Find the triplet from given Bitwise XOR and Bitwise AND values of all its pairs

Given six positive integers representing the Bitwise XOR and Bitwise AND of all possible pairs of a triplet (a, b, c), the task is to find the triplet.

Examples:

Input: aXORb = 30, aANDb = 0, aXORc = 10, aANDc = 20, aXORb = 20, aANDb = 10 
Output: a = 10, b = 20, c= 30 
Explanation:
If a = 10, b = 20, c= 30 
a ^ b = 30, a & b = 0 
a ^ c = 10, a & c = 20 
a ^ b = 20, a & b = 10 
Therefore, the required output is (a, b, c) = (10, 20, 30).

Input: aXORb = 3, aANDb = 0, aXORc = 2, aANDc = 1, aXORb = 1, aANDb = 2 
Output: a = 1, b = 2, c = 3

Approach: The idea is to find the sum of every possible pairs of triplet using their Bitwise XOR and Bitwise AND values based on the following observations:

a + b = a ^ b + 2 * (a & b)

Follow the steps below to solve the problem:

• Find the sum of every possible pair of triplets i.e, (a + b, b + c, c + a) using the above formula.
• The value of a can be calculated as ((a + b) + (a + c) – (b + c)) / 2.
• The value of b can be calculated as ((a + b) – a).
• The value of c can be calculated as ((b + c) – b).
• Finally, print the value of the triplet (a, b, c).

Below is the implementation of the above approach:

C++

// C++ program to implement
// the above approach

#include <bits/stdc++.h>
using namespace std;

// Function to find the triplet with given
// Bitwise XOR and Bitwise AND values of all
// possible pairs of the triplet
void findNumbers(int aXORb, int aANDb, int aXORc, int aANDc,
                 int bXORc, int bANDc)
{
    // Stores values of
    // a triplet
    int a, b, c;

    // Stores a + b
    int aSUMb;

    // Stores a + c
    int aSUMc;

    // Stores b + c
    int bSUMc;

    // Calculate aSUMb
    aSUMb = aXORb + aANDb * 2;

    // Calculate aSUMc
    aSUMc = aXORc + aANDc * 2;

    // Calculate bSUMc
    bSUMc = bXORc + bANDc * 2;

    // Calculate a
    a = (aSUMb - bSUMc + aSUMc) / 2;

    // Calculate b
    b = aSUMb - a;

    // Calculate c
    c = aSUMc - a;

    // Print a
    cout << "a = " << a;

    // Print b
    cout << ", b = " << b;

    // Print c
    cout << ", c = " << c;
}

// Driver Code
int main()
{
    int aXORb = 30, aANDb = 0, aXORc = 20, aANDc = 10,
        bXORc = 10, bANDc = 20;

    findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc);
}

Java

// Java program to implement
// the above approach
class GFG{

// Function to find the triplet with given
// Bitwise XOR and Bitwise AND values of all
// possible pairs of the triplet
static void findNumbers(int aXORb, int aANDb,
                        int aXORc, int aANDc,
                        int bXORc, int bANDc)
{

    // Stores values of
    // a triplet
    int a, b, c;

    // Stores a + b
    int aSUMb;

    // Stores a + c
    int aSUMc;

    // Stores b + c
    int bSUMc;

    // Calculate aSUMb
    aSUMb = aXORb + aANDb * 2;

    // Calculate aSUMc
    aSUMc = aXORc + aANDc * 2;

    // Calculate bSUMc
    bSUMc = bXORc + bANDc * 2;

    // Calculate a
    a = (aSUMb - bSUMc + aSUMc) / 2;

    // Calculate b
    b = aSUMb - a;

    // Calculate c
    c = aSUMc - a;

    // Print a
    System.out.print("a = " + a);

    // Print b
    System.out.print(", b = " + b);

    // Print c
    System.out.print(", c = " + c);
}

// Driver Code
public static void main(String[] args)
{
    int aXORb = 30, aANDb = 0,
        aXORc = 20, aANDc = 10,
        bXORc = 10, bANDc = 20;

    findNumbers(aXORb, aANDb, aXORc,
                aANDc, bXORc, bANDc);
}
}

// This code is contributed by 29AjayKumar

Python3

# Python program to implement
# the above approach

# Function to find the triplet with given
# Bitwise XOR and Bitwise AND values of all
# possible pairs of the triplet
def findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc):

    # Stores values of
    # a triplet
    a, b, c = 0, 0, 0;

    # Stores a + b
    aSUMb = 0;

    # Stores a + c
    aSUMc = 0;

    # Stores b + c
    bSUMc = 0;

    # Calculate aSUMb
    aSUMb = aXORb + aANDb * 2;

    # Calculate aSUMc
    aSUMc = aXORc + aANDc * 2;

    # Calculate bSUMc
    bSUMc = bXORc + bANDc * 2;

    # Calculate a
    a = (aSUMb - bSUMc + aSUMc) // 2;

    # Calculate b
    b = aSUMb - a;

    # Calculate c
    c = aSUMc - a;

    # Pra
    print("a = " , a, end = "");

    # Prb
    print(", b = " , b, end = "");

    # Prc
    print(", c = " , c, end = "");


# Driver Code
if __name__ == '__main__':
    aXORb = 30; aANDb = 0; aXORc = 20; aANDc = 10; bXORc = 10; bANDc = 20;

    findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc);

# This code contributed by shikhasingrajput

C#

// C# code for above approach
using System;
public class GFG
{

  // Function to find the triplet with given
  // Bitwise XOR and Bitwise AND values of all
  // possible pairs of the triplet
  static void findNumbers(int aXORb, int aANDb,
                          int aXORc, int aANDc,
                          int bXORc, int bANDc)
  {

    // Stores values of
    // a triplet
    int a, b, c;

    // Stores a + b
    int aSUMb;

    // Stores a + c
    int aSUMc;

    // Stores b + c
    int bSUMc;

    // Calculate aSUMb
    aSUMb = aXORb + aANDb * 2;

    // Calculate aSUMc
    aSUMc = aXORc + aANDc * 2;

    // Calculate bSUMc
    bSUMc = bXORc + bANDc * 2;

    // Calculate a
    a = (aSUMb - bSUMc + aSUMc) / 2;

    // Calculate b
    b = aSUMb - a;

    // Calculate c
    c = aSUMc - a;

    // Print a
    System.Console.Write("a = " + a);

    // Print b
    System.Console.Write(", b = " + b);

    // Print c
    System.Console.Write(", c = " + c);
  }

  // Driver code
  static public void Main ()
  {
    int aXORb = 30, aANDb = 0,
    aXORc = 20, aANDc = 10,
    bXORc = 10, bANDc = 20;

    findNumbers(aXORb, aANDb, aXORc,
                aANDc, bXORc, bANDc);
  }
}

// This code is contributed by offbeat.

Javascript

<script>
// JavaScript program to implement
// the above approach


// Function to find the triplet with given
// Bitwise XOR and Bitwise AND values of all
// possible pairs of the triplet
function findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc)
{
    // Stores values of
    // a triplet
    let a, b, c;

    // Stores a + b
    let aSUMb;

    // Stores a + c
    let aSUMc;

    // Stores b + c
    let bSUMc;

    // Calculate aSUMb
    aSUMb = aXORb + aANDb * 2;

    // Calculate aSUMc
    aSUMc = aXORc + aANDc * 2;

    // Calculate bSUMc
    bSUMc = bXORc + bANDc * 2;

    // Calculate a
    a = Math.floor((aSUMb - bSUMc + aSUMc) / 2);

    // Calculate b
    b = aSUMb - a;

    // Calculate c
    c = aSUMc - a;

    // Print a
    document.write("a = " + a);

    // Print b
    document.write(", b = " + b);

    // Print c
    document.write(", c = " + c);
}

// Driver Code

    let aXORb = 30, aANDb = 0, aXORc = 20, aANDc = 10,
        bXORc = 10, bANDc = 20;

    findNumbers(aXORb, aANDb, aXORc, aANDc, bXORc, bANDc);

// This code is contributed by Surbhi Tyagi.

</script>

Output:

a = 10, b = 20, c = 30

Time Complexity: O(1)
Auxiliary Space: O(1)