mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-18 01:00:15 +00:00
90 lines
3.0 KiB
Python
90 lines
3.0 KiB
Python
"""
|
||
In the game of darts a player throws three darts at a target board which is
|
||
split into twenty equal sized sections numbered one to twenty.
|
||

|
||
The score of a dart is determined by the number of the region that the dart
|
||
lands in. A dart landing outside the red/green outer ring scores zero. The black
|
||
and cream regions inside this ring represent single scores. However, the red/green
|
||
outer ring and middle ring score double and treble scores respectively.
|
||
|
||
At the centre of the board are two concentric circles called the bull region, or
|
||
bulls-eye. The outer bull is worth 25 points and the inner bull is a double,
|
||
worth 50 points.
|
||
|
||
There are many variations of rules but in the most popular game the players will
|
||
begin with a score 301 or 501 and the first player to reduce their running total
|
||
to zero is a winner. However, it is normal to play a "doubles out" system, which
|
||
means that the player must land a double (including the double bulls-eye at the
|
||
centre of the board) on their final dart to win; any other dart that would reduce
|
||
their running total to one or lower means the score for that set of three darts
|
||
is "bust".
|
||
|
||
When a player is able to finish on their current score it is called a "checkout"
|
||
and the highest checkout is 170: T20 T20 D25 (two treble 20s and double bull).
|
||
|
||
There are exactly eleven distinct ways to checkout on a score of 6:
|
||
|
||
D3
|
||
D1 D2
|
||
S2 D2
|
||
D2 D1
|
||
S4 D1
|
||
S1 S1 D2
|
||
S1 T1 D1
|
||
S1 S3 D1
|
||
D1 D1 D1
|
||
D1 S2 D1
|
||
S2 S2 D1
|
||
|
||
Note that D1 D2 is considered different to D2 D1 as they finish on different
|
||
doubles. However, the combination S1 T1 D1 is considered the same as T1 S1 D1.
|
||
|
||
In addition we shall not include misses in considering combinations; for example,
|
||
D3 is the same as 0 D3 and 0 0 D3.
|
||
|
||
Incredibly there are 42336 distinct ways of checking out in total.
|
||
|
||
How many distinct ways can a player checkout with a score less than 100?
|
||
|
||
Solution:
|
||
We first construct a list of the possible dart values, separated by type.
|
||
We then iterate through the doubles, followed by the possible 2 following throws.
|
||
If the total of these three darts is less than the given limit, we increment
|
||
the counter.
|
||
"""
|
||
|
||
from itertools import combinations_with_replacement
|
||
|
||
|
||
def solution(limit: int = 100) -> int:
|
||
"""
|
||
Count the number of distinct ways a player can checkout with a score
|
||
less than limit.
|
||
>>> solution(171)
|
||
42336
|
||
>>> solution(50)
|
||
12577
|
||
"""
|
||
singles: list[int] = [*list(range(1, 21)), 25]
|
||
doubles: list[int] = [2 * x for x in range(1, 21)] + [50]
|
||
triples: list[int] = [3 * x for x in range(1, 21)]
|
||
all_values: list[int] = singles + doubles + triples + [0]
|
||
|
||
num_checkouts: int = 0
|
||
double: int
|
||
throw1: int
|
||
throw2: int
|
||
checkout_total: int
|
||
|
||
for double in doubles:
|
||
for throw1, throw2 in combinations_with_replacement(all_values, 2):
|
||
checkout_total = double + throw1 + throw2
|
||
if checkout_total < limit:
|
||
num_checkouts += 1
|
||
|
||
return num_checkouts
|
||
|
||
|
||
if __name__ == "__main__":
|
||
print(f"{solution() = }")
|