## Valid Number

### 描述

Validate if a given string is numeric.

Some examples:

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


Note: It is intended for the problem statement to be ambiguous. You should gather all requirements up front before implementing one.

### 有限自动机

// Valid Number
// @author 龚陆安 (http://weibo.com/luangong)
// finite automata，时间复杂度O(n)，空间复杂度O(n)
class Solution {
public:
bool isNumber(const string& s) {
enum InputType {
INVALID,    // 0
SPACE,      // 1
SIGN,       // 2
DIGIT,      // 3
DOT,        // 4
EXPONENT,   // 5
NUM_INPUTS  // 6
};
const int transitionTable[][NUM_INPUTS] = {
-1, 0, 3, 1, 2, -1, // next states for state 0
-1, 8, -1, 1, 4, 5,     // next states for state 1
-1, -1, -1, 4, -1, -1,     // next states for state 2
-1, -1, -1, 1, 2, -1,     // next states for state 3
-1, 8, -1, 4, -1, 5,     // next states for state 4
-1, -1, 6, 7, -1, -1,     // next states for state 5
-1, -1, -1, 7, -1, -1,     // next states for state 6
-1, 8, -1, 7, -1, -1,     // next states for state 7
-1, 8, -1, -1, -1, -1,     // next states for state 8
};

int state = 0;
for (auto ch : s) {
InputType inputType = INVALID;
if (isspace(ch))
inputType = SPACE;
else if (ch == '+' || ch == '-')
inputType = SIGN;
else if (isdigit(ch))
inputType = DIGIT;
else if (ch == '.')
inputType = DOT;
else if (ch == 'e' || ch == 'E')
inputType = EXPONENT;

// Get next state from current state and input symbol
state = transitionTable[state][inputType];

// Invalid input
if (state == -1) return false;
}
// If the current state belongs to one of the accepting (final) states,
// then the number is valid
return state == 1 || state == 4 || state == 7 || state == 8;

}
};