Overlapping Disks

Overlapping Disks

Given a list of disks on the two-dimensional plane represented as tuples (x, y, r) so that x, y is the center point and r is the radius of that disk, count how many pairs of disks intersect.

Two disks (x1, y1, r1) and (x2, y2, r2) intersect if and only if they satisfy the Pythagorean inequality (x2-x1)**2+(y2-y1)**2<=(r1+r2)**2.

Note how this precise formula runs on pure integer arithmetic whenever its arguments are integers, so no square roots or any other irrational numbers gum up the works with all that decimal noise. (This formula also uses the operator <= to count two kissing disks as an intersecting pair).

For this problem, crudely looping through all possible pairs of disks would work, but also become horrendously inefficient for large lists. However, a sweep line algorithm can solve this problem not just effectively, but also efficiently (a crucial but often overlooked “eff-ing” distinction) by looking at a far fewer pairs of disks.

Here is a scheme for [(0, 0, 3), (6, 0, 3), (6, 6, 3), (0, 6, 3)]:

example

Input: List of tuples (tuple) of integers (int).

Output: Integer (int).

Examples:

assert overlapping_disks([(0, 0, 3), (6, 0, 3), (6, 6, 3), (0, 6, 3)]) == 4
assert overlapping_disks([(4, -1, 3), (-3, 3, 2), (-3, 4, 2), (3, 1, 4)]) == 2
assert (
    overlapping_disks([(-10, 6, 2), (6, -4, 5), (6, 3, 5), (-9, -8, 1), (1, -5, 3)])
    == 2
)
assert (
    overlapping_disks(
        [
            (2, 2, 1),
            (3, 3, 1),
            (4, 4, 2),
            (5, 5, 2),
            (6, 6, 3),
            (7, 7, 3),
            (8, 8, 4),
            (9, 9, 4),
            (10, 10, 5),
            (11, 11, 5),
            (12, 12, 6),
            (13, 13, 6),
            (14, 14, 7),
            (15, 15, 7),
            (16, 16, 8),
            (17, 17, 8),
            (18, 18, 9),
            (19, 19, 9),
            (20, 20, 10),
            (21, 21, 10),
            (22, 22, 11),
            (23, 23, 11),
            (24, 24, 12),
            (25, 25, 12),
            (26, 26, 13),
            (27, 27, 13),
            (28, 28, 14),
            (29, 29, 14),
            (30, 30, 15),
            (31, 31, 15),
            (32, 32, 16),
            (33, 33, 16),
            (34, 34, 17),
            (35, 35, 17),
            (36, 36, 18),
            (37, 37, 18),
            (38, 38, 19),
            (39, 39, 19),
            (40, 40, 20),
            (41, 41, 20),
            (42, 42, 21),
            (43, 43, 21),
            (44, 44, 22),
            (45, 45, 22),
            (46, 46, 23),
            (47, 47, 23),
            (48, 48, 24),
            (49, 49, 24),
            (50, 50, 25),
            (51, 51, 25),
            (52, 52, 26),
            (53, 53, 26),
            (54, 54, 27),
            (55, 55, 27),
            (56, 56, 28),
            (57, 57, 28),
            (58, 58, 29),
            (59, 59, 29),
            (60, 60, 30),
            (61, 61, 30),
            (62, 62, 31),
            (63, 63, 31),
            (64, 64, 32),
            (65, 65, 32),
            (66, 66, 33),
            (67, 67, 33),
            (68, 68, 34),
            (69, 69, 34),
            (70, 70, 35),
            (71, 71, 35),
            (72, 72, 36),
            (73, 73, 36),
            (74, 74, 37),
            (75, 75, 37),
            (76, 76, 38),
            (77, 77, 38),
            (78, 78, 39),
            (79, 79, 39),
            (80, 80, 40),
            (81, 81, 40),
            (82, 82, 41),
            (83, 83, 41),
            (84, 84, 42),
            (85, 85, 42),
            (86, 86, 43),
            (87, 87, 43),
            (88, 88, 44),
            (89, 89, 44),
            (90, 90, 45),
            (91, 91, 45),
            (92, 92, 46),
            (93, 93, 46),
            (94, 94, 47),
            (95, 95, 47),
            (96, 96, 48),
            (97, 97, 48),
            (98, 98, 49),
            (99, 99, 49),
            (100, 100, 50),
        ]
    )
    == 2563
)

The mission was taken from Python CCPS 109. It is taught for Ryerson Chang School of Continuing Education by Ilkka Kokkarinen

Settings
Code:
Other:
Invalid hot key. Each hot key should be unique and valid
Hot keys:
CheckiO Extensions

CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

pip3 install checkio_client

Configure your tool

checkio --domain=py config --key=

Sync solutions into your local folder

checkio sync

(in beta testing) Launch local server so your browser can use it and sync solution between local file end extension on the fly. (doesn't work for safari)

checkio serv -d

Alternatevly, you can install Chrome extension or FF addon

checkio install-plugin
checkio install-plugin --ff
checkio install-plugin --chromium

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.

Pair Programming (Beta-version)

Welcome to Pair Programming! Engage in real-time collaboration on coding projects by starting a session and sharing the provided unique URL with friends or colleagues. This feature is perfect for joint project development, debugging, or learning new skills together. Simply click 'Start Session' to begin your collaborative coding journey!

Waiting for Pair Programming to start...

You are trying to join a pair programming session that has not started yet.

Please wait for the session creator to join.

Waiting for Pair Programming to reconnect...

It looks like the creator of the pair programming session closed the editor window.

It might happen accidentally, so that you can wait for reconnection.

×
 
 
<< <
> >>
exec show

Whats Next?

Free accounts will see Best CheckiO solutions with some delay.
Best Solutions will be opened in a moment
Become Awesome and Don't wait
The next stage is ""
Will be activated in
View More Solutions Random Review Solutions Go to the next mission