Find the values of X and Y in the Given Equations

• Last Updated : 15 Apr, 2021

Given two numbers and . Find the values of X and Y in the equations.

1. A = X + Y
2. B = X xor Y

The task is to make X as minimum as possible. If it is not possible to find any valid values for X and Y then print -1.
Examples:

Input : A = 12, B = 8
Output : X = 2, Y = 10

Input : A = 12, B = 9
Output : -1

Let’s take a look at some bit in X, which is equal to 1. If the respective bit in Y is equal to 0, then one can swap these two bits, thus reducing X and increasing Y without changing their sum and xor. We can conclude that if some bit in X is equal to 1 then the respective bit in Y is also equal to 1. Thus, Y = X + B. Taking into account that X + Y = X + X + B = A, one can obtain the following formulas for finding X and Y:

• X = (A – B) / 2
• Y = X + B = (A + B) / 2

One should also notice that if A < B or A and B have different parity, then the answer doesn’t exist and output is -1. If X and (A – X) not equal to X then the answer is also -1.
Below is the implementation of the above approach :

C++

 // CPP program to find the values of// X and Y using the given equations #include using namespace std; // Function to find the// values of X and Yvoid findValues(int a, int b){    // base condition    if ((a - b) % 2 == 1) {        cout << "-1";        return;    }     // required answer    cout << (a - b) / 2 << " " << (a + b) / 2;} // Driver Codeint main(){    int a = 12, b = 8;     findValues(a, b);     return 0;}

Java

 // Java program to find the values of// X and Y using the given equationsimport java.io.*; class GFG{     // Function to find the// values of X and Ystatic void findValues(int a, int b){    // base condition    if ((a - b) % 2 == 1)    {            System.out.println ("-1");        return;    }     // required answer    System.out.println (((a - b) / 2)+ " " +                            ((a + b) / 2));}     // Driver Code    public static void main (String[] args)    {        int a = 12, b = 8;        findValues(a, b);    }} // This code is contributed by ajit...

Python3

 # Python3 program to find the values of# X and Y using the given equations # Function to find the values of X and Ydef findValues(a, b):     # base condition    if ((a - b) % 2 == 1):        print("-1");        return;     # required answer    print((a - b) // 2, (a + b) // 2); # Driver Codea = 12; b = 8; findValues(a, b); # This code is contributed# by Akanksha Rai

C#

 // C# program to find the values of// X and Y using the given equationsusing System; class GFG{         // Function to find the// values of X and Ystatic void findValues(int a, int b){    // base condition    if ((a - b) % 2 == 1)    {            Console.Write ("-1");        return;    }     // required answer    Console.WriteLine(((a - b) / 2)+ " " +                        ((a + b) / 2));} // Driver Codestatic public void Main (){    int a = 12, b = 8;    findValues(a, b);}} // This code is contributed by @Tushil..



Javascript


Output:
2 10

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