英文:
Memoisation - Bernoulli numbers
问题
我理解你只需要对代码进行翻译，以下是代码的翻译部分：
from fractions import Fractionfrom scipy.special import combimport numpy as np# 缓存bernoulli_cache = {}def bernoulli(n: float):# 检查输入，如果存在则返回值if n in bernoulli_cache:return bernoulli_cache[n]# 当输入为0或1时if n == 0:value = Fraction(1)else:value = Fraction(1)for k in range(n):value -= Fraction(comb(n, k)) * Fraction(bernoulli(k), (n - k + 1))# 写入缓存bernoulli_cache[n] = value# 分数部分用于输出numerator = value.numeratordenominator = value.denominatorreturn numerator, denominator# 测试是否有效 - 缓存中已有部分bernoulli_cache = {}bernoulli(0) # 1bernoulli(1) # 1/2bernoulli(2) # 1/6bernoulli(3) # 0bernoulli(4) # −1/30bernoulli(5) # 0bernoulli(6) # 1/42bernoulli(7) # 0bernoulli(8) # -1/30# 这个不会有效 - 缓存中没有部分bernoulli_cache = {}bernoulli(8) # -1/30
希望这对你有所帮助！
英文:
I am trying to compute some Bernoulli numbers and am trying to use memoisation. In the example below, I can get the Bernoulli number for 8 when I run 1-7 before it, but not if the cache is clear. What changes would I need to make to run it when the cache is clear?
from fractions import Fractionfrom scipy.special import combimport numpy as np# memoisationbernoulli_cache = {}def bernoulli(n: float):# check input, if it exists, return valueif n in bernoulli_cache:return bernoulli_cache[n]# when input is 0 or 1if n == 0:value = Fraction(1)else:value = Fraction(1)for k in range(n):value -= Fraction(comb(n, k)) * Fraction(bernoulli(k), (n - k + 1))# write to cachebernoulli_cache[n] = value# fraction parts for outputnumerator = value.numeratordenominator = value.denominatorreturn numerator, denominator# test this works- bits in cache aleadybernoulli_cache = {}bernoulli(0) # 1bernoulli(1) # 1/2bernoulli(2) # 1/6bernoulli(3) # 0bernoulli(4) # −1/30bernoulli(5) # 0bernoulli(6) # 1/42bernoulli(7) # 0bernoulli(8) # -1/30# this doesn't - bits not in cachebernoulli_cache = {}bernoulli(8) # -1/30
答案1
得分: 1
Your cache is storing a Fraction so when you have a cache hit you're returning a Fraction. When you have a cache miss you're returning a tuple. You can fix this by changing return numerator, denominator to return Fraction(numerator, denominator).
英文:
Your cache is storing a Fraction so when you have a cache hit you're returning a Fraction. When you have a cache miss you're returning a tuple. You can fix this by changing return numerator, denominator to return Fraction(numerator, denominator).
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