Submission #68688300

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Source Code Expand

from itertools import product
from functools import cache
from collections import defaultdict
from fractions import Fraction as F
A=list(map(int,input().split()))

# 値が0-5の大きさnの多重集合を列挙
deme=[defaultdict(lambda: F(0,1)) for _ in range(6)]
for n in range(1,6):
  deno=6**n
  for idxs in product(range(6),repeat=n):
    deme[n][tuple(sorted(idxs))]+=F(1,deno)

@cache
def f(rest_turn, keep_idxs):
  # rest_turn ターン残って、キープしてる出目のindexの集合がkeep_idxsのときの最終的な得点の期待値
  if len(keep_idxs)==5:
    count = defaultdict(int)
    for idx in keep_idxs: count[A[idx]] += 1
    return max(k*v for k,v in count.items())
  rest_dice = 5-len(keep_idxs)
  ans = 0
  for deme_idxs in product(range(6), repeat=rest_dice):
    prob = F(1, 6**rest_dice)
    M=0
    for keep in (range(1<<rest_dice) if rest_turn!=1 else [(1<<rest_dice)-1]):
      M=max(M,f(rest_turn-1, tuple(sorted(keep_idxs+tuple(idx for i,idx in enumerate(deme_idxs) if (keep>>i)&1)))))
    ans+=M*prob
  return ans

print(f"{float(f(3,tuple())):.10f}")

Submission Info

Judge Result