Calculate Bitwise OR of two integers from their given Bitwise AND and Bitwise XOR values
Last Updated :
11 Sep, 2024
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 values
int 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 Code
int main()
{
int X = 5, Y = 2;
cout << findBitwiseORGivenXORAND(X, Y);
}
// Java program to implement the above approach
import 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
# Python program to implement the above approach
# Function to calculate Bitwise OR from given
# bitwise XOR and bitwise AND values
def 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 Code
def main():
X = 5
Y = 2
print(findBitwiseORGivenXORAND(X, Y))
if __name__ == "__main__":
main()
# This code is contributed by Susobhan Akhuli
// C# program to implement the above approach
using 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 program to implement the above approach
// Function to calculate Bitwise OR from given
// bitwise XOR and bitwise AND values
function 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 Code
let X = 5, Y = 2;
console.log(findBitwiseORGivenXORAND(X, Y));
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 values
int findBitwiseORGivenXORAND(int X, int Y) { return X + Y; }
// Driver Code
int main()
{
int X = 5, Y = 2;
cout << findBitwiseORGivenXORAND(X, Y);
}
// 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 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 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# 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
<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>
Time Complexity: O(1)
Auxiliary Space: O(1)
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