Given a binary number s represented as a string. The task is to return its 1's complement and 2's complement in form of an array as [onesComplement, twosComplement].

The 1's complement of a binary number is obtained by flipping all its bits. 0 becomes 1, and 1 becomes 0. Positive numbers remain unchanged whereas negative numbers are represented by taking the 1's complement of their positive counterparts.

For example, in 8-bit notation:

• +9 is represented as 00001001.
• -9 is represented as 11110110, which is the 1's complement of 00001001.

Examples: 

Input: s = "0111"
Output: 1000
Explanation: Each bit is flipped, i.e. 0 becomes 1, and 1 becomes 0.

Input: s= "1100"
Output: 0011
Explanation: Each bit is flipped, i.e. 0 becomes 1, and 1 becomes 0.

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The 2's complement of a binary number is obtained by finding the 1's complement (flipping all bits) and then adding 1 to the result. In 2's complement representation, the Most Significant Bit (MSB) represents the sign. A 0 indicates a positive number, while a 1 indicates a negative number. The remaining bits represent the magnitude.

Positive numbers are represented the same way as in 1's complement and sign-bit representation. Negative numbers are obtained by taking the 2's complement of their positive counterparts.

Examples:

Input: s = "0111"
Output: 1001
Explanation: Find 1's complement -> 1000, then add 1 -> 1000 + 1 = 1001

Input: "1100"
Output: 0100
Explanation: Find 1's complement -> 0011, then add 1 -> 0011 + 1 = 0100

The idea is to first compute the 1's complement by flipping each bit of the binary string. Then, to find the 2's complement, we add 1 to the 1's complement, starting from the rightmost bit. If all bits are flipped, an extra '1' is added at the beginning. This ensures correct representation in signed binary numbers.

Steps to implement the above idea:

• onesComplement() iterates through s and flip each '0' to '1' and '1' to '0'.
• twosComplement() calls onesComplement, then add 1 to the least significant bit.
• Traverse s from right to left, flipping '1' to '0' until the first '0', which is changed to '1'.
• If no '0' is found, prepend '1' to s to maintain the correct two’s complement representation.

// C++ program to find 1's and 2's 
// complement of a binary number
#include <bits/stdc++.h>
using namespace std;

// Function to find 1's complement
string onesComplement(string s) {
    
    // Traverse each bit and flip it
    for (char &c : s) {
        if (c == '0') {
            c = '1';
        } else {
            c = '0';
        }
    }
    
    return s;
}

// Function to find 2's complement
string twosComplement(string s) {
    
    // Get 1's complement of the binary number
    s = onesComplement(s); 
    int n = s.size();

    // Add 1 to the 1's complement
    for (int i = n - 1; i >= 0; i--) {
        
        // If we find '0', change it 
        // to '1' and stop
        if (s[i] == '0') {
            s[i] = '1';
            break;
        } 
        
        // If we find '1', change it 
        // to '0' and continue
        else {
            s[i] = '0';
        }
    }

    // If all bits were flipped, we need
    // to add an extra '1'
    // at the beginning to maintain 
    // correct two's complement
    if (s[0] == '0') {
        s = '1' + s;
    }

    return s;
}

// Function to compute both 1's and 2's complements 
vector<string> findComplement(string s) {
    
    // Compute 1's complement
    string ones = onesComplement(s);
    
    // Compute 2's complement
    string twos = twosComplement(s);

    return {ones, twos};
}

// Driver code
int main() {
    
    string s = "1001";

    vector<string> result = findComplement(s);

    cout << result[0] << " " << result[1] << endl;

    return 0;
}

// C++ program to find 1's and 2's 

// complement of a binary number

#include <bits/stdc++.h>

using namespace std;

​

// Function to find 1's complement

string onesComplement(string s) {

    // Traverse each bit and flip it

    for (char &c : s) {

        if (c == '0') {

            c = '1';

        } else {

            c = '0';

        }

    }

    return s;

}

​

// Function to find 2's complement

string twosComplement(string s) {

    // Get 1's complement of the binary number

    s = onesComplement(s); 

    int n = s.size();

​

    // Add 1 to the 1's complement

    for (int i = n - 1; i >= 0; i--) {

        // If we find '0', change it 

        // to '1' and stop

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

            s[i] = '1';

            break;

        } 

        // If we find '1', change it 

        // to '0' and continue

        else {

            s[i] = '0';

        }

    }

​

    // If all bits were flipped, we need

    // to add an extra '1'

    // at the beginning to maintain 

    // correct two's complement

    if (s[0] == '0') {

        s = '1' + s;

    }

​

    return s;

}

​

// Function to compute both 1's and 2's complements 

vector<string> findComplement(string s) {

    // Compute 1's complement

    string ones = onesComplement(s);

    // Compute 2's complement

    string twos = twosComplement(s);

​

    return {ones, twos};

}

​

// Driver code

int main() {

    string s = "1001";

​

    vector<string> result = findComplement(s);

​

    cout << result[0] << " " << result[1] << endl;

​

    return 0;

}

// Java program to find 1's and 2's 
// complement of a binary number

import java.util.*;

class GfG {
    
    // Function to find 1's complement
    static String onesComplement(String s) {
        
        // Traverse each bit and flip it
        StringBuilder result = new StringBuilder(s);
        for (int i = 0; i < s.length(); i++) {
            if (s.charAt(i) == '0') {
                result.setCharAt(i, '1');
            } else {
                result.setCharAt(i, '0');
            }
        }
        
        return result.toString();
    }

    // Function to find 2's complement
    static String twosComplement(String s) {
        
        // Get 1's complement of the binary number
        s = onesComplement(s);
        int n = s.length();

        // Add 1 to the 1's complement
        StringBuilder result = new StringBuilder(s);
        for (int i = n - 1; i >= 0; i--) {
            
            // If we find '0', change it 
            // to '1' and stop
            if (s.charAt(i) == '0') {
                result.setCharAt(i, '1');
                break;
            } 
            
            // If we find '1', change it 
            // to '0' and continue
            else {
                result.setCharAt(i, '0');
            }
        }

        // If all bits were flipped, we need
        // to add an extra '1'
        // at the beginning to maintain 
        // correct two's complement
        if (result.charAt(0) == '0') {
            result.insert(0, '1');
        }

        return result.toString();
    }

    // Function to compute both 1's and 2's complements 
    static String[] findComplement(String s) {
        
        // Compute 1's complement
        String ones = onesComplement(s);
        
        // Compute 2's complement
        String twos = twosComplement(s);

        return new String[]{ones, twos};
    }

    // Driver code
    public static void main(String[] args) {
        
        String s = "1001";

        String[] result = findComplement(s);

        System.out.println(result[0] + " " + result[1]);
    }
}

# Python program to find 1's and 2's 
# complement of a binary number

# Function to find 1's complement
def onesComplement(s):
    
    # Traverse each bit and flip it
    result = ""
    for c in s:
        if c == '0':
            result += '1'
        else:
            result += '0'
    
    return result

# Function to find 2's complement
def twosComplement(s):
    
    # Get 1's complement of the binary number
    s = onesComplement(s)
    n = len(s)

    # Add 1 to the 1's complement
    result = list(s)
    for i in range(n - 1, -1, -1):
        
        # If we find '0', change it 
        # to '1' and stop
        if s[i] == '0':
            result[i] = '1'
            break
        
        # If we find '1', change it 
        # to '0' and continue
        else:
            result[i] = '0'

    # If all bits were flipped, we need
    # to add an extra '1'
    # at the beginning to maintain 
    # correct two's complement
    if result[0] == '0':
        result.insert(0, '1')

    return "".join(result)

# Function to compute both 1's and 2's complements 
def findComplement(s):
    
    # Compute 1's complement
    ones = onesComplement(s)
    
    # Compute 2's complement
    twos = twosComplement(s)

    return [ones, twos]

# Driver code
if __name__ == "__main__":
    
    s = "1001"

    result = findComplement(s)

    print(result[0], result[1])

// C# program to find 1's and 2's 
// complement of a binary number

using System;

class GfG {
    
    // Function to find 1's complement
    static string onesComplement(string s) {
        
        // Traverse each bit and flip it
        char[] result = s.ToCharArray();
        for (int i = 0; i < s.Length; i++) {
            if (s[i] == '0') {
                result[i] = '1';
            } else {
                result[i] = '0';
            }
        }
        
        return new string(result);
    }

    // Function to find 2's complement
    static string twosComplement(string s) {
        
        // Get 1's complement of the binary number
        s = onesComplement(s);
        int n = s.Length;

        // Add 1 to the 1's complement
        char[] result = s.ToCharArray();
        for (int i = n - 1; i >= 0; i--) {
            
            // If we find '0', change it 
            // to '1' and stop
            if (s[i] == '0') {
                result[i] = '1';
                break;
            } 
            
            // If we find '1', change it 
            // to '0' and continue
            else {
                result[i] = '0';
            }
        }

        // If all bits were flipped, we need
        // to add an extra '1'
        // at the beginning to maintain 
        // correct two's complement
        if (result[0] == '0') {
            return "1" + new string(result);
        }

        return new string(result);
    }

    // Function to compute both 1's and 2's complements 
    static string[] findComplement(string s) {
        
        // Compute 1's complement
        string ones = onesComplement(s);
        
        // Compute 2's complement
        string twos = twosComplement(s);

        return new string[]{ones, twos};
    }

    // Driver code
    public static void Main() {
        
        string s = "1001";

        string[] result = findComplement(s);

        Console.WriteLine(result[0] + " " + result[1]);
    }
}

// JavaScript program to find 1's and 2's 
// complement of a binary number

// Function to find 1's complement
function onesComplement(s) {
    
    // Traverse each bit and flip it
    let result = "";
    for (let i = 0; i < s.length; i++) {
        if (s[i] === '0') {
            result += '1';
        } else {
            result += '0';
        }
    }
    
    return result;
}

// Function to find 2's complement
function twosComplement(s) {
    
    // Get 1's complement of the binary number
    s = onesComplement(s);
    let n = s.length;
    let result = s.split("");

    // Add 1 to the 1's complement
    for (let i = n - 1; i >= 0; i--) {
        
        // If we find '0', change it 
        // to '1' and stop
        if (s[i] === '0') {
            result[i] = '1';
            break;
        } 
        
        // If we find '1', change it 
        // to '0' and continue
        else {
            result[i] = '0';
        }
    }

    // If all bits were flipped, we need
    // to add an extra '1'
    // at the beginning to maintain 
    // correct two's complement
    if (result[0] === '0') {
        result.unshift('1');
    }

    return result.join("");
}

// Function to compute both 1's and 2's complements 
function findComplement(s) {
    
    // Compute 1's complement
    let ones = onesComplement(s);
    
    // Compute 2's complement
    let twos = twosComplement(s);

    return [ones, twos];
}

// Driver code
let s = "1001";

let result = findComplement(s);

console.log(result[0], result[1]);

0110 10111

Time Complexity: O(n), as each bit is processed once.
Space Complexity: O(1), as no extra space is used.