Calculate Bitwise OR of two integers from their given Bitwise AND and Bitwise XOR values

Last Updated : 09 Dec, 2020

Given two integers X and Y, representing Bitwise XOR and Bitwise AND of two positive integers, the task is to calculate the Bitwise OR value of those two positive integers.

Examples:

Input: X = 5, Y = 2
Output: 7
Explanation:
If A and B are two positive integers such that A ^ B = 5, A & B = 2, then the possible value of A and B is 3 and 6 respectively.
Therefore, (A | B) = (3 | 6) = 7.

Input: X = 14, Y = 1
Output: 15
Explanation:
If A and B are two positive integers such that A ^ B = 14, A & B = 1, then the possible value of A and B is 7 and 9 respectively.
Therefore, (A | B) = (7 | 9) = 15.

Naive Approach: The simplest approach to solve this problem is to iterate up to the maximum of X and Y, say N, and generate all possible pairs of the first N natural numbers. For each pair, check if Bitwise XOR and the Bitwise AND of the pair is X and Y, respectively, or not. If found to be true, then print the Bitwise OR of that pair.

Time Complexity: O(N²), where N = max(X, Y)
Auxiliary Space: O(1)

Efficient Approach: To optimize the above approach, the idea is based on the following observations:

(A ^ B) = (A | B) – (A & B)
=> (A | B) = (A ^ B) + (A & B) = X + Y

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 calculate Bitwise OR from given
// bitwise XOR and bitwise AND values
int findBitwiseORGivenXORAND(int X, int Y)
{
    return X + Y;
}
 
// Driver Code
int main()
{
    int X = 5, Y = 2;
    cout << findBitwiseORGivenXORAND(X, Y);
}

Java

// Java program to implement
// the above approach
class GFG {
 
    // Function to calculate Bitwise OR from given
    // bitwise XOR and bitwise AND values
    static int findBitwiseORGivenXORAND(int X, int Y)
    {
        return X + Y;
    }
     
    // Driver Code
    public static void main (String[] args)
    {
        int X = 5, Y = 2;
        System.out.print(findBitwiseORGivenXORAND(X, Y));
    }
}
 
// This code is contributed by AnkitRai01

Python3

# Python3 program to implement
# the above approach
 
# Function to calculate Bitwise OR from
# given bitwise XOR and bitwise AND values
def findBitwiseORGivenXORAND(X, Y):
 
    return X + Y
 
# Driver Code
if __name__ == "__main__" :
     
    X = 5
    Y = 2
     
    print(findBitwiseORGivenXORAND(X, Y))
 
# This code is contributed by AnkitRai01

C#

// C# program to implement
// the above approach
using System;
 
class GFG{
     
// Function to calculate Bitwise OR from given
// bitwise XOR and bitwise AND values
static int findBitwiseORGivenXORAND(int X, int Y)
{
    return X + Y;
}
 
// Driver Code
public static void Main(string []args)
{
    int X = 5, Y = 2;
     
    Console.Write(findBitwiseORGivenXORAND(X, Y));
}
}
 
// This code is contributed by ipg2016107

Output:

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

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