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# Program to find whether a no is power of two

• Difficulty Level : Easy
• Last Updated : 01 Jul, 2021

Given a positive integer, write a function to find if it is a power of two or not.
Examples :

```Input : n = 4
Output : Yes
22 = 4

Input : n = 7
Output : No

Input : n = 32
Output : Yes
25 = 32```

1. 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

## C++

 `// C++ Program to find whether a``// no is power of two``#include``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 program``int` `main()``{``    ``isPowerOfTwo(31)? cout<<``"Yes"``<

## C

 `// C Program to find whether a``// no is power of two``#include``#include``#include` `/* 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 program``int` `main()``{``    ``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

 `// Java Program to find whether a``// no is power of two``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)``{``    ``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

 `# 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``(isPowerOfTwo(``31``)):``    ``print``(``"Yes"``);``else``:``    ``print``(``"No"``);` `if``(isPowerOfTwo(``64``)):``    ``print``(``"Yes"``);``else``:``    ``print``(``"No"``);``    ` `# This code is contributed``# by mits`

## C#

 `// 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()``{``    ``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)`

## PHP

 ``

## Javascript

 ``

Output:

```No
Yes```

Time Complexity: O(1)
Auxiliary Space: O(1)

2. Another solution is to 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.

## C++

 `#include ``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()``{``    ``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

 `#include``#include` `/* 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 program to test above function*/``int` `main()``{``  ``isPowerOfTwo(31)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);``  ``isPowerOfTwo(64)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);``  ``return` `0;``}`

## Java

 `// 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 program``    ``public` `static` `void` `main(String args[])``    ``{``        ``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.`

## Python3

 `# 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``(isPowerOfTwo(``31``)):``    ``print``(``'Yes'``)``else``:``    ``print``(``'No'``)``if``(isPowerOfTwo(``64``)):``    ``print``(``'Yes'``)``else``:``    ``print``(``'No'``)` `# This code is contributed by Danish Raza`

## C#

 `// 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 program``    ``public` `static` `void` `Main()``    ``{``        ``Console.WriteLine(isPowerOfTwo(31) ? ``"Yes"` `: ``"No"``);``        ``Console.WriteLine(isPowerOfTwo(64) ? ``"Yes"` `: ``"No"``);` `    ``}``}` `// This code is contributed by Sam007`

## PHP

 ``

## Javascript

 ``

Output :

```No
Yes```

Time Complexity: O(log2n)

Auxiliary Space: O(1)

3. Another way is to use this simple recursive solution. It uses the same logic as the above iterative solution but uses recursion instead of iteration.

## C++

 `// C++ program for above approach``#include ``using` `namespace` `std;` `// Function which checks whether a``// number is a power of 2``bool` `powerOf2(``int` `n)``{``    ``// base cases``    ``// '1' is the only odd number``    ``// which is a power of 2(2^0)``    ``if` `(n == 1)``      ``return` `true``;``    ` `    ``// all other odd numbers are not powers of 2``    ``else` `if` `(n % 2 != 0 || n ==0)``      ``return` `false``;``    ` `    ``// recursive function call``    ``return` `powerOf2(n / 2);``}` `// Driver Code``int` `main()``{``    ``int` `n = 64;``//True``    ``int` `m = 12;``//False` `    ``if` `(powerOf2(n) == 1)``      ``cout << ``"True"` `<< endl;` `    ``else` `cout << ``"False"` `<< endl;` `    ``if` `(powerOf2(m) == 1)``      ``cout << ``"True"` `<< endl;` `    ``else``      ``cout << ``"False"` `<< endl;``}` `//code contributed by Moukthik a.k.a rowdyninja`

## Java

 `// Java program for``// the above approach``import` `java.util.*;``class` `GFG{` `// Function which checks``// whether a number is a``// power of 2``static` `boolean` `powerOf2(``int` `n)``{``  ``// base cases``  ``// '1' is the only odd number``  ``// which is a power of 2(2^0)``  ``if` `(n == ``1``)``    ``return` `true``;` `  ``// all other odd numbers are``  ``// not powers of 2``  ``else` `if` `(n % ``2` `!= ``0` `||``           ``n ==``0``)``    ``return` `false``;` `  ``// recursive function call``  ``return` `powerOf2(n / ``2``);``}` `// Driver Code``public` `static` `void` `main(String[] args)``{``  ``//True``  ``int` `n = ``64``;``  ` `  ``//False``  ``int` `m = ``12``;` `  ``if` `(powerOf2(n) == ``true``)``    ``System.out.print(``"True"` `+ ``"\n"``);``  ``else` `System.out.print(``"False"` `+ ``"\n"``);` `  ``if` `(powerOf2(m) == ``true``)``    ``System.out.print(``"True"` `+ ``"\n"``);``  ``else``    ``System.out.print(``"False"` `+ ``"\n"``);``}``}` `// This code is contributed by Princi Singh`

## Python3

 `# Python program for above approach` `# function which checks whether a``# number is a power of 2``def` `powerof2(n):``  ` `    ``# base cases``    ``# '1' is the only odd number``    ``# which is a power of 2(2^0)``    ``if` `n ``=``=` `1``:``        ``return` `True``    ` `    ``# all other odd numbers are not powers of 2``    ``elif` `n``%``2` `!``=` `0` `or` `n ``=``=` `0``:``        ``return` `False``    ` `    ``#recursive function call``    ``return` `powerof2(n``/``2``)``  ` `# Driver Code``if` `__name__ ``=``=` `"__main__"``:``  ` `  ``print``(powerof2(``64``)) ``#True``  ``print``(powerof2(``12``)) ``#False``  ` `#code contributed by Moukthik a.k.a rowdyninja`

## C#

 `// C# program for above approach``using` `System;` `class` `GFG{``    ` `// Function which checks whether a``// number is a power of 2``static` `bool` `powerOf2(``int` `n)``{``    ` `    ``// Base cases``    ``// '1' is the only odd number``    ``// which is a power of 2(2^0)``    ``if` `(n == 1)``      ``return` `true``;``     ` `    ``// All other odd numbers``    ``// are not powers of 2``    ``else` `if` `(n % 2 != 0 || n == 0)``      ``return` `false``;``     ` `    ``// Recursive function call``    ``return` `powerOf2(n / 2);``}` `// Driver code``static` `void` `Main()``{``  ` `    ``int` `n = 64;``//True``    ``int` `m = 12;``//False``    ` `    ``if` `(powerOf2(n))``    ``{``        ``Console.Write(``"True"` `+ ``"\n"``);``    ``}``    ``else``    ``{``        ``Console.Write(``"False"` `+ ``"\n"``);``    ``}``    ` `    ``if` `(powerOf2(m))``    ``{``        ``Console.Write(``"True"``);``    ``}``    ``else``    ``{``        ``Console.Write(``"False"``);``    ``}``}``}` `// This code is contributed by rutvik_56`

## Javascript

 ``
Output
```True
False```

4. 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.

5. 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 –> 01111

So, 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.geeksforgeeks.org/program-to-find-whether-a-no-is-power-of-two/Mohammad for adding this case).

Below is the implementation of this method.

Time complexity : O(1)

Space complexity : O(1)

## C++

 `#include ``using` `namespace` `std;``#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()``{``    ``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

 `#include``#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 program to test above function*/``int` `main()``{``  ``isPowerOfTwo(31)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);``  ``isPowerOfTwo(64)? ``printf``(``"Yes\n"``): ``printf``(``"No\n"``);``  ``return` `0;``}`

## Java

 `// Java program to efficiently``// check for power for 2` `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 method``    ``public` `static` `void` `main(String[] args)``    ``{``         ``System.out.println(isPowerOfTwo(``31``) ? ``"Yes"` `: ``"No"``);``         ``System.out.println(isPowerOfTwo(``64``) ? ``"Yes"` `: ``"No"``);``        ` `    ``}``}``// This program is contributed by Gaurav Miglani   `

## Python

 `# Python program to check if given``# number is power of 2 or not` `# 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``(isPowerOfTwo(``31``)):``    ``print``(``'Yes'``)``else``:``    ``print``(``'No'``)``    ` `if``(isPowerOfTwo(``64``)):``    ``print``(``'Yes'``)``else``:``    ``print``(``'No'``)``    ` `# This code is contributed by Danish Raza   `

## C#

 `// C# program to efficiently``// check for power for 2``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 method``    ``public` `static` `void` `Main()``    ``{``        ``Console.WriteLine(isPowerOfTwo(31) ? ``"Yes"` `: ``"No"``);``        ``Console.WriteLine(isPowerOfTwo(64) ? ``"Yes"` `: ``"No"``);``        ` `    ``}``}` `// This code is contributed by Sam007`

## PHP

 ``

## Javascript

 ``

Output :

```No
Yes```

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.

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