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Suppose I could have a string with length 8 bytes, each byte is a character from one of the next ranges: 0-9,a-z,A-Z, totally 62 variants. Total number of permutations of this string is 62 to the power of 8 = 218340105584896. I need to write a function which will accept number in range
0-218340105584896 and return unique string. Under the unique I mean that function cannot return the same string for two different numbers in this range. Any code examples and hints will be appreciated.

User590254
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  • Unfortunately this is [off topics on Stack Overflow](https://stackoverflow.com/help/on-topic). What you want to do is however called *lexicographical order unranking*, and you may find [this paper](https://ldc.usb.ve/~bonet/reports/AAAI08-ws10-ranking.pdf) useful. – LSerni Jan 29 '18 at 00:44
  • @LSerni Thank you, I will study this paper and try to provide working code example for my question by my own, maybe it will be useful for someone. – User590254 Jan 29 '18 at 00:52
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    @LSerni: that paper is about *permutations*; although OP uses the word permutations, the question is about [Cartesian powers](https://en.wikipedia.org/wiki/Cartesian_product#Cartesian_power) of a set, which is quite a different thing. Moreover, [ask] does specifically allow questions about "a software algorithm", so it is not completely clear that the question is off-topic. It has, however, been answered many times. – rici Jan 29 '18 at 01:47

2 Answers2

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You could treat the number as a base 62 number, and fill in the string "digits" (base-62 bits) accordingly.

Let's see how we do this with the decimal number 1234 in different bases. note that division below is always integer division (fractional parts are chopped off).

Base 10 (decimal): 0-9

1234 / 10^3 = 1, 1234 mod 10^3 = 234
234 / 10^2 = 2, 234 mod 10^2 = 34
34 / 10^1 = 3, 34 mod 10^1 = 4
4 / 10^0 = 4, 4 mod 10^0 = 0
Thus we represent this number in base-10 as "1234"

Base 16 (hexadecimal): 0-9,a-f (where a=10, b=11, ...)

1234 / 16^2 = 4, 1234 mod 16^2 = 210
210 / 16^1 = d, 210 mod 16^1 = 2
2 / 16^0 = 2, 2 mod 16^0 = 0
Thus we represent this number in base-16 as "4d2"

This could extend to any base, including base-62: 0-9,a-z,A-Z

1234 / 62^1 = j, 1234 mod 62^1 = 56
56 / 62^0 = U, 56 mod 62^0 = 0
Thus we represent this number in base-62 as "jU"

I didn't bother doing leading 0's, but you could see that 1234 / 62^2 = 0, and 1234 mod 62^2 = 1234, so in base-62 you can have "000000jU".

Note that you could only do this for numbers in the range [0, 218340105584896), so it wouldn't be possible to represent 218340105584896.

yoyoyango
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If I understand your question correctly, then just yesterday I put a JavaScript code that answers it to another question Get offset in combinations without generating all possible combinations The method you are interested in is indexToPermutation. Note that JS has some limitations on number types so it will not work for your range but if you translate it into some other language that supports 64-bit long integer type, it should work. Unfortunately you didn't put any language tag so I can't do a translation myself.

SergGr
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  • Thank you for your answer, it helped me and i upvoted it, but yoyoyango provided explanation here, so I accepted his answer. – User590254 Jan 29 '18 at 01:25
  • @User590254, obviously you are free to accept any answer that you think deserves it. In my defense I think that the referenced answer contains "Some math behind it" section with similar explanation so I didn't provide it here. – SergGr Jan 29 '18 at 01:26