Binary representation of next number

Difficulty Level : Easy
Last Updated : 26 Apr, 2021

Given a binary input that represents binary representation of positive number n, find a binary representation of n+1.
The binary input may be and may not fit even in unsigned long long int.
Examples:

Input : 10011
Output : 10100
Here n = (19)₁₀ = (10011)₂
next greater integer = (20)₁₀ = (10100)₂ 

Input : 111011101001111111
Output : 111011101010000000

We store input as a string so that large numbers can be handled. We traverse the string from the rightmost character and convert all 1s to 0s until we find a 0. Finally, convert the found 0 to 1. If we do not find a 0, we append a 1 to the overall string.

string nextGreater(num)
  l = num.length

  // Find first 0 from right side. While
  // searching, convert 1s to 0s
  for i = l-1 to 0
    if num[i] == '0'
       num[i] = '1'
       break
    else
       num[i] = '0'
         
  // If there was no 0  
  if i < 0
      num = '1' + num
  return num

Below is the implementation of the above idea.

C++

// C++ implementation to find the binary
// representation of next greater integer
#include <bits/stdc++.h>
using namespace std;
 
// function to find the required
// binary representation
string nextGreater(string num)
{
    int l = num.size();
 
    // examine bits from the right
    for (int i=l-1; i>=0; i--)
    {
        // if '0' is encountered, convert
        // it to '1' and then break
        if (num.at(i) == '0')
        {
            num.at(i) = '1';
            break;
        }
 
        // else convert '1' to '0'
        else
            num.at(i) = '0';
    }
 
    // if the binary representation
    // contains only the set bits
    if (i < 0)
        num = "1" + num;
 
    // final binary representation
    // of the required integer
    return num;
}
 
// Driver program to test above
int main()
{
    string num = "10011";
    cout << "Binary representation of next number = "
         << nextGreater(num);
    return 0;
}

Java

// Java implementation to find the binary
// representation of next greater integer
 
class GFG {
 
// function to find the required
// binary representation
    static String nextGreater(String num) {
 
        int l = num.length();
        int i;
        // examine bits from the right
        for (i = l - 1; i >= 0; i--) {
            // if '0' is encountered, convert
            // it to '1' and then break
            if (num.charAt(i) == '0') {
                num = num.substring(0, i) + '1' + num.substring(i+1);
                break;
            } // else convert '1' to '0'
            else {
                num = num.substring(0, i) + '0' + num.substring(i + 1);
            }
            // num[i] = '0';
        }
 
        // if the binary representation
        // contains only the set bits
        if (i < 0) {
            num = "1" + num;
        }
 
        // final binary representation
        // of the required integer
        return num;
    }
 
// Driver program to test above
    public static void main(String[] args) {
        String num = "10011";
        System.out.println("Binary representation of next number = "
                + nextGreater(num));
    }
}
//this code contributed by Rajput-Ji

Python3

# Python3 implementation to find the binary
# representation of next greater integer
 
# function to find the required
# binary representation
def nextGreater(num1):
 
    l = len(num1);
    num = list(num1);
 
    # examine bits from the right
    i = l-1;
    while(i >= 0):
        # if '0' is encountered, convert
        # it to '1' and then break
        if (num[i] == '0'):
            num[i] = '1';
            break;
 
        # else convert '1' to '0'
        else:
            num[i] = '0';
        i-=1;
 
    # if the binary representation
    # contains only the set bits
    num1 = ''.join(num);
    if (i < 0):
        num1 = '1' + num1;
 
    # final binary representation
    # of the required integer
    return num1;
 
# Driver Code
num = "10011";
print("Binary representation of next number = ",nextGreater(num));
 
# This code is contributed by mits

C#

     
// C# implementation to find the binary
// representation of next greater integer
 using System;
public class GFG {
  
// function to find the required
// binary representation
    static String nextGreater(String num) {
  
        int l = num.Length;
        int i;
        // examine bits from the right
        for (i = l - 1; i >= 0; i--) {
            // if '0' is encountered, convert
            // it to '1' and then break
            if (num[i] == '0') {
                num = num.Substring(0, i) + '1' + num.Substring(i+1);
                break;
            } // else convert '1' to '0'
            else {
                num = num.Substring(0, i) + '0' + num.Substring(i + 1);
            }
            // num[i] = '0';
        }
  
        // if the binary representation
        // contains only the set bits
        if (i < 0) {
            num = "1" + num;
        }
  
        // final binary representation
        // of the required integer
        return num;
    }
  
// Driver program to test above
    public static void Main() {
        String num = "10011";
        Console.WriteLine("Binary representation of next number = "
                + nextGreater(num));
    }
}
//this code contributed by Rajput-Ji

PHP

<?php
// PHP implementation to find the binary
// representation of next greater integer
 
// function to find the required
// binary representation
function nextGreater($num)
{
    $l = strlen($num);
 
    // examine bits from the right
    for ($i = $l - 1; $i >= 0; $i--)
    {
        // if '0' is encountered, convert
        // it to '1' and then break
        if ($num[$i] == '0')
        {
            $num[$i] = '1';
            break;
        }
 
        // else convert '1' to '0'
        else
            $num[$i] = '0';
    }
 
    // if the binary representation
    // contains only the set bits
    if ($i < 0)
        $num = "1" . $num;
 
    // final binary representation
    // of the required integer
    return $num;
}
 
// Driver Code
$num = "10011";
echo "Binary representation of next number = " .
                              nextGreater($num);
 
// This code is contributed by ita_c
?>

Javascript

<script>
 
// Javascript implementation to find the binary
// representation of next greater integer
     
    // function to find the required
    // binary representation
    function nextGreater(num)
    {
        let l = num.length;
        let i;
        // examine bits from the right
        for (i = l - 1; i >= 0; i--) {
            // if '0' is encountered, convert
            // it to '1' and then break
            if (num[i] == '0') {
                num = num.substring(0, i) + '1'
                + num.substring(i+1);
                break;
            } // else convert '1' to '0'
            else {
                num = num.substring(0, i) + '0'
                + num.substring(i + 1);
            }
            // num[i] = '0';
        }
   
        // if the binary representation
        // contains only the set bits
        if (i < 0) {
            num = "1" + num;
        }
   
        // final binary representation
        // of the required integer
        return num;
    }
     
    // Driver program to test above
    let num = "10011";
    document.write(
    "Binary representation of next number = "
                            + nextGreater(num)
    );
     
     
    // This code is contributed by rag2127
     
</script>

Output:

Binary representation of next number = 10100

Time Complexity: O(n) where n is the number of bits in the input.
This article is contributed by Ayush Jauhari. 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.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

My Personal Notes