Binary representation of next number

Last Updated : 28 Apr, 2025

Given a binary string that represents binary representation of positive number n, the task is to find the binary representation of n+1. The binary input may or may not fit in an integer, so we need to return a string.

Examples:

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

Input: s = “111011101001111111”
Output: “111011101010000000”

Approach:

The idea is to use the binary counting pattern where incrementing a number requires turning all trailing 1s to 0s and then changing the rightmost 0 to 1 (or adding a new leading 1 if all digits are 1s). This approach directly simulates the carry operation of binary addition without converting to decimal.

Step by step approach:

Remove any leading zeros as they don’t affect the number’s value.
Scan from right to left (least significant bit to most significant bit).
- Change all consecutive 1s from right to 0s until finding a 0.
- Change the first encountered 0 to 1 and stop the process.
If no 0 is found (all bits are 1), prepend a new leading 1 and set all other bits to 0.

C++

// C++ program to find Binary representation of next number
#include <bits/stdc++.h>
using namespace std;

// Function to find Binary representation of next number
string binaryNextNumber(string s) {
    int n = s.length();
    
    // Remove leading zeros
    int i = 0;
    while (i < n && s[i] == '0') {
        i++;
    }
    
    // If string is all zeros, return "1"
    if (i == n) {
        return "1";
    }
    
    s = s.substr(i);
    n = s.length();
    
    // Start from the rightmost bit
    for (i = n - 1; i >= 0; i--) {
        
        if (s[i] == '0') {
            
            // Convert first '0' from right to '1'
            s[i] = '1';
            break;
        }
        
        // Convert all 1's to 0 till first 
        // 0 from right is found 
        else {
            s[i] = '0';
        }
    }
    
    // If all bits are '1', add a '1' at the beginning
    if (i == -1) {
        s = "1" + s;
    }
    
    return s;
}

int main() {
    string s = "10011";
    cout << binaryNextNumber(s);
    return 0;
}

Java

// Java program to find Binary representation of next number
class Main {

    // Function to find Binary representation of next number
    static String binaryNextNumber(String s) {
        int n = s.length();

        // Remove leading zeros
        int i = 0;
        while (i < n && s.charAt(i) == '0') {
            i++;
        }

        // If string is all zeros, return "1"
        if (i == n) {
            return "1";
        }

        s = s.substring(i);
        n = s.length();

        // Convert string to char array for mutability
        char[] arr = s.toCharArray();

        // Start from the rightmost bit
        for (i = n - 1; i >= 0; i--) {

            if (arr[i] == '0') {

                // Convert first '0' from right to '1'
                arr[i] = '1';
                break;
            }

            // Convert all 1's to 0 till first 
            // 0 from right is found 
            else {
                arr[i] = '0';
            }
        }

        // If all bits are '1', add a '1' at the beginning
        if (i == -1) {
            return "1" + new String(arr);
        }

        return new String(arr);
    }

    public static void main(String[] args) {
        String s = "10011";
        System.out.println(binaryNextNumber(s));
    }
}

Python

# Python program to find Binary representation of next number

# Function to find Binary representation of next number
def binaryNextNumber(s):
    n = len(s)

    # Remove leading zeros
    i = 0
    while i < n and s[i] == '0':
        i += 1

    # If string is all zeros, return "1"
    if i == n:
        return "1"

    s = s[i:]
    n = len(s)
    s = list(s)  
    allOnes = True

    # Start from the rightmost bit
    for i in range(n - 1, -1, -1):

        if s[i] == '0':

            # Convert first '0' from right to '1'
            s[i] = '1'
            allOnes = False
            break

        # Convert all 1's to 0 till first 
        # 0 from right is found 
        else:
            s[i] = '0'

    # If all bits are '1', add a '1' at the beginning
    if allOnes == True:
        s = ['1'] + s

    return ''.join(s)

if __name__ == "__main__":
    s = "10011"
    print(binaryNextNumber(s))

// C# program to find Binary representation of next number
using System;

class GfG {

    // Function to find Binary representation of next number
    static string binaryNextNumber(string s) {
        int n = s.Length;

        // Remove leading zeros
        int i = 0;
        while (i < n && s[i] == '0') {
            i++;
        }

        // If string is all zeros, return "1"
        if (i == n) {
            return "1";
        }

        s = s.Substring(i);
        n = s.Length;
        char[] arr = s.ToCharArray();

        // Start from the rightmost bit
        for (i = n - 1; i >= 0; i--) {

            if (arr[i] == '0') {

                // Convert first '0' from right to '1'
                arr[i] = '1';
                break;
            }

            // Convert all 1's to 0 till first 
            // 0 from right is found 
            else {
                arr[i] = '0';
            }
        }

        // If all bits are '1', add a '1' at the beginning
        if (i == -1) {
            return "1" + new string(arr);
        }

        return new string(arr);
    }

    static void Main(string[] args) {
        string s = "10011";
        Console.WriteLine(binaryNextNumber(s));
    }
}

JavaScript

// JavaScript program to find Binary representation of next number

// Function to find Binary representation of next number
function binaryNextNumber(s) {
    let n = s.length;

    // Remove leading zeros
    let i = 0;
    while (i < n && s[i] === '0') {
        i++;
    }

    // If string is all zeros, return "1"
    if (i === n) {
        return "1";
    }

    s = s.substring(i);
    n = s.length;
    let arr = s.split('');

    // Start from the rightmost bit
    for (i = n - 1; i >= 0; i--) {

        if (arr[i] === '0') {

            // Convert first '0' from right to '1'
            arr[i] = '1';
            break;
        }

        // Convert all 1's to 0 till first 
        // 0 from right is found 
        else {
            arr[i] = '0';
        }
    }

    // If all bits are '1', add a '1' at the beginning
    if (i === -1) {
        arr.unshift('1');
    }

    return arr.join('');
}

let s = "10011";
console.log(binaryNextNumber(s));

Output

Time Complexity: O(n), where n is the length of string. The input string is traversed at most 3 times.
Auxiliary Space: O(n), due to substring.

Min flips of continuous characters to make all characters same in a string

Ayush Jauhari

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Binary representation of next number

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