class Solution {public:    // a valid number should be in the below form    // -/+digit.digitE/e+/-digit    bool isNumber(const char *s) {        if (s == NULL) return false;        int end = 0;        while (s[end] != ‘\0‘) end++;        while (s[--end] == ‘ ‘);        end++;        // 0-initial, 1-sign-collected, 2-integer_part digit collected, 3-float_point collected,        // 4-fraction part digit collected, 5-e/E collected, 6-sign of E collected, 7-digit of E collected,        // 8-mid_space        int stage = 0;         int pos = 0;        char ch = ‘\0‘;                int stages = 0;;        while ((ch = s[pos]) != ‘\0‘ && pos < end) {            switch(stage) {                case 0: // initial                    if (ch == ‘ ‘) {                        // white spaces, just skip                        pos++;                    } else if (ch == ‘+‘ || ch == ‘-‘) {                        // sign found                        stage = 1;                        pos++;                    } else if (ch == ‘.‘) {                        // float point found                        stage = 3;                        pos++;                    } else if (ch >= ‘0‘ && ch <= ‘9‘) {                        // digit found                        stage = 2;                    } else {                        // the other chars are invalid in [initial stage]                        return false;                    }                    break;                case 1: // sign collected                    stages |= 1<<(stage - 1);                    if (ch >= ‘0‘ && ch <= ‘9‘) {                        // digit found                        stage = 2;                    } else if (ch == ‘.‘) {                        // float point found                        stage = 3;                        pos++;                    } else {                        // the other chars are invalid in [sign collected stage]                        return false;                    }                    break;                case 2: // integer part digit collected                    stages |= 1<<(stage - 1);                    if (ch >= ‘0‘ && ch <= ‘9‘) {                        // integer part digit found                        pos++;                    } else if (ch == ‘.‘){                        // float point found                        pos++;                        stage = 3;                    } else if (ch == ‘e‘ || ch == ‘E‘) {                        // E found                        pos++;                        stage = 5;                    } else {                        // the other chars are invalid                        return false;                    }                    break;                case 3: // float point collected                    stages |= 1<<(stage - 1);                    if (ch >= ‘0‘ && ch <= ‘9‘) {                        // fraction part digit found                        stage = 4;                    } else if (ch == ‘E‘ || ch == ‘e‘) {                        // E/e found                        pos++;                        stage = 5;                    } else {                        // the other chars are invalid                        return false;                    }                    break;                case 4: // fraction part digit collected                    stages |= 1<<(stage - 1);                    if (ch >= ‘0‘ && ch <= ‘9‘) {                        // fraction part digit found                        pos++;                    } else if (ch == ‘e‘ || ch == ‘E‘) {                        // e/E found;                        pos++;                        stage = 5;                    } else {                        return false;                    }                    break;                case 5: // e/E collected                    stages |= 1<<(stage - 1);                    if (ch >= ‘0‘ && ch <= ‘9‘) {                        // E digit found                        stage = 7;                    } else if (ch == ‘-‘ || ch == ‘+‘) {                        // sign of e found                        pos++;                        stage = 6;                    } else {                        return false;                    }                    break;                case 6: // sign of E collected                    stages |= 1<<(stage - 1);                    if (ch >= ‘0‘ && ch <= ‘9‘) {                        // E digit found                        stage = 7;                    } else {                        // others are invalid                        return false;                    }                    break;                case 7: // digit of E collected                    stages |= 1<<(stage - 1);                    if (ch >= ‘0‘ && ch <= ‘9‘) {                        pos++;                    } else {                        return false;                    }                    break;                default:                    cout<<"case should not happen"<<endl;                    return false;            }        }                // should not end with these stage        if (stage == 0 || stage == 1 || stage == 5 || stage == 6) {            return false;        }        // float point collected and no preceed integer found        // (hasn‘t walk through integer part stage)        if (stage == 3 && !(stages & 1<<1)) {            return false;        }                // E collected but no base number collected        // (hasn‘t walk through neither integer part digit stage or fraction part digit stage)        if ((stages & 1<<4) && !(stages & 1<<1) && !(stages & 1<<3)) {            return false;        }        return true;    }};