Leetcode (Python): Valid Number

Validate if a given string is numeric.

Some examples:
"0" => true
" 0.1 " => true
"abc" => false
"1 a" => false
"2e10" => true

Solution:

This problem deals with a common problem in compilers in the lexical analysis, i.e.  knowing if a certain string is a valid token.

We accept the following regular grammar, shown as UNIX regular expression by simplicity:
\s*[\+\-]?(([0-9]+(\.[0-9]*)?)|\.[0-9]+)([eE][+-]?[0-9]+)?\s*
where \s represents [ \t].

This regular expression is accepted by the underneath DFA(Deterministic Finite Automata):

where any transition not shown takes to an error state, that in the code is represented by -1.

class Solution:
    # @param s, a string
    # @return a boolean
    def isNumber(self, s):
        state = 0
        for i in xrange(0,len(s)):
            state = self.nextState(state, s[i])
            if state == -1: 
                return False
        state = self.nextState(state, ' ')
        return state == 8
    
    def nextState(self, state,char):
        transititionTable = [[0,2,1,3,-1,-1], [-1,2,-1,3,-1,-1], [8,2,-1,4,5,-1], [-1,4,-1,-1,-1,-1], [8,4,-1,-1,5,-1],[-1,7,6,-1,-1,-1],[-1,7,-1,-1,-1,-1], [8,7,-1,-1,-1,-1], [8,-1,-1,-1,-1,-1]];
        return transititionTable[state][self.getSymbol(char)]
    
    def getSymbol(self, char):
        if char == ' ' or char == '\t':
            return 0
        if char.isdigit():
            return 1
        if char == '+'  or char == '-':
            return 2
        if char == '.':
            return 3
        if char == 'E' or char =='e':
            return 4
        return 5

More information:
[1, Chapter 1] J. Glen Brookshear, "Theory of Computation: Formal Languages, Automata, and Complexity", Addison-Wesley.

[2, Chapters 2-3] Rajeev Motwani, Jeffrey Ullman, and John Hopcroft, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley.