Valid Number

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.

class Solution {
public:
    bool isNumber(const char *s) {
        // Start typing your C/C++ solution below
        // DO NOT write int main() function
        int dot_cnt_e = 0;
        int e_dot_cnt = 0;
        int flag_cnt_e = 0;
        int e_flag_cnt = 0;
        bool has_number_e = false;
        bool e_has_number = false;
        bool has_e = false;
        bool start = false;
        const char* p = s;
        
        while (*p) {
            if (invalid_char(*p)) {
                return false;
            }
            
            if (*p == ' ' && start && !(*(p+1) == ' ' || *(p+1) == '\0')) {
                return false;
            }
            
            if (*p == '+' || *p == '-') {
                if (has_number_e && *(p-1) != 'e') {
                    return false;
                }
                if (is_digit(*(p-1)) || *(p-1) == '.') {
                    return false;
                }
                if (has_e) {
                    ++e_flag_cnt;
                } else {
                    ++flag_cnt_e;
                }
                if (e_flag_cnt > 1 || flag_cnt_e > 1) {
                    return false;
                }
                start = true;
            }
            
            if (*p == '.') {
                if (!start) {
                    start = true;
                }
                if (has_e) {
                    ++e_dot_cnt; 
                } else {
                    ++dot_cnt_e;
                }
                if (e_dot_cnt > 0 || dot_cnt_e > 1) {
                    return false;
                }
            }
            
            if (*p == 'e') {
                if (has_e) {
                    return false;
                } else {
                    has_e = true;
                }
                if (!is_digit(*(p+1)) && *(p+1) != '+' && *(p+1) != '-') {
                    return false;
                }
                if (!has_number_e) {
                    return false;
                }
            }
            
            if (is_digit(*p)) {
                if (!start) {
                   start = true;
                }
                if (!has_number_e) {
                    has_number_e = true;
                }
                if (has_e && !e_has_number) {
                    e_has_number = true;
                }
                
            }
            ++p;
        }
        if (has_e) {
            return e_has_number;
        } else {
            return has_number_e;
        }
    }
    
private: 
   bool invalid_char(char ch) {
       return !(ch == 'e' || ch == '.' || ch == '+' || ch == '-' || ch == ' ' || is_digit(ch));
   }
   
   bool is_digit(char ch) {
       return ch >= '0' && ch <= '9';
   }
};