如何从 itertools 排列中调用索引值而不将其转换为列表？

Question

I need to create all combinations of these characters:

'0123456789qwertyuiopasdfghjklzxcvbnmQWERTYUIOPASDFGHJKLZXCVBNM. '

That are 100 letters long, such as:

'0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001'

I'm currently using this code:

import itertools
babel = itertools.product(k_c, repeat = 100)

This code works, but I need to be able to return the combination at a certain index, however itertools.product does not support indexing, turning the product into a list yields a MemoryError, and iterating through the product until I reaches a certain value takes too long for values over a billion.

Thanks for any help

Answer 1

With 64 characters and 100 letters there will be 64^100 combinations. For each value of the first letter, there will be 64^99 combinations of the remaining letters, then 64^98, 64^97, and so on.

This means that your Nth combination can be expressed as N in base 64 where each "digit" represents the index of the letter in the string.

An easy solution would be to build the string recursively by progressively determining the index of each position and getting the rest of the string with the remainder of N:

chars = '0123456789qwertyuiopasdfghjklzxcvbnmQWERTYUIOPASDFGHJKLZXCVBNM. '

def comboNumber(n,size=100):
    if size == 1: return chars[n]
    return comboNumber(n//len(chars),size-1)+chars[n%len(chars)]

output:

c = comboNumber(123456789000000000000000000000000000000000000123456789)
print(c)
# 000000000000000000000000000000000000000000000000000000000000000000000059.90jDxZuy6drpQdWATyZ8007dNJs


c = comboNumber(1083232247617211325080159061900470944719547986644358934)
print(c)
# 0000000000000000000000000000000000000000000000000000000000000000000000Python.Person says Hello World

Conversely, if you want to know at which combination index a particular string is located, you can compute the base64 value by combining the character index (digit) at each position:

s = "Python.Person says Hello World" # leading zeroes are implied
i = 0
for c in s:
    i = i*len(chars)+chars.index(c)
print(i) # 1083232247617211325080159061900470944719547986644358934

You are now this much closer to understanding base64 encoding which is the same thing applied to 24bit numbers coded over 4 characters (ie 3 binary bytes --> 4 alphanumeric characters) or any variant thereof