![Overlapping Disks](https://d17mnqrx9pmt3e.cloudfront.net/media/logos/task/middle/overlapping-disks-unsolved.png)
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)]
:
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
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.
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