What base is this number in?

Question

Here's a nice easy challenge:

Given a string that represents a number in an unknown base, determine the lowest possible base that number might be in. The string will only contain 0-9, a-z. If you like, you may choose to take uppercase letters instead of lowercase, but please specify this. You must output this lowest possible base in decimal.

Here is a more concrete example. If the input string was "01234", it is impossible for this number to be in binary, since 2, 3, and 4 are all undefined in binary. Similarly, this number cannot be in base 3, or base 4. Therefore, this number must be in base-5, or a higher base, so you should output '5'.

Your code must work for any base between base 1 (unary, all '0's) and base 36 ('0-9' and 'a-z').

You may take input and provide output in any reasonable format. Base-conversion builtins are allowed. As usual, standard loopholes apply, and the shortest answer in bytes is the winner!

Test IO:

#Input          #Output
00000       --> 1
123456      --> 7
ff          --> 16
4815162342  --> 9
42          --> 5
codegolf    --> 25
0123456789abcdefghijklmnopqrstuvwxyz    --> 36

Answer 1

Perl, 30 27 bytes

Includes +1 for -p

Run with the input on STDIN, e.g.

base.pl <<< codegolf

base.pl:

#!/usr/bin/perl -p
\@F[unpack"W*"];$_=@F%39-9

Answer 2

LiveScript, 32 bytes

->1+parseInt (it/'')sort!pop!,36

A port of this answer in my favorite language that compile to JavaScript. If base~number operator worked with variables I could write ->1+36~(it/'')sort!pop! (23 bytes), but it conflicts with the function bind operator :/

Answer 3

PowerShell full program, 56 62 bytes

lowercase letters required.

([int]((read-host).ToCharArray()|sort|select -l 1)-8)%39

Answer 4

R, 59 57 bytes

Thanks to @Andreï-Kostyrka for two bytes.

max(which(c(0:9,letters)%in%strsplit(scan(,""),"")[[1]]))

scan(,'') takes the input and coerces it to a string. Then strsplit divides it into its individual characters. [[1]] is because that returns a list. %in% then checks which of the vector 0,1,2,...,8,9,a,b,c,...,x,y,z is in the input. which tells us the place in that vector of items in the input -- and max finds the biggest place -- which corresponds to the base.

Answer 5

05AB1E, 3 bytes

Hà>

Try it online or validate all test cases.

Explanation:

          # implicit input
H         # convert each digit to decimal
 à        # maximum
  >       # add 1
          # implicit output

Answer 6

Thunno 2 G, 4 bytes

36b⁺

Try it online!

Takes input in uppercase.

Explanation

36b⁺  # Implicit input
36b   # Convert each character from base-36
   ⁺  # Increment each integer
      # Implicit output of maximum