Smallest power of 2 greater than or equal to n

Write a function that, for a given no n, finds a number p which is greater than or equal to n and is a smallest power of 2.
Examples :

Input : n = 5
Output: 8

Input  : n = 17
Output : 32

Input  : n = 32
Output : 32

There are plenty of solutions for this. Let us take the example of 17 to explain some of them.

Method 1(Using Log of the number)

1.  Calculate Position of set bit in p(next power of 2):
pos =  ceil(lgn)  (ceiling of log n with base 2)
2.  Now calculate p:
p   = pow(2, pos)

Example :

Let us try for 17
pos = 5
p   = 32

Method 2 (By getting the position of only set bit in result )

/* If n is a power of 2 then return n */
1  If (n & !(n&(n-1))) then return n
2  Else keep right shifting n until it becomes zero
and count no of shifts
a. Initialize: count = 0
b. While n ! = 0
n = n>>1
count = count + 1

/* Now count has the position of set bit in result */
3  Return (1 << count)

Example :

Let us try for 17
count = 5
p     = 32

C++

 // C++ program to find  // smallest power of 2  // greater than or equal to n #include using namespace std;    unsigned int nextPowerOf2(unsigned int n)  {      unsigned count = 0;             // First n in the below condition      // is for the case where n is 0      if (n && !(n & (n - 1)))          return n;             while( n != 0)      {          n >>= 1;          count += 1;      }             return 1 << count;  }     // Driver Code  int main()  {      unsigned int n = 0;      cout << nextPowerOf2(n);      return 0;  }     // This code is contributed by rathbhupendra

C

 #include    unsigned int nextPowerOf2(unsigned int n) { unsigned count = 0;    // First n in the below condition // is for the case where n is 0 if (n && !(n & (n - 1)))     return n;    while( n != 0) {     n >>= 1;     count += 1; }    return 1 << count; }    // Driver Code int main() { unsigned int n = 0; printf("%d", nextPowerOf2(n)); return 0; }

Java

 // Java program to find  // smallest power of 2  // greater than or equal to n import java.io.*;    class GFG {     static int nextPowerOf2(int n)     {         int count = 0;            // First n in the below          // condition is for the          // case where n is 0         if (n > 0 && (n & (n - 1)) == 0)             return n;            while(n != 0)         {             n >>= 1;             count += 1;         }            return 1 << count;     }        // Driver Code     public static void main(String args[])     {         int n = 0;         System.out.println(nextPowerOf2(n));     } }    // This article is contributed // by Anshika Goyal.

Python3

 def nextPowerOf2(n):     count = 0;        # First n in the below      # condition is for the      # case where n is 0     if (n and not(n & (n - 1))):         return n            while( n != 0):         n >>= 1         count += 1            return 1 << count;       # Driver Code n = 0 print(nextPowerOf2(n)) # This code is contributed # by Smitha Dinesh Semwal

C#

 // C# program to find smallest  // power of 2 greater than  // or equal to n using System;    class GFG {     static int nextPowerOf2(int n)     {         int count = 0;            // First n in the below          // condition is for the         // case where n is 0         if (n > 0 && (n & (n - 1)) == 0)             return n;            while(n != 0)         {             n >>= 1;             count += 1;         }            return 1 << count;     }        // Driver Code     public static void Main()     {         int n = 0;         Console.WriteLine(nextPowerOf2(n));     } }    // This code is contributed by anuj_67.

PHP

 >= 1;     \$count += 1; }    return 1 << \$count; }    // Driver Code \$n = 0; echo (nextPowerOf2(\$n));    // This code is contributed by vt_m ?>

Output :

1

Method 3(Shift result one by one)

Thanks to coderyogi for suggesting this method . This method is a variation of method 2 where instead of getting count, we shift the result one by one in a loop.

C

 #include unsigned int nextPowerOf2(unsigned int n) {     unsigned int p = 1;     if (n && !(n & (n - 1)))         return n;        while (p < n)          p <<= 1;            return p; }    // Driver Code int main() { unsigned int n = 5; printf("%d", nextPowerOf2(n)); return 0; }

Java

 // Java program to find smallest  // power of 2 greater than or  // equal to n import java.io.*;    class GFG {     static int nextPowerOf2(int n)     {         int p = 1;         if (n > 0 && (n & (n - 1)) == 0)             return n;            while (p < n)              p <<= 1;                return p;     }        // Driver Code     public static void main(String args[])     {         int n = 5;         System.out.println(nextPowerOf2(n));     } }    // This article is contributed // by Anshika Goyal.

Python3

 def nextPowerOf2(n):        p = 1     if (n and not(n & (n - 1))):         return n        while (p < n) :         p <<= 1                return p;       # Driver Code n = 5 print(nextPowerOf2(n));    # This code is contributed by # Smitha Dinesh Semwal

C#

 // C# program to find smallest  // power of 2 greater than or  // equal to n using System;    class GFG  {        static int nextPowerOf2(int n)     {         int p = 1;         if (n > 0 && (n & (n - 1)) == 0)             return n;            while (p < n)              p <<= 1;                return p;     }        // Driver Code     public static void Main()     {         int n = 5;         Console.Write(nextPowerOf2(n));     } }    // This code is contributed by Smitha.

PHP



Output :

8

Time Complexity: O(lgn)

Method 4(Customized and Fast)

1. Subtract n by 1
n = n -1

2. Set all bits after the leftmost set bit.

/* Below solution works only if integer is 32 bits */
n = n | (n >> 1);
n = n | (n >> 2);
n = n | (n >> 4);
n = n | (n >> 8);
n = n | (n >> 16);
3. Return n + 1

Example :

Steps 1 & 3 of above algorithm are to handle cases
of power of 2 numbers e.g., 1, 2, 4, 8, 16,

Let us try for 17(10001)
step 1
n = n - 1 = 16 (10000)
step 2
n = n | n >> 1
n = 10000 | 01000
n = 11000
n = n | n >> 2
n = 11000 | 00110
n = 11110
n = n | n >> 4
n = 11110 | 00001
n = 11111
n = n | n >> 8
n = 11111 | 00000
n = 11111
n = n | n >> 16
n = 11110 | 00000
n = 11111

step 3: Return n+1
We get n + 1 as 100000 (32)

Program:

C

 #include // Finds next power of two  // for n. If n itself is a  // power of two then returns n unsigned int nextPowerOf2(unsigned int n) {     n--;     n |= n >> 1;     n |= n >> 2;     n |= n >> 4;     n |= n >> 8;     n |= n >> 16;     n++;     return n; }    // Driver Code  int main() {     unsigned int n = 5;     printf("%d", nextPowerOf2(n));     return 0; }

Java

 // Java program to find smallest  // power of 2 greater than or // equal to n import java.io.*;    class GFG {     // Finds next power of two      // for n. If n itself is a     // power of two then returns n     static int nextPowerOf2(int n)     {         n--;         n |= n >> 1;         n |= n >> 2;         n |= n >> 4;         n |= n >> 8;         n |= n >> 16;         n++;                    return n;     }        // Driver Code     public static void main(String args[])     {         int n = 5;         System.out.println(nextPowerOf2(n));     } }     // This article is contributed  // by Anshika Goyal.

Python 3

 # Finds next power of two # for n. If n itself is a # power of two then returns n def nextPowerOf2(n):        n -= 1     n |= n >> 1     n |= n >> 2     n |= n >> 4     n |= n >> 8     n |= n >> 16     n += 1     return n    # Driver program to test  # above function  n = 5 print(nextPowerOf2(n))    # This code is contributed # by Smitha

C#

 // C# program to find smallest  // power of 2 greater than or  // equal to n using System;    class GFG {        // Finds next power of two      // for n. If n itself is a      // power of two then returns n     static int nextPowerOf2(int n)     {         n--;         n |= n >> 1;         n |= n >> 2;         n |= n >> 4;         n |= n >> 8;         n |= n >> 16;         n++;                    return n;     }        // Driver Code     public static void Main()     {         int n = 5;         Console.WriteLine(nextPowerOf2(n));     } }     // This code is contributed by anuj_67.

PHP

 > 1;     \$n |= \$n >> 2;     \$n |= \$n >> 4;     \$n |= \$n >> 8;     \$n |= \$n >> 16;     \$n++;     return \$n; }        // Driver Code     \$n = 5;     echo nextPowerOf2(\$n);    // This code contributed by Ajit ?>

Output :

8

Time Complexity : O(lgn)

Related Post :
Highest power of 2 less than or equal to given number

References :
http://en.wikipedia.org/wiki/Power_of_2

tags:

Bit Magic Bit Magic