Length of the Longest Consecutive 1s in Binary Representation

Given a number n, find length of the longest consecutive 1s in its binary representation.

Examples :

Input : n = 14
Output : 3
The binary representation of 14 is 1110.

Input : n = 222
Output : 4
The binary representation of 222 is 11011110.

Naive Approach: One simple way would be to simply loop over the bits, and keep track of the number of consecutive set bits, and the maximum that this value has reached. In this approach, we need to convert it to binary (base-2) representation and then find and print the result.



Using Bit Magic: The idea is based on the concept that if we AND a bit sequence with a shifted version of itself, we’re effectively removing the trailing 1 from every sequence of consecutive 1s.

      11101111   (x)
    & 11011110   (x << 1)
    ----------
      11001110   (x & (x << 1)) 
        ^    ^
        |    |
   trailing 1 removed

So the operation x = (x & (x << 1)) reduces length of every sequence of 1s by one in binary representation of x. If we keep doing this operation in a loop, we end up with x = 0. The number of iterations required to reach 0 is actually length of the longest consecutive sequence of 1s.

C++

filter_none

edit
close

play_arrow

link
brightness_4
code

// C++ program to find length of the longest
// consecutive 1s in binary reprsentation of
// a number.
#include<bits/stdc++.h>
using namespace std;
  
int maxConsecutiveOnes(int x)
{
    // Initialize result
    int count = 0;
  
    // Count the number of iterations to
    // reach x = 0.
    while (x!=0)
    {
        // This operation reduces length
        // of every sequence of 1s by one.
        x = (x & (x << 1));
  
        count++;
    }
  
    return count;
}
  
// Driver code
int main()
{
    cout << maxConsecutiveOnes(14) << endl;
    cout << maxConsecutiveOnes(222) << endl;
    return 0;
}

chevron_right


Java

filter_none

edit
close

play_arrow

link
brightness_4
code

// Java program to find length of the longest
// consecutive 1s in binary reprsentation of
// a number.
class MaxConsecutiveOnes
{
    private static int maxConsecutiveOnes(int x)
    {
        // Initialize result
        int count = 0;
  
        // Count the number of iterations to
        // reach x = 0.
        while (x!=0)
        {
            // This operation reduces length
            // of every sequence of 1s by one.
            x = (x & (x << 1));
  
            count++;
        }
  
        return count;
    }
  
    // Driver code
    public static void main(String strings[])
    {
        System.out.println(maxConsecutiveOnes(14));
        System.out.println(maxConsecutiveOnes(222));
    }
}

chevron_right


Python3

filter_none

edit
close

play_arrow

link
brightness_4
code

# Python program to find
# length of the longest
# consecutive 1s in
# binary reprsentation of
# a number.
  
def maxConsecutiveOnes(x):
  
    # Initialize result
    count = 0
   
    # Count the number of iterations to
    # reach x = 0.
    while (x!=0):
      
        # This operation reduces length
        # of every sequence of 1s by one.
        x = (x & (x << 1))
   
        count=count+1
      
    return count
  
# Driver code
  
print(maxConsecutiveOnes(14))
print(maxConsecutiveOnes(222))
  
# This code is contributed
# by Anant Agarwal.

chevron_right


C#

filter_none

edit
close

play_arrow

link
brightness_4
code

// C# program to find length of the 
// longest consecutive 1s in binary
// reprsentation of a number.
using System;
  
class GFG {
      
    // Function to find length of the 
    // longest consecutive 1s in binary
    // reprsentation of a number 
    private static int maxConsecutiveOnes(int x)
    {
          
        // Initialize result
        int count = 0;
  
        // Count the number of iterations
        // to reach x = 0.
        while (x != 0)
        {
              
            // This operation reduces length
            // of every sequence of 1s by one.
            x = (x & (x << 1));
  
            count++;
        }
  
        return count;
    }
  
    // Driver code
    public static void Main()
    {
        Console.WriteLine(maxConsecutiveOnes(14));
        Console.Write(maxConsecutiveOnes(222));
    }
}
  
// This code is contributed by Nitin Mittal.

chevron_right


PHP

filter_none

edit
close

play_arrow

link
brightness_4
code

<?php
// PHP program to find length 
// of the longest consecutive 
// 1s in binary reprsentation of
// a number.
  
function maxConsecutiveOnes($x)
{
    // Initialize result
    $count = 0;
  
    // Count the number of 
    // iterations to reach x = 0.
    while ($x != 0)
    {
        // This operation reduces 
        // length of every sequence
        // of 1s by one.
        $x = ($x & ($x << 1));
  
        $count++;
    }
  
    return $count;
}
  
// Driver code
echo maxConsecutiveOnes(14), "\n";
echo maxConsecutiveOnes(222), "\n";
  
// This code is contributed by Ajit
?>

chevron_right



Output :

3
4

This article is contributed by Pankaj Kumar. 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.

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



My Personal Notes arrow_drop_up

Improved By : nitin mittal, jit_t