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.
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 valuesint findBitwiseORGivenXORAND(int X, int Y){ int range = X + Y; // Find the max range int ans = 0; // Traversing all the number from 0 to rangr for (int i = 1; i <= range; i++) { for (int j = 1; j <= range; j++) { // If X and Y satisfie if ((i ^ j) == X && (i & j) == Y) { ans = (i | j); // Calculate the OR break; } } } return ans;}// Driver Codeint main(){ int X = 5, Y = 2; cout << findBitwiseORGivenXORAND(X, Y);} |
Java
// Java program to implement the above approachimport java.util.*;public class GFG { // Function to calculate Bitwise OR from given // bitwise XOR and bitwise AND values static int findBitwiseORGivenXORAND(int X, int Y) { int range = X + Y; // Find the max range int ans = 0; // Traversing all the numbers from 0 to range for (int i = 1; i <= range; i++) { for (int j = 1; j <= range; j++) { // If X and Y satisfy the conditions if ((i ^ j) == X && (i & j) == Y) { ans = (i | j); // Calculate the OR break; } } } return ans; } // Driver Code public static void main(String[] args) { int X = 5, Y = 2; System.out.println(findBitwiseORGivenXORAND(X, Y)); }}// This code is contributed by Susobhan Akhuli |
Python3
# Python program to implement the above approach# Function to calculate Bitwise OR from given# bitwise XOR and bitwise AND valuesdef findBitwiseORGivenXORAND(X, Y): range_val = X + Y # Find the max range ans = 0 # Traversing all the numbers from 0 to range_val for i in range(1, range_val + 1): for j in range(1, range_val + 1): # If X and Y satisfy the conditions if (i ^ j) == X and (i & j) == Y: ans = (i | j) # Calculate the OR break return ans# Driver Codedef main(): X = 5 Y = 2 print(findBitwiseORGivenXORAND(X, Y))if __name__ == "__main__": main()# This code is contributed by Susobhan Akhuli |
C#
// C# program to implement the above approachusing System;public class GFG { // Function to calculate Bitwise OR from given // bitwise XOR and bitwise AND values static int FindBitwiseORGivenXORAND(int X, int Y) { int range = X + Y; int ans = 0; // Traversing all the numbers from 0 to range for (int i = 1; i <= range; i++) { for (int j = 1; j <= range; j++) { // If X and Y satisfy the conditions if ((i ^ j) == X && (i & j) == Y) { ans = (i | j); // Calculate the OR break; } } } return ans; } static void Main() { int X = 5, Y = 2; Console.WriteLine(FindBitwiseORGivenXORAND(X, Y)); }}// This code is contributed by Susobhan Akhuli |
Javascript
// Javascript program to implement the above approach// Function to calculate Bitwise OR from given// bitwise XOR and bitwise AND valuesfunction findBitwiseORGivenXORAND(X, Y) { let range = X + Y; // Find the max range let ans = 0; // Traversing all the number from 0 to range for (let i = 1; i <= range; i++) { for (let j = 1; j <= range; j++) { // If X and Y satisfy if ((i ^ j) === X && (i & j) === Y) { ans = (i | j); // Calculate the OR break; } } } return ans;}// Driver Codelet X = 5, Y = 2;console.log(findBitwiseORGivenXORAND(X, Y)); |
Output
7
Time Complexity: O(N2), where N = (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 valuesint findBitwiseORGivenXORAND(int X, int Y) { return X + Y; }// Driver Codeint 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 valuesint findBitwiseORGivenXORAND(int X, int Y) { return X + Y; }// Driver Codeint 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 approachclass 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 valuesdef findBitwiseORGivenXORAND(X, Y): return X + Y# Driver Codeif __name__ == "__main__": X = 5 Y = 2 print(findBitwiseORGivenXORAND(X, Y))# This code is contributed by AnkitRai01 |
C#
// C# program to implement// the above approachusing 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 valuesfunction 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
7
Time Complexity: O(1)
Auxiliary Space: O(1)
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