6.27 - hard - 15

65. Valid Number

这道题一眼看上去会觉得什么鬼题目，但是看了答案里有一种用DFA的解法，感觉很妙，DFA是个啥我也不知道，但是我觉得可以理解为确定状态机

valid_number_dfa.png

class Solution(object):
    def isNumber(self, s):
        """
        :type s: str
        :rtype: bool
        """
        #define DFA state transition tables
        states = [{},
                 # State (1) - initial state (scan ahead thru blanks)
                 {'blank': 1, 'sign': 2, 'digit':3, '.':4},
                 # State (2) - found sign (expect digit/dot)
                 {'digit':3, '.':4},
                 # State (3) - digit consumer (loop until non-digit)
                 {'digit':3, '.':5, 'e':6, 'blank':9},
                 # State (4) - found dot (only a digit is valid)
                 {'digit':5},
                 # State (5) - after dot (expect digits, e, or end of valid input)
                 {'digit':5, 'e':6, 'blank':9},
                 # State (6) - found 'e' (only a sign or digit valid)
                 {'sign':7, 'digit':8},
                 # State (7) - sign after 'e' (only digit)
                 {'digit':8},
                 # State (8) - digit after 'e' (expect digits or end of valid input) 
                 {'digit':8, 'blank':9},
                 # State (9) - Terminal state (fail if non-blank found)
                 {'blank':9}]
        currentState = 1
        for c in s:
            # If char c is of a known class set it to the class name
            if c in '0123456789':
                c = 'digit'
            elif c in ' \t\n':
                c = 'blank'
            elif c in '+-':
                c = 'sign'
            # If char/class is not in our state transition table it is invalid input
            if c not in states[currentState]:
                return False
            # State transition
            currentState = states[currentState][c]
        # The only valid terminal states are end on digit, after dot, digit after e, or white space after valid input    
        if currentState not in [3,5,8,9]:
            return False
        return True