Smallest power of 2 greater than or equal to n

01 Jul, 2022
Write a function that, for a given no n, finds a number p which is greater than or equal to n and is the smallest power of 2. 
Examples : 
Input: n = 5Output: 8     
Input: n = 17Output: 32     
Input  : n = 32Output: 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   
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// C++ program to find// smallest power of 2// greater than or equal to n#include <bits/stdc++.h>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 Codeint main(){    unsigned int n = 0;    cout << nextPowerOf2(n);    return 0;} // This code is contributed by rathbhupendra
#include<stdio.h> unsigned int nextPowerOf2(unsigned int n){unsigned count = 0; // First n in the below condition// is for the case where n is 0if (n && !(n & (n - 1)))    return n; while( n != 0){    n >>= 1;    count += 1;} return 1 << count;} // Driver Codeint main(){unsigned int n = 0;printf("%d", nextPowerOf2(n));return 0;}
// Java program to find// smallest power of 2// greater than or equal to nimport 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.
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 Coden = 0print(nextPowerOf2(n))# This code is contributed# by Smitha Dinesh Semwal
// C# program to find smallest// power of 2 greater than// or equal to nusing 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// PHP program to find smallest// power of 2 greater than or// equal to n function nextPowerOf2($n){$count = 0; // First n in the below condition// is for the case where n is 0if ($n && !($n&($n - 1)))    return $n; while($n != 0){    $n >>= 1;    $count += 1;} return 1 << $count;} // Driver Code$n = 0;echo (nextPowerOf2($n)); // This code is contributed by vt_m?>
<script> // JavaScript program to find// smallest power of 2// greater than or equal to n function nextPowerOf2(n){    var 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 Codevar n = 0;document.write(nextPowerOf2(n));     </script>
1
Time Complexity: O(log n)Auxiliary Space: O(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. 
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// C++ program to find smallest// power of 2 greater than or// equal to n#include<bits/stdc++.h>using namespace std;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 Codeint main(){    unsigned int n = 5;    cout << nextPowerOf2(n);    return 0;} // This code is contributed by rathbhupendra
#include<stdio.h>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 Codeint main(){unsigned int n = 5;printf("%d", nextPowerOf2(n));return 0;}
// Java program to find smallest// power of 2 greater than or// equal to nimport 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.
def nextPowerOf2(n):     p = 1    if (n and not(n & (n - 1))):        return n     while (p < n) :        p <<= 1             return p;  # Driver Coden = 5print(nextPowerOf2(n)); # This code is contributed by# Smitha Dinesh Semwal
// C# program to find smallest// power of 2 greater than or// equal to nusing 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 function nextPowerOf2($n){    $p = 1;    if ($n && !($n & ($n - 1)))        return $n;     while ($p < $n)        $p <<= 1;         return $p;} // Driver Code$n = 5;echo ( nextPowerOf2($n)); // This code is contributed by vt_m.?>
<script>// Program to find smallest// power of 2 greater than or// equal to n function  nextPowerOf2( n){    p = 1;    if (n && !(n & (n - 1)))        return n;      while (p < n)        p <<= 1;          return p;}  // Driver Code      n = 5;    document.write (nextPowerOf2(n));         //This code is contributed by simranarora5sos</script>
8
Time Complexity: O(log(n)) Auxiliary Space: O(1)
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: 
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// C++ program to // Finds next power of two// for n. If n itself is a// power of two then returns n#include <bits/stdc++.h>using namespace std;   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;     cout << nextPowerOf2(n);     return 0; }    // This code is contributed by SHUBHAMSINGH10
#include <stdio.h>// Finds next power of two// for n. If n itself is a// power of two then returns nunsigned 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 Codeint main(){    unsigned int n = 5;    printf("%d", nextPowerOf2(n));    return 0;}    
// Java program to find smallest// power of 2 greater than or// equal to nimport 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.
# Finds next power of two# for n. If n itself is a# power of two then returns ndef 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 functionn = 5print(nextPowerOf2(n)) # This code is contributed# by Smitha
// C# program to find smallest// power of 2 greater than or// equal to nusing 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// PHP program to find smallest// power of 2 greater than or// equal to n // Finds next power of// two for n. If n itself// is a power of two then// returns nfunction nextPowerOf2($n){    $n--;    $n |= $n >> 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?>
<script> // Javascript program to find smallest// power of 2 greater than or// equal to n  // Finds next power of// two for n. If n itself// is a power of two then// returns nfunction nextPowerOf2(n){    n -= 1    n |= n >> 1    n |= n >> 2    n |= n >> 4    n |= n >> 8    n |= n >> 16    n += 1    return n}   // Driver Coden = 5;document.write (nextPowerOf2(n)); // This code is contributed by bunnyram19 </script>
8
Time Complexity : O(log(n)) Auxiliary Space: O(1)
Efficient approach:If the given number is the power of two then it is the required number otherwise set only the left bit of most significant bit which gives us the required number.
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// C++ program to find// smallest power of 2// greater than or equal to n#include <iostream>using namespace std; long long nextPowerOf2(long long N){    // if N is a power of two simply return it    if (!(N & (N - 1)))        return N;    // else set only the left bit of most significant bit    return 0x8000000000000000 >> (__builtin_clzll(N) - 1);} // Driver Codeint main(){    long long n = 5;    cout << nextPowerOf2(n);    return 0;} // This code is contributed by Kasina Dheeraj.
// C program to find// smallest power of 2// greater than or equal to n#include <stdio.h> long long nextPowerOf2(long long N){    // if N is a power of two simply return it    if (!(N & (N - 1)))        return N;    // else set only the left bit of most significant bit    return 0x8000000000000000 >> (__builtin_clzll(N) - 1);} // Driver Codeint main(){    long long n = 5;    printf("%lld", nextPowerOf2(n));    return 0;} // This code is contributed by Kasina Dheeraj.
// Java program to find// smallest power of 2// greater than or equal to nimport java.io.*; class GFG {    static long nextPowerOf2(long N)    {        // if N is a power of two simply return it        if ((N & (N - 1)) == 0)            return N;        // else set only the left bit of most significant        // bit as in Java right shift is filled with most        // significant bit we consider        return 0x4000000000000000L            >> (Long.numberOfLeadingZeros(N) - 2);    }     // Driver Code    public static void main(String args[])    {        long n = 5;        System.out.println(nextPowerOf2(n));    }} // This code is contributed// by Kasina Dheeraj.
# Python program to find# smallest power of 2# greater than or equal to n#include <iostream>def nextPowerOf2(N):    # if N is a power of two simply return it    if not (N & (N - 1)):        return N    # else set only the left bit of most significant bit    return  int("1" + (len(bin(N)) - 2) * "0", 2) # Driver Coden = 5print(nextPowerOf2(n)) # this code is contributed by phasing17
// C# program to find// smallest power of 2// greater than or equal to nusing System;using System.Linq; class GFG {   static int nextPowerOf2(int N)  {     // if N is a power of two simply return it    if ((N & (N - 1)) == 0)      return N;     // else set only the left bit of most significant    // bit    return Convert.ToInt32(      "1"      + new string('0',                   Convert.ToString(N, 2).Length),      2);  }   // Driver Code  public static void Main(string[] args)  {    int n = 5;     // Function call    Console.WriteLine(nextPowerOf2(n));  }} // This code is contributed// by phasing17
// JavaScript program to find// smallest power of 2// greater than or equal to nfunction nextPowerOf2(N){    // if N is a power of two simply return it    if (!(N & (N - 1)))        return N;             // else set only the left bit of most significant bit    return  parseInt("1" + "0".repeat(N.toString(2).length), 2);} // Driver Codelet n = 5;console.log(nextPowerOf2(n)); // this code is contributed by phasing17
8
Time Complexity : O(1) as counting leading zeroes can cause at most O(64) time complexity.Auxiliary Space: O(1)
Related Post : Highest power of 2 less than or equal to given numberReferences : http://en.wikipedia.org/wiki/Power_of_2 
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