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First solution in Clear category for Probably Dice by andriutwich
def generating(coef, power):
if power == 0:
return [1]
elif power % 2 == 0:
tmp = generating(coef, power / 2)
ans = [0] * (2 * len(tmp) - 1)
for i1, v1 in enumerate(tmp):
for i2, v2 in enumerate(tmp):
ans[i1 + i2] += v1 * v2
return ans
else:
tmp = generating(coef, power - 1)
ans = [0] * (len(tmp) + len(coef) - 1)
for i1, v1 in enumerate(tmp):
for i2, v2 in enumerate(coef):
ans[i1 + i2] += v1 * v2
return ans
def probability(dice_number, sides, target):
try:
return round(float(generating([0] + [1] * sides, dice_number)[target]) / (sides ** dice_number), 4)
except IndexError:
return 0.
if __name__ == '__main__':
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"
Jan. 12, 2017
