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
