# Solution Review: Missing Number

We solved the problem using lookup (hashtable) and using the mathematical formula for the sum of n natural numbers, Let's solve this more efficiently using bit-level operations with XOR.

## Solution review: Bit manipulation

We are dealing with bit manipulation and want to solve all of these problems with Bitwise operators.

### Concepts

If we take XOR of zero and a bit, it will return that bit.

`a ^ 0 = a`

If we take XOR of two same bits, it will return 0.

`a ^ a = 0`

For `n`

numbers, the math below can be applied.

`a ^ b ^ a = (a ^ a) ^ b = 0 ^ b = b;`

For example:

`1 ^ 5 ^ 1 = (1 ^ 1) ^ 5 = 0 ^ 5 = 5;`

So, we can XOR all bits together to find the unique number.

### Algorithm

- Initialize a variable,
`res = 0`

. - Iterate over array elements from
`0`

to`length + 1`

and do`^`

of each with the above-initialized variable. - Iterate over all the elements and store the value in the variable.

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