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

Difficulty Level : Basic
Last Updated : 04 Mar, 2021

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

Javascript

<script>
// JavaScript program to implement
// the above approach
 
// Function to calculate Bitwise OR from given
// bitwise XOR and bitwise AND values
function findBitwiseORGivenXORAND(X, Y)
{
    return X + Y;
}
 
// Driver Code
 
    let X = 5, Y = 2;
    document.write(findBitwiseORGivenXORAND(X, Y));
 
// This code is contributed by Surbhi Tyagi.
 
</script>

Output:

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

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer Complete Interview Preparation Course.

In case you wish to attend live classes with industry experts, please refer DSA Live Classes

My Personal Notes

Related Articles

C++

Java

Python3

C#

Javascript