Question

I’m looking for an algorithm or function that is able to map a string to a number in such way that the resulting values correspond the lexicographic ordering of strings. Example:

"book" -> 50000
"car"  -> 60000
"card" -> 65000
"a longer string" -> 15000
"another long string" -> 15500
"awesome" -> 16000

As a function it should be something like: f(x) = y, so that for any x1 < x2 => f(x1) < f(x2), where x is an arbitrary string and y is a number.

If the input set of x is finite, then I could always do a sort and assign the proper values, but I’m looking for something generic for an unlimited input set for x.

Answer 1

If you require that f map to integers this is impossible.

Suppose that there is such a map f. Consider the strings a, aa, aaa, etc. Consider the values f(a), f(aa), f(aaa), etc. As we require that f(a) < f(aa) < f(aaa) < ... we see that f(a_n) tends to infinity as n tends to infinity; here I am using the obvious notation that a_n is the character a repeated n times. Now consider the string b. We require that f(a_n) < f(b) for all n. But f(b) is some finite integer and we just showed that f(a_n) goes to infinity. We have a contradiction. No such map is possible.

Maybe you could tell us what you need this for? This is fairly abstract and we might be able to suggest something more suitable. Further, don’t necessarily worry about solving “it” generally. YAGNI and all that.