求使E=4N+0.3n最小的筹码组合的正确Python代码实现

给定面额数组 denominations = [0.1, 0.5, 1, 5, 20, 100, 500]，需为指定金额A找到最优筹码组合，使得目标函数 E = 4N + 0.3n 的值最小。其中：

• N：使用的不同类型筹码的总数
• n：所有筹码的总个数

示例：当金额A=6.8时，符合要求的组合为 [8, 0, 6, 0, 0, 0, 0]（对应0.1元筹码8个、1元筹码6个），对应的E = 4*2 + 0.3*14 = 12.2（N=2，n=8+6=14）。

我尝试编写的代码无法得到正确结果，请求协助编写正确代码，尝试代码如下：

from itertools import permutations
from itertools import combinations 
import math 

def elem_index(elem, arr):
  try:
    index = arr.index(elem)
  except ValueError:
    index = -1
  return index

def comb(arr, pos):
    comb_temp = combinations(arr, pos)
    result = [list(p) for p in comb_temp]
    return result

def chip_denomination(amt_low, denominations):
  #denominations = [x for x in original_denominations if x <= amt_low]
  E = 1000
  temp_low = amt_low
  final = [0 for i in range(len(denominations))]
  length = len(denominations)
  N = 1
  while (N < length):
    comb_arr = comb(denominations, N)
    chip_count_low = [0 for i in range(N)]
    for denom_new in comb_arr:
      denom_new.sort(reverse=True)
      i = 0
      while (i < N):
        chip_count_low[i] = math.floor(temp_low/denom_new[i])
        temp_low = temp_low%denom_new[i]
        if (chip_count_low[i] == 0 or (i == N-1 and temp_low > 0)):
          i = N
        else:
          i = i + 1
      if (elem_index(0, chip_count_low) == -1):
        E_new = 4*N + 0.3*sum(chip_count_low)
        if (E_new < E):
          E = E_new
          for j in range(N):
            final[elem_index(denom_new[j], denominations)] = chip_count_low[j]
    if (E - 4*(N+1) < 0):
      N = length
    else:
      print(f"Chips = {final} and Effort = {E} and N={N}")
      N = N + 1

denominations = [0.1, 0.5, 1, 5, 20, 100, 500]
amt_low = 6.8
chip_denomination(amt_low, denominations)

内容的提问来源于stack exchange，提问作者Vineet Mangal