65有效數字

驗證給定的字符串是否可以解釋爲十進制數字。

例如:

"0" => true
" 0.1 " => true
"abc" => false
"1 a" => false
"2e10" => true
" -90e3   " => true
" 1e" => false
"e3" => false
" 6e-1" => true
" 99e2.5 " => false
"53.5e93" => true
" --6 " => false
"-+3" => false
"95a54e53" => false

說明: 我們有意將問題陳述地比較模糊。在實現代碼之前，你應當事先思考所有可能的情況。這裏給出一份可能存在於有效十進制數字中的字符列表：

    數字 0-9
    指數 - "e"
    正/負號 - "+"/"-"
    小數點 - "."

當然，在輸入中，這些字符的上下文也很重要。

更新於 2015-02-10:
C++函數的形式已經更新了。如果你仍然看見你的函數接收 const char * 類型的參數，請點擊重載按鈕重置你的代碼。

//自動機 狀態轉移圖 條件 狀態太多太容易出錯了
//注意點
//1 table初始化時括號的位置
//2 返回true的結果可能是多個，不唯一
//3 前後空格情況："  1.2e-3  " true
//4 小數點前後有沒有數字情況： " -.2e-3 " true    " +1.e-3 " true    ".e-3 " false
//5 用int代替string表示狀態名稱應該可以更快

//一個究極完整的數字裏面的可以分爲 SA.BeCS or SA.eCS or S.BeCS
//S: 連續空格
//A：可帶符號數
//B：無符號數字
//C：可帶符號數
class Solution {
    unordered_map<string,vector<string>>table{//vector的大小等於轉移條件的總個數
        {"start",{"S2","S1","S3_1","S8","start","S8"}},
        {"S1",{"S2","S8","S3_1","S8","S8","S8"}},
        {"S2",{"S2","S8","S3_2","S5","S9","S8"}},
        {"S3_1",{"S3_2","S8","S8","S8","S8","S8"}},
        {"S3_2",{"S4","S8","S8","S5","S9","S8"}},
        {"S4",{"S4","S8","S8","S5","S9","S8"}},
        {"S5",{"S7","S6","S8","S8","S8","S8"}},
        {"S6",{"S7","S8","S8","S8","S8","S8"}},
        {"S7",{"S7","S8","S8","S8","S9","S8"}},
        {"S8",{"S8","S8","S8","S8","S8","S8"}},
        {"S9",{"S8","S8","S8","S8","S9","S8"}},
    };    
public:
    bool isNumber(string s) {
        string state="start";
        for(auto c:s)
            state=table[state][getIndex(c)];
        if(state=="S2"||state=="S4"||state=="S7"||state=="S9"||state=="S3_2")
            return true;
        else return false;
    }
    int getIndex(char c){
        if(isdigit(c))return 0;
        if(c=='+'||c=='-')return 1;
        if(c=='.')return 2;
        if(c=='e')return 3;
        if(c==' ')return 4;
        return 5;

//方法二：一遍掃描 正則表達式
//去頭空格
//有無符號
    //連續數字.e
    //.連續數字e
    //連續數字.連續數字e
//有無符號
//連續數字
//去尾空格