# Count smaller numbers whose XOR with n produces greater value in C++

C++Server Side ProgrammingProgramming

We are given an integer number let’s say, num and the task is to count the smaller numbers less than num whose XOR with num will result in a value greater than the XOR value..

The truth table for XOR operation is given below

 A B A XOR B 0 0 0 1 0 1 0 1 1 1 1 0

Input − int num = 11

Output − Count of smaller numbers whose XOR with n produces greater value are − 4

Explanation

We are given with the num as 11 which means we need to find XOR of num with the numbers less than num. So the numbers are 1 XOR 11 < 11(FALSE), 2 XOR 11 < 11(FALSE), 3 XOR 11 < 11(FALSE), 4 XOR 11 > 11(TRUE), 5 XOR 11 > 11(TRUE), 6 XOR 11 > 11(TRUE), 7 XOR 11> 11(TRUE), 8 XOR 11< 11(FALSE), 9 XOR 11 < 11(FALSE), 10 XOR 11 < 11(FALSE).

Input − int num = 12

Output − Count of smaller numbers whose XOR with n produces greater value are − 3

Explanation

We are given with the num as 12 which means we need to find XOR of num with the numbers less than num. So the numbers are 1 XOR 12 > 12(TRUE), 2 XOR 12 > 12(TRUE), 3 XOR 12 > 12(TRUE), 4 XOR 12 < 12(FALSE), 5 XOR 12 < 12(FALSE), 6 XOR 12 < 12(FALSE), 7 XOR 12< 12(FALSE), 8 XOR 12< 12(FALSE), 9 XOR 12 < 12(FALSE), 10 XOR 12 < 12(FALSE), 11 XOR 12 < 12(FALSE).

## Approach used in the below program is as follows

• Input an integer element and store it in a variable named num.

• Pass the value of num to the function for further processing

• Create a temporary variable count to store the result.

• Start loop WHILE till num > 0

• Inside the loop, check IF num & 1 == TRUE then set the count as count + pow(2, temp)

• Increment the value of temp by 1

• And set num to num >> = 1

• Return the count

• Print the result

## Example

Live Demo

#include
using namespace std;
//Count smaller numbers whose XOR with n produces greater value
int XOR_greater(int n){
int temp = 0;
int count = 0;
while (n > 0){
if ((n&1) == 0){
count += pow(2, temp);
}
temp++;
n >>= 1;
}
return count;
}
int main(){
int n = 20;
cout<<"Count of smaller numbers whose XOR with n produces greater value are: "<<XOR_greater(n) << endl;
return 0;
}

## Output

If we run the above code it will generate the following output −

Count of smaller numbers whose XOR with n produces greater value are: 11