LeetCode "Valid Number"

It took me +20 submissions to get AC... Actually the statement is too vague. I would rather ask for requirements f2f.

Apparently the code below can be simplified..

class Solution {
public:
    bool isPureNum(string s, int radix)
    {        
        if (s.length() > 1 && s[s.length() - 1] == '.')
        {
            s = s.substr(0, s.length() - 1);
        }
        int i = 0;
        while(i < s.length())
        {
            char c = s[i++];
            switch(radix)
            {
            case 10:
                if(!(c >= '0' && c <= '9')) return false;
                break;
            case 16:
                if(!((c >= '0' && c <= '9') || (c >= 'a' && c <= 'f'))) return false;
                break;
            }
        }
        return true;
    }
    bool isFloat(string str)
    {
        size_t pos = str.find('.', 0);
        string s1 = str.substr(0, pos);
        if(s1.find('.', 0) != string::npos) return false;
        string s2 = str.substr(pos + 1, str.length() - pos - 1);
        if(s2.find('.', 0) != string::npos) return false;
        if (s1.empty() && s2.empty()) return false;
        return isPureNum(s1, 10) && 
                isPureNum(s2, 10);
    }
    bool isNumber(const char *s) {
        int len = strlen(s);
        if(len == 0) return false;
        //    Trim
        int il = 0, ir = len - 1;
        while(*(s + il) == ' ') il ++;
        while(*(s + ir) == ' ') ir --;
        if(ir < il) return false;
        //    ToLower
        string str; str.assign(s + il, s + ir + 1);
        std::transform(str.begin(), str.end(), str.begin(), ::tolower);
        if(str[0] == '-' || str[0] == '+') str = str.substr(1, str.length() - 1);
        len = str.length();

        char c = str[0];
        size_t pos1 = str.find('e', 0);
        if(pos1 != string::npos)
        {
            //    2e10
            string s1 = str.substr(0, pos1);
            if(s1.empty()) return false;
            if(s1.find('e', 0) != string::npos) return false;
            string s2 = str.substr(pos1 + 1, str.length() - pos1 - 1);
            if(s2.find('e', 0) != string::npos) return false;
            if(s2.find('.', 0) != string::npos) return false;                    
            if(s2[0] == '-' ||s2[0] == '+') s2 = s2.substr(1, s2.length() - 1);
            if(s2.empty()) return false;
            return (isPureNum(s1, 10) || isFloat(s1)) && 
                    isPureNum(s2, 10);
        }
        else
        {
            if(isdigit(c))
            {
                if(len == 1) return true;
                if(str[1] == 'x')
                {
                    if(str[0] == '0')    return isPureNum(str.substr(2, str.length() - 2), 16);
                    else return false;
                }
                else
                {
                    size_t pos = str.find('.', 0);            
                    if(pos != string::npos)
                    {
                        //    float
                        string s1 = str.substr(0, pos);
                        if(s1.find('.', 0) != string::npos) return false;
                        string s2 = str.substr(pos + 1, str.length() - pos - 1);
                        if(s2.find('.', 0) != string::npos) return false;
                        if(s2.find('+', 0) != string::npos) return false;
                        if(s2.find('-', 0) != string::npos) return false;
                        if (s1.empty() && s2.empty()) return false;
                        return isPureNum(s1, 10) && 
                               isPureNum(s2, 10);
                    }
                    return isPureNum(str, 10);
                }
            }
            else if (c == '.')    // ".123"
            {
                string s2 = str.substr(1, str.length() - 1);
                if(s2.find('.', 0) != string::npos) return false;
                if(s2.find(' ', 0) != string::npos) return false;
                if(s2.find('+', 0) != string::npos) return false;
                if(s2.find('-', 0) != string::npos) return false;
                return isNumber(s2.c_str());
            }
        }
        return false;
    }
};

 Update: this is a very clear solution: https://leetcode.com/discuss/35947/a-clear-c-solution