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Length of the Longest Consecutive 1s in Binary Representation

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  • Difficulty Level : Medium
  • Last Updated : 14 Sep, 2022
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Given a number N, The task is to find the length of the longest consecutive 1s series in its binary representation.
Examples : 

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

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

Recommended Practice

Naive Approach: Below is the idea to solve the problem

Traverse the bits of binary representation of N and keep a track of the number of consecutive set bits, and the maximum length of consecutive 1s found so far.

Time Complexity: O(X), Here X is the length of binary representation of N.
Auxiliary Space: O(1)

Find the length of the longest consecutive 1s series using Bit Magic:

Below is the idea to solve the problem:

The idea is based on the concept that the AND of bit sequence with a left shifted by 1 version of itself effectively removes the trailing 1 from every sequence of consecutive 1s.  

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

Illustration:

        11101111   (x)

    & 11011110   (x << 1)

    —————————

      11001110   (x & (x << 1)) 

         ^         ^
          |           |

   Trailing 1 removed

Follow the below steps to implement the above approach:

  • Create a variable count initialized with value 0.
  • Run a while loop till N is not 0.
    • In each iteration perform the operation N = (N & (N << 1))
    • Increment count by one.
  • Return count

Below is the Implementation of above approach:

C++




// C++ program to find length of the longest
// consecutive 1s in binary representation 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()
{
    // Function Call
    cout << maxConsecutiveOnes(14) << endl;
    cout << maxConsecutiveOnes(222) << endl;
    return 0;
}


Java




// Java program to find length of the longest
// consecutive 1s in binary representation 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));
    }
}


Python3




# Python program to find
# length of the longest
# consecutive 1s in
# binary representation 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.


C#




// C# program to find length of the
// longest consecutive 1s in binary
// representation of a number.
using System;
 
class GFG {
     
    // Function to find length of the
    // longest consecutive 1s in binary
    // representation 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.


PHP




<?php
// PHP program to find length
// of the longest consecutive
// 1s in binary representation 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
?>


Javascript




<script>
 
// Javascript program to find length
// of the longest consecutive 1s in
// binary representation of a number.
function maxConsecutiveOnes(x)
{
     
    // Initialize result
    let 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
document.write(maxConsecutiveOnes(14) + "<br/>");
document.write(maxConsecutiveOnes(222));
 
// This code is contributed by code_hunt   
 
</script>


Output

3
4

Time Complexity: O(log X), Here X is the length of binary representation of N 
Auxiliary Space: O(1)

This article is contributed by Pankaj Kumar. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@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.
 


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