Highest power of 2 less than or equal to given number

Given a number n, find the highest power of 2 that is smaller than or equal to n.

Examples :

Input : n = 10
Output : 8

Input : n = 19
Output : 16

Input : n = 32
Output : 32

A simple solution is to start checking from n and keep decrementing until we find a power of 2.

C++

// C++ program to find highest power of 2 smaller
// than or equal to n.
#include<bits/stdc++.h>
using namespace std;

int highestPowerof2(int n)
{
    int res = 0;
    for (int i=n; i>=1; i--)
    {
        // If i is a power of 2
        if ((i & (i-1)) == 0)
        {
            res = i;
            break;
        }
    }
    return res;
}

// Driver code
int main()
{
    int n = 10;
    cout << highestPowerof2(n);
    return 0;
}

Java

// Java code to find highest power
// of 2 smaller than or equal to n.
class GFG
{
   static int highestPowerof2(int n)
   {
     int res = 0;
     for (int i = n; i >= 1; i--)
        {
         // If i is a power of 2
          if ((i & (i - 1)) == 0)
             {
                  res = i;
                break;
             }
        }
     return res;
   }

   // Driver code
   public static void main(String[] args)
   {
      int n = 10;
      System.out.println(highestPowerof2(n));
   }
}
// This code is contributed by prerna saini.

Python3

# Python3 program to find highest
# power of 2 smaller than or
# equal to n.
def highestPowerof2(n):

    res = 0;
    for i in range(n, 0, -1):

        # If i is a power of 2
        if ((i & (i - 1)) == 0):

            res = i;
            break;

    return res;

# Driver code
n = 10;
print(highestPowerof2(n));

# This code is contributed by mits

C#

// C# code to find highest power
// of 2 smaller than or equal to n.
using System;

class GFG
{
public static int highestPowerof2(int n)
{
    int res = 0;
    for (int i = n; i >= 1; i--)
        {
        // If i is a power of 2
        if ((i & (i - 1)) == 0)
            {
                res = i;
                break;
            }
        }
    return res;
}

    // Driver Code
    static public void Main ()
    {
        int n = 10;
        Console.WriteLine(highestPowerof2(n));
    }
}

// This code is contributed by ajit

PHP

<?php
// PHP program to find highest
// power of 2 smaller than or
// equal to n.
function highestPowerof2($n)
{
    $res = 0;
    for ($i = $n; $i >= 1; $i--)
    {
        // If i is a power of 2
        if (($i & ($i - 1)) == 0)
        {
            $res = $i;
            break;
        }
    }
    return $res;
}

// Driver code
$n = 10;
echo highestPowerof2($n);

// This code is contributed by m_kit
?>

Output :

8

Time complexity : O(n). In worst case, the loop runs floor(n/2) times. The worst case happens when n is of the form 2^x – 1.

An efficient solution is to use bitwise left shift operator to find all powers of 2 starting from 1. For every power check if it is smaller than or equal to n or not. Below is the implementation of the idea.

C++

// C++ program to find highest power of 2 smaller
// than or equal to n.
#include<bits/stdc++.h>
using namespace std;

int highestPowerof2(unsigned int n)
{
    // Invalid input
    if (n < 1)
        return 0;

    int res = 1;

    // Try all powers starting from 2^1
    for (int i=0; i<8*sizeof(unsigned int); i++)
    {
        int curr = 1 << i;

        // If current power is more than n, break
        if (curr > n)
           break;

        res = curr;
    }

    return res;
}

// Driver code
int main()
{
    int n = 10;
    cout << highestPowerof2(n);
    return 0;
}

Java

// Java program to find
// highest power of 2 smaller
// than or equal to n.
import java.io.*;

class GFG
{
static int highestPowerof2(int n)
{
    // Invalid input
    if (n < 1)
        return 0;

    int res = 1;

    // Try all powers
    // starting from 2^1
    for (int i = 0; i < 8 * Integer.BYTES; i++)
    {
        int curr = 1 << i;

        // If current power is
        // more than n, break
        if (curr > n)
        break;

        res = curr;
    }

    return res;
}

// Driver code
public static void main(String[] args)
{
    int n = 10;
    System.out.println(highestPowerof2(n));
}
}

// This code is contributed aj_36

python3

# Python3 program to find highest power of 2 smaller
# than or equal to n.

import sys

def highestPowerof2( n):

    # Invalid input
    if (n < 1):
        return 0

    res = 1

    #Try all powers starting from 2^1
    for i in range(8*sys.getsizeof(n)):

        curr = 1 << i

        # If current power is more than n, break
        if (curr > n):
             break

        res = curr

    return res

# Driver code
if __name__ == "__main__":

    n = 10
    print(highestPowerof2(n))

C#

// C# program to find
// highest power of 2 smaller
// than or equal to n.
using System;

class GFG
{
static int highestPowerof2(int n)
{
    // Invalid input
    if (n < 1)
        return 0;

    int res = 1;

    // Try all powers
    // starting from 2^1
    for (int i = 0; i < 8 * sizeof(uint); i++)
    {
        int curr = 1 << i;

        // If current power is
        // more than n, break
        if (curr > n)
        break;

        res = curr;
    }

    return res;
}

// Driver code
static public void Main ()
{
    int n = 10;
    Console.WriteLine(highestPowerof2(n));
}
}

// This code is contributed ajit

PHP

<?php
// PHP program to find highest
// power of 2 smaller
// than or equal to n.

function highestPowerof2($n)
{
    // Invalid input
    if ($n < 1)
        return 0;

    $res = 1;

    // Try all powers starting
    // from 2^1
    for ($i = 0; $i < 8 * PHP_INT_SIZE; $i++)
    {
        $curr = 1 << $i;

        // If current power is
        // more than n, break
        if ($curr > $n)
        break;

        $res = $curr;
    }

    return $res;
}

// Driver code
$n = 10;
echo highestPowerof2($n);

// This code is contributed
// by m_kit
?>

Output :

8

A Solution using Log
Thanks to Anshuman Jha for suggesting this solution.

C++

// C++ program to find highest power of 2 smaller
// than or equal to n.
#include<bits/stdc++.h>
using namespace std;

int highestPowerof2(int n)
{
   int p = (int)log2(n);
   return (int)pow(2, p);
}

// Driver code
int main()
{
    int n = 10;
    cout << highestPowerof2(n);
    return 0;
}

Java

// Java program to find
// highest power of 2
// smaller than or equal to n.
import java.io.*;

class GFG
{
static int highestPowerof2(int n)
{

    int p = (int)(Math.log(n) /
                  Math.log(2));
    return (int)Math.pow(2, p);
}

// Driver code
public static void main (String[] args)
{
    int n = 10;
    System.out.println(highestPowerof2(n));
}
}

// This code is contributed
// by m_kit

Python3

# Python3 program to find highest
# power of 2 smaller than or
# equal to n.
import math

def highestPowerof2(n):

    p = int(math.log(n, 2));
    return int(pow(2, p));

# Driver code
n = 10;
print(highestPowerof2(n));

# This code is contributed by mits

C#

// C# program to find
// highest power of 2
// smaller than or equal to n.
using System;

class GFG
{
static int highestPowerof2(int n)
{
    int p = (int)(Math.Log(n) /
                   Math.Log(2));
    return (int)Math.Pow(2, p);
}

// Driver code
static public void Main ()
{
    int n = 10;
    Console.WriteLine(highestPowerof2(n));
}
}

// This code is contributed
// by ajit

PHP

<?php
// PHP program to find highest
// power of 2 smaller than or
// equal to n.
function highestPowerof2($n)
{
    $p = (int)log($n, 2);
    return (int)pow(2, $p);
}

// Driver code
$n = 10;
echo highestPowerof2($n);

// This code is contributed by ajit
?>

Output :

8

Application Problem:
Some people are standing in a queue. A selection process follows a rule where people standing on even positions are selected. Of the selected people a queue is formed and again out of these only people on even position are selected. This continues until we are left with one person. Find out the position of that person in the original queue.
Print the position(original queue) of that person who is left.
Examples :

Input: n = 10
Output:8
Explanation : 
1 2 3 4 5 6 7 8 9 10  ===>Given queue
    2 4 6 8 10
       4 8
        8

Input: n = 17
Input: 16
Explanation : 
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17  ===>Given queue
        2 4 6 8 10 12 14 16
            4 8 12 16
              8 16
               16

This article is contributed by Sahil Chhabra. If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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