Efficient method for 2’s complement of a binary string

06 Jul, 2022
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 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 complementIn 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++
Java
Python3
C#
PHP
Javascript
// An efficient C++ program to find 2's complement#include<bits/stdc++.h>using namespace std; // Function to find two's complementstring 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 codeint main(){    string str = "00000101";    cout << findTwoscomplement(str);    return 0;}             
// 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));    }}
# An efficient Python 3 program to# find 2's complement # Function to find two's complementdef 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 codeif __name__ == '__main__':    str = "00000101"    print(findTwoscomplement(str)) # This code is contributed by# Sanjit_Prasad
// An efficient c# program to find 2's complementusing System;using System.Text; class GFG{// Method to find two's complementpublic 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 Codepublic static void Main(string[] args){    StringBuilder str = new StringBuilder("00000101");    Console.WriteLine(findTwoscomplement(str));}} // This code is contributed by Shrikant13
<?php// An efficient PHP program to find 2's// complement // Function to find two's complementfunction 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.?>
<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>
11111011
Time complexity : O(n) Auxiliary Space : O(1)
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