Today I learned about the symmetry in indexing from the beginning and end of a list with the bitwise invert operator.

As you might be aware of, Python allows indexing with negative indices:

```
>>> s = "Hello, there!"
>>> s[-1]
'!'
```

In case this is new to you, you can check out this Pydon't on the subject.

One thing to note is that the index for the `n`

th element is `n - 1`

,
but the index for the `n`

th element from the end is `-n`

.
This is just “how it works”, but it is kind of a bummer because it is very asymmetrical:

```
>>> seq = "ABCDCBA"
>>> seq[0], seq[-1] # 0 and -1
('A', 'A')
>>> seq[1], seq[-2] # 1 and -2
('B', 'B')
>>> seq[2], seq[-3] # 2 and -3
('C', 'C')
>>> seq[3], seq[-4] # 3 and -4
('D', 'D')
```

By looking at the correspondences above,
we can see that the positive index `n`

pairs up with the index `-n - 1`

.

Python has a couple of bitwise operations, one of them being bitwise invert `~`

.
Bitwise invert `~n`

is defined as `-(n+1)`

:

```
>>> n = 38
>>> ~n
-39
>>> -(n+1)
-39
>>> n = -73
>>> ~n
72
>>> -(n+1)
72
```

Now, maybe you can see where I'm going with this, but `-(n+1)`

simplifies to `-n - 1`

.

If we put these two pieces of knowledge together,
we can see how we can use bitwise inversion `~`

to index symmetrically from the beginning
*and* end of a sequence, like a string or a list:

```
>>> seq = "abccba"
>>> seq[1], seq[~1]
('b', 'b')
>>> for i in range(len(seq) // 2):
... print(seq[i], seq[~i])
...
a a
b b
c c
```

Doesn't this look beautiful?

I feel like this is one of those things that you really won't use that often,
but there will come a time in your life when you'll want to exploit this symmetry!
And, you either remember what you just learned about `~`

, or you'll be writing the uglier version with subtractions:

```
>>> seq = "abccba"
>>> seq[1], seq[~1]
('b', 'b')
>>> for i in range(len(seq) // 2):
... print(seq[i], seq[-i - 1])
...
a a
b b
c c
```

Thanks a lot to Tushar Sadhwani from bringing this to my attention:

🐍Python Tip of the day:

— Tushar Sadhwani (@sadhlife) November 28, 2021

You can use `~i` to index a list in python from behind, instead of `-1 - i`: pic.twitter.com/cVm4JE2aZA

That's it for now! Stay tuned and I'll see you around!

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- Python 3 Documentation, The Python Language Reference, https://docs.python.org/3/reference/expressions.html#unary-arithmetic-and-bitwise-operations [last consulted 28-11-2021];
- Tushar Sadhwani's tweet about
`~`

in indexing, https://twitter.com/sadhlife/status/1464993896346181637 [last consulted 28-11-2021];