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DP solution in Clear category for Pearls in the Box by martin_b
def probability(marbles, step):
t = len(marbles)
dp = [(1, marbles.count('w'))]
for s in range(step - 1):
d = []
for p, w in dp:
if w > 0:
d.append((p * w / t, w - 1))
if w < t:
d.append((p * (t - w) / t, w + 1))
dp = d
return round(sum([p * w / t for p, w in dp]), 2)
checkio = probability
#These "asserts" using only for self-checking and not necessary for auto-testing
if __name__ == '__main__':
assert checkio('bbw', 3) == 0.48, "1st example"
assert checkio('wwb', 3) == 0.52, "2nd example"
assert checkio('www', 3) == 0.56, "3rd example"
assert checkio('bbbb', 1) == 0, "4th example"
assert checkio('wwbb', 4) == 0.5, "5th example"
assert checkio('bwbwbwb', 5) == 0.48, "6th example"
Feb. 1, 2016
