Pythonで式の結果の最大発生頻度値の期待値を見つけるプログラム

例

理解を深めるために、次の実装を見てみましょう-

combination = {}
def nCr(n, k_in):
   k = min(k_in, n - k_in)
   if n < k or k < 0:
      return 0
   elif (n, k) in combination:
      return combination[(n, k)]
   elif k == 0:
      return 1
   elif n == k:
      return 1
   else:
      a = 1
      for cnt in range(k):
         a *= (n - cnt)
         a //= (cnt + 1)
         combination[(n, cnt + 1)] = a
      return a

def solve(M, N):
   arr = []
   for k in range(2, M + 2):
      a = 1
      s = 0
      for i in range(M // k + 2):
         if (M < i * k):
            break
         s += a * nCr(N, i) * nCr(N - 1 + M - i * k, M - i * k)
         a *= -1
      arr.append(s)
   total = arr[-1]
   diff = [arr[0]] + [arr[cnt + 1] - arr[cnt] for cnt in range(M - 1)]
   output = sum(diff[cnt] * (cnt + 1) / total for cnt in range(M))
   return output

M = 3
N = 3
print(solve(M, N))

入力

3, 3

出力

1