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First solution in Clear category for Probably Dice by aya.kanazawa
from functools import lru_cache
@lru_cache(maxsize=None)
def combination_count(dice_number, sides, target):
count = 0
if dice_number == 1:
if target in list(range(1, sides + 1)):
count += 1
else:
for side in range(1, sides + 1):
count += combination_count(dice_number -1, sides, target - side)
return count
def probability(dice_number, sides, target):
print((dice_number, sides, target))
count = combination_count(dice_number, sides, target)
print(round(count / (sides ** dice_number), 4))
return round(count / (sides ** dice_number), 4)
if __name__ == '__main__':
#These are only used for self-checking and are not necessary for auto-testing
def almost_equal(checked, correct, significant_digits=4):
precision = 0.1 ** significant_digits
return correct - precision < checked < correct + precision
assert(almost_equal(probability(2, 6, 3), 0.0556)), "Basic example"
assert(almost_equal(probability(2, 6, 4), 0.0833)), "More points"
assert(almost_equal(probability(2, 6, 7), 0.1667)), "Maximum for two 6-sided dice"
assert(almost_equal(probability(2, 3, 5), 0.2222)), "Small dice"
assert(almost_equal(probability(2, 3, 7), 0.0000)), "Never!"
assert(almost_equal(probability(3, 6, 7), 0.0694)), "Three dice"
assert(almost_equal(probability(10, 10, 50), 0.0375)), "Many dice, many sides"
April 25, 2019