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

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

#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