## Problem Link :

**Author:** Amrutansu Garanaik , Abhishek Patnaik

**Tester:** Keshow Sablaka, Amit Das

**Editorialist:** Amrutansu Garanaik , Amit Kumar Sahu

## Difficulty :

easy

# Pre-requisite simple math ## Problem : Given a set of numbers from 0 to n (both inclusive), you have to find a pair of number with maximum XOR and print the maximum XOR value.

## Explanation

XOR of two bits is 1 if they are different, otherwise it’s zero. In order to maximize XOR, we

must ensure that the two numbers have as many bits different at a given position as possible.

Since the list is sequencial and is starting from 0, we cannot have a number whose Most

Significant Bit is higher than that of ‘n’. So, we find the positions of ‘n’ where it is 1, and create a

number with those bits set to zero and vice-versa, i.e.

if n=1001101

we find the other number as

x=0110010

Now this number is less than ‘n’ and is bound to be inside the list.

The XOR of the numbers is 1111111.

From this we can see, the result of the XOR operation is all 1 and where number of 1 is number of

bits in ‘n’. If n already contains all 1, we can simply XOR it with 0.

Pseudo code :

```
int ans=0,pow=1;
while(n)
{
ans+=pow;
pow<<=1;
n>>=1;
}
```