bool isPowerofTwo(long long n)
{
if (n <= 0)
return 0;
if ((n & (~(n - 1))) == n)
return 1;
return 0;
}
// Driver code
int main()
{
// Function call
isPowerofTwo(30) ? cout << "Yes\n" : cout << "No\n";
isPowerofTwo(128) ? cout << "Yes\n" : cout << "No\n";
return 0;
}
// This code is contributed by Sachin
// Java program of the above approach
import java.io.*;
class GFG {
// Function to check if x is power of 2
static boolean isPowerofTwo(int n)
{
if (n == 0)
return false;
if ((n & (~(n - 1))) == n)
return true;
return false;
}
// Driver code
public static void main(String[] args)
{
// Function call
if (isPowerofTwo(30) == true)
System.out.println("Yes");
else
System.out.println("No");
if (isPowerofTwo(128) == true)
System.out.println("Yes");
else
System.out.println("No");
}
}
// This code is contributed by rajsanghavi9.
# Python program of the above approach
# Function to check if x is power of 2*/
def isPowerofTwo(n):
if (n == 0):
return 0
if ((n & (~(n - 1))) == n):
return 1
return 0
# Driver code
if __name__ == "__main__":
# Function call
if(isPowerofTwo(30)):
print('Yes')
else:
print('No')
if(isPowerofTwo(128)):
print('Yes')
else:
print('No')
# This code is contributed by shivanisinghss2110
// C# program of the above approach
using System;
public class GFG {
// Function to check if x is power of 2
static bool isPowerofTwo(int n)
{
if (n == 0)
return false;
if ((n & (~(n - 1))) == n)
return true;
return false;
}
// Driver code
public static void Main(String[] args)
{
// Function call
if (isPowerofTwo(30) == true)
Console.WriteLine("Yes");
else
Console.WriteLine("No");
if (isPowerofTwo(128) == true)
Console.WriteLine("Yes");
else
Console.WriteLine("No");
}
}
// This code contributed by gauravrajput1
<script>
// javascript program of the above approach
// Function to check if x is power of 2
function isPowerofTwo(n)
{
if (n == 0)
return false;
if ((n & (~(n - 1))) == n)
return true;
return false;
}
if (isPowerofTwo(30) == true)
document.write("Yes<br/>");
else
document.write("No<br/>");
if (isPowerofTwo(128) == true)
document.write("Yes<br/>");
else
document.write("No<br/>");
// This code is contributed by umadevi9616
</script>
Output
No Yes
Time complexity: O(1)
Auxiliary Space: O(1)
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