Calculate Bitwise OR of two integers from their given Bitwise AND and Bitwise XOR values
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); } |
C
// C program to implement // the above approach #include <stdio.h> // 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; printf ( "%d\n" , findBitwiseORGivenXORAND(X, Y)); } // This code is contributed by phalashi. |
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> |
7
Time Complexity: O(1)
Auxiliary Space: O(1)