# Skyline¶

A skyline is set of points which is not dominated by any other point.

This implementation uses a block nested loop. Identical observations are all part of the skyline if applicable.

## Parameters¶

• minimize (list) – defaults to None

A list of features for which the values need to be minimized. Can be omitted as long as maximize is specified.

• maximize (list) – defaults to None

A list of features for which the values need to be maximized. Can be omitted as long as minimize is specified.

## Examples¶

Here is an example taken from this blog post.

>>> import random
>>> from river import misc
>>> import matplotlib.pyplot as plt

>>> city_prices = {
...     'Bordeaux': 4045,
...     'Lyon': 4547,
...     'Toulouse': 3278
... }

>>> def random_house():
...     city = random.choice(['Bordeaux', 'Lyon', 'Toulouse'])
...     size = round(random.gauss(200, 50))
...     price = round(random.uniform(0.8, 1.2) * city_prices[city] * size)
...     return {'city': city, 'size': size, 'price': price}

>>> skyline = misc.Skyline(minimize=['price'], maximize=['size'])

>>> random.seed(42)

>>> for _ in range(100):
...     house = random_house()
...     skyline = skyline.update(house)

>>> print(len(skyline))
13

>>> print(skyline[0])
{'city': 'Toulouse', 'size': 280, 'price': 763202}

>>> fig, ax = plt.subplots()
>>> scatter = ax.scatter(
...     x=[h['size'] for h in skyline],
...     y=[h['price'] for h in skyline]
... )
>>> grid = ax.grid()
>>> title = ax.set_title('Houses skyline')
>>> xlabel = ax.set_xlabel('Size')
>>> ylabel = ax.set_ylabel('Price')


.. image:: ../../docs/img/skyline_docstring.svg :align: center

Here is another example using the kart data from Mario Kart: Double Dash!!.

>>> import collections
>>> from river import misc

>>> Kart = collections.namedtuple(
...      'Kart',
...      'name speed off_road acceleration weight turbo'
... )

>>> karts = [
...     Kart('Red Fire', 5, 4, 4, 5, 2),
...     Kart('Green Fire', 7, 3, 3, 4, 2),
...     Kart('Heart Coach', 4, 6, 6, 5, 2),
...     Kart('Bloom Coach', 6, 4, 5, 3, 2),
...     Kart('Turbo Yoshi', 4, 5, 6, 6, 2),
...     Kart('Turbo Birdo', 6, 4, 4, 7, 2),
...     Kart('Goo-Goo Buggy', 1, 9, 9, 2, 3),
...     Kart('Rattle Buggy', 2, 9, 8, 2, 3),
...     Kart('Toad Kart', 3, 9, 7, 2, 3),
...     Kart('Toadette Kart', 1, 9, 9, 2, 3),
...     Kart('Koopa Dasher', 2, 8, 8, 3, 3),
...     Kart('Para-Wing', 1, 8, 9, 3, 3),
...     Kart('DK Jumbo', 8, 2, 2, 8, 1),
...     Kart('Barrel Train', 8, 7, 3, 5, 3),
...     Kart('Koopa King', 9, 1, 1, 9, 1),
...     Kart('Bullet Blaster', 8, 1, 4, 1, 3),
...     Kart('Wario Car', 7, 3, 3, 7, 1),
...     Kart('Waluigi Racer', 5, 9, 5, 6, 2),
...     Kart('Piranha Pipes', 8, 7, 2, 9, 1),
...     Kart('Boo Pipes', 2, 9, 8, 9, 1),
...     Kart('Parade Kart', 7, 3, 4, 7, 3)
... ]

>>> skyline = misc.Skyline(
...     minimize=['weight']
... )

>>> for kart in karts:
...     skyline = skyline.update(kart._asdict())

>>> best_cart_names = [kart['name'] for kart in skyline]
>>> for name in best_cart_names:
...     print(f'- {name}')
- Green Fire
- Heart Coach
- Bloom Coach
- Goo-Goo Buggy
- Rattle Buggy
- Barrel Train
- Koopa King
- Bullet Blaster
- Waluigi Racer

>>> for name in sorted(set(kart.name for kart in karts) - set(best_cart_names)):
...     print(f'- {name}')
- Boo Pipes
- DK Jumbo
- Koopa Dasher
- Para-Wing
- Piranha Pipes
- Red Fire
- Turbo Birdo
- Turbo Yoshi
- Wario Car


## Methods¶

append

S.append(value) -- append value to the end of the sequence

Parameters

• item
clear

S.clear() -> None -- remove all items from S

copy
count

S.count(value) -> integer -- return number of occurrences of value

Parameters

• item
extend

S.extend(iterable) -- extend sequence by appending elements from the iterable

Parameters

• other
index

S.index(value, [start, [stop]]) -> integer -- return first index of value. Raises ValueError if the value is not present.

Supporting start and stop arguments is optional, but recommended.

Parameters

• item
• args
insert

S.insert(index, value) -- insert value before index

Parameters

• i
• item
pop

S.pop([index]) -> item -- remove and return item at index (default last). Raise IndexError if list is empty or index is out of range.

Parameters

• i – defaults to -1
remove

S.remove(value) -- remove first occurrence of value. Raise ValueError if the value is not present.

Parameters

• item
reverse

S.reverse() -- reverse IN PLACE

sort
update