[Python] Split number into chunks according to rank

This is a very practical task. I have a number of items that need to be distributed into several stores, according to store rank. So the higher the rank, the more items store will get, so store with rank 1 will get most items and store with rank 100 least.

So the inputs are:

• number of items to distribute
• stores, represented by their rank, can have duplicates as well, and does not follow any pattern, for instance [1, 4, 40]

Right now, I have the following:

• I inverse the ranks, so that smaller number would become biggest (sum(n...) - n)
• I take percentage of each store: inversed_rank \ sum(inversed_ranks)
• Multiply the amount I need to distribute by the percentage

It works fine on some of the numbers, like:

[1, 4, 40]
1 = 147.2
4 = 137.1
40 = 16.7


Clearly, the store with rank 40 gets the least, but with more stores it flattens:

[6,3,24,10, 25, 12, 14,35,40, 16,28,29,17,1,26,23,8,10]
1 = 17.7
3 = 17.5
6 = 17.4
8 = 17.3
10 = 17.2
10 = 17.2
12 = 17.1
14 = 16.9
16 = 16.8
17 = 16.8
23 = 16.5
24 = 16.4
25 = 16.4
26 = 16.3
28 = 16.2
29 = 16.1
35 = 15.8
40 = 15.5


So store with rank 40 gets only a fraction less than the top. How can I make it a bit more "curved"?

My Python code:

number = 301

ranks = [6,3,24,10, 25, 12, 14,35,40, 16,28,29,17,1,26,23,8,10]
#ranks = [1,4,40]

ranks.sort()

total = sum(ranks)
tmp = 0

reversed = []

for value in ranks:
reversed.append(total - value)

total = sum(reversed)
print('Items per rank:')
for i in range(len(ranks)):
percent = reversed / total
print(str(ranks) + ' = ' + "{:10.1f}".format(percent * number))
tmp = tmp + percent * number

print('')
print('Total = ' + str(tmp))


You may play with it here: https://trinket.io/python/a15c54b978 Would be perfect to have a more math rather than library solution as I will need to translate it into Excel VBA

Solution

I have also added a factor to control the distribution:

number = 301

ranks = [6,3,24,10, 25, 12, 14,35,40, 16,28,29,17,1,26,23,8,10]
#ranks = [1,4,40]
factor = 1

ranks.sort()

total = sum(ranks)
tmp = 0
max = max(ranks) + 1

reversed = []

for value in ranks:
reversed_value = max - value
reversed_value = pow(reversed_value, factor)
reversed.append(reversed_value)

total = sum(reversed)
print('Items per rank:')
for i in range(len(ranks)):
percent = reversed / total
value = percent * number

print(str(ranks) + ' = ' + "{:10.1f}".format(value))
tmp = tmp + value


print('')
print('Total = ' + str(tmp))

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