Efficient method for 2’s complement of a binary string

Given a Binary Number as string, print its 2’s complements.
2’s complement of a binary number is 1 added to the 1’s complement of the binary number. Note that 1’s complement is simply flip of given binary number. 

Examples:

2's complement of "0111" is  "1001"
2's complement of "1100" is  "0100" 

We strongly recommend that you click here and practice it, before moving on to the solution.

We have discussed 1’s and 2’s complements in below post.
1’s and 2’s complement of a Binary Number.

The method discussed in above post traverses binary string twice to find 2’s complement, first finds 1’s complement, then finds 2’s complement using 1’s complement
In this post an efficient method for 2’s complement is discussed that traverses string only once. We traverse the string from last till the single 1 is not traversed and after that flip all values of string i.e. 0 to 1 and 1 to 0.

Note: Here to handle the corner case i.e. if 1 doesn’t exist in the string then just append 1 in the starting of string. 

Illustration :

Input:  str = "1000100"
Output:        0111100
Explanation: Starts traversing the string from last,
we got first '1' at index 4 then just flip the bits 
of 0 to 3 indexes to make the 2's complement. 

Input:  str =  "0000"
Output:        10000
Explanation: As there is no 1 in the string so just 
append '1' at starting.

Implementation:

C++

// An efficient C++ program to find 2's complement
#include<bits/stdc++.h>
using namespace std;

// Function to find two's complement
string findTwoscomplement(string str)
{
    int n = str.length();

    // Traverse the string to get first '1' from
    // the last of string
    int i;
    for (i = n-1 ; i >= 0 ; i--)
        if (str[i] == '1')
            break;

    // If there exists no '1' concatenate 1 at the
    // starting of string
    if (i == -1)
        return '1' + str;

    // Continue traversal after the position of
    // first '1'
    for (int k = i-1 ; k >= 0; k--)
    {
        //Just flip the values
        if (str[k] == '1')
            str[k] = '0';
        else
            str[k] = '1';
    }

    // return the modified string
    return str;
}

// Driver code
int main()
{
    string str = "00000101";
    cout << findTwoscomplement(str);
    return 0;
}

Java

// An efficient Java program to find 2's complement

class Test
{
    // Method to find two's complement
    static String findTwoscomplement(StringBuffer str)
    {
        int n = str.length();

        // Traverse the string to get first '1' from
        // the last of string
        int i;
        for (i = n-1 ; i >= 0 ; i--)
            if (str.charAt(i) == '1')
                break;

        // If there exists no '1' concat 1 at the
        // starting of string
        if (i == -1)
            return "1" + str;

        // Continue traversal after the position of
        // first '1'
        for (int k = i-1 ; k >= 0; k--)
        {
            //Just flip the values
            if (str.charAt(k) == '1')
                str.replace(k, k+1, "0");
            else
                str.replace(k, k+1, "1");
        }

        // return the modified string
        return str.toString();
    }

    // Driver method
    public static void main(String[] args)
    {
        StringBuffer str = new StringBuffer("00000101");
        System.out.println(findTwoscomplement(str));
    }
}

Python3

# An efficient Python 3 program to
# find 2's complement

# Function to find two's complement
def findTwoscomplement(str):
    n = len(str)

    # Traverse the string to get first
    # '1' from the last of string
    i = n - 1
    while(i >= 0):
        if (str[i] == '1'):
            break

        i -= 1

    # If there exists no '1' concatenate 1
    # at the starting of string
    if (i == -1):
        return '1'+str

    # Continue traversal after the
    # position of first '1'
    k = i - 1
    while(k >= 0):

        # Just flip the values
        if (str[k] == '1'):
            str = list(str)
            str[k] = '0'
            str = ''.join(str)
        else:
            str = list(str)
            str[k] = '1'
            str = ''.join(str)

        k -= 1

    # return the modified string
    return str

# Driver code
if __name__ == '__main__':
    str = "00000101"
    print(findTwoscomplement(str))

# This code is contributed by
# Sanjit_Prasad

C#

// An efficient c# program to find 2's complement
using System;
using System.Text;

class GFG
{
// Method to find two's complement
public static string findTwoscomplement(StringBuilder str)
{
    int n = str.Length;

    // Traverse the string to get
    // first '1' from the last of string
    int i;
    for (i = n - 1 ; i >= 0 ; i--)
    {
        if (str[i] == '1')
        {
            break;
        }
    }

    // If there exists no '1' concat 1
    // at the starting of string
    if (i == -1)
    {
        return "1" + str;
    }

    // Continue traversal after the
    // position of first '1'
    for (int k = i - 1 ; k >= 0; k--)
    {
        // Just flip the values
        if (str[k] == '1')
        {
            str.Remove(k, k + 1 - k).Insert(k, "0");
        }
        else
        {
            str.Remove(k, k + 1 - k).Insert(k, "1");
        }
    }

    // return the modified string
    return str.ToString();
}

// Driver Code
public static void Main(string[] args)
{
    StringBuilder str = new StringBuilder("00000101");
    Console.WriteLine(findTwoscomplement(str));
}
}

// This code is contributed by Shrikant13

PHP

<?php
// An efficient PHP program to find 2's
// complement

// Function to find two's complement
function findTwoscomplement($str)
{
    $n = strlen($str);

    // Traverse the string to get first
    // '1' from the last of string
    $i;
    for ($i = $n-1 ; $i >= 0 ; $i--)
        if ($str[$i] == '1')
            break;

    // If there exists no '1' concatenate
    // 1 at the starting of string
    if ($i == -1)
        return '1' + $str;

    // Continue traversal after the
    // position of first '1'
    for ($k = $i-1 ; $k >= 0; $k--)
    {
        // Just flip the values
        if ($str[$k] == '1')
            $str[$k] = '0';
        else
            $str[$k] = '1';
    }

    // return the modified string
    return $str;;
}

// Driver code
$str = "00000101";
echo findTwoscomplement($str);

// This code is contributed by jit.
?>

Javascript

<script>

// An efficient javascript program to find 2's complement

    // Method to find two's complement
    function findTwoscomplement( str) {
        var n = str.length;

        // Traverse the string to get first '1' from
        // the last of string
        var i;
        for (i = n - 1; i >= 0; i--)
            if (str.charAt(i) == '1')
                break;

        // If there exists no '1' concat 1 at the
        // starting of string
        if (i == -1)
            return "1" + str;

        // Continue traversal after the position of
        // first '1'
        for (k = i - 1; k >= 0; k--) {
            // Just flip the values
            if (str.charAt(k) == '1')
                str = str.substring(0,k)+"0"+str.substring(k+1, str.length);
            else
                str = str.substring(0,k)+"1"+str.substring(k+1, str.length);
        }

        // return the modified string
        return str.toString();
    }

    // Driver method

        var str = "00000101";
        document.write(findTwoscomplement(str));

// This code contributed by umadevi9616
</script>

Output

11111011

Time complexity : O(n) 
Auxiliary Space : O(1)

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