Valid Number

class Solution {
public:
    bool isInteger(string s) {
        if(s.empty())
            return false;
        
        //1. (Optional) A sign character (either '+' or '-').
        if(s[0] == '+' || s[0] == '-')
            s = s.substr(1);
        
        int n = s.length();
        if(n == 0)
            return false;

        //2. At least one digit.
        for(int i = 0; i<n; i++) {
            //since, e or E are filtered now. If we get any alpha char, we return false
            if(s[i] >= '0' && s[i] <= '9')
                continue;
            return false;
        }
        return true;
    }
    
    bool isDecimal(string s) {
        if(s.empty())
            return false;
        
        //1. (Optional) A sign character (either '+' or '-').
        if(s[0] == '+' || s[0] == '-')
            s = s.substr(1);
        
        int cntDot = 0;
        int idxDot = -1;
        int n = s.length();
        for(int i = 0; i<n; i++) {
            if(s[i] == '.') {
                cntDot++;
                idxDot = i;
            }
        }
        
        if(cntDot > 1)
            return false;
        if(cntDot) {
            //2. At least one digit, followed by a dot '.', followed by at least one digit.
            for(int i = 0; i<idxDot; i++) {
                if(s[i] >= '0' && s[i] <= '9')
                    continue;
                return false;
            }
            //3. A dot '.', followed by at least one digit.
            for(int i = idxDot+1; i<n; i++) {
                if(s[i] >= '0' && s[i] <= '9')
                    continue;
                return false;
            }
            return s.length() > 1; //1 char is dot already
        }
        
        return false;
    }
    
    bool isNumber(string s) {
        /*
            A decimal number or an integer.
            (Optional) An 'e' or 'E', followed by an integer.
        */
        int cntE = 0;
        int eIdx = -1;
        for(int i = 0; i<s.length(); i++) {
            if(s[i] == 'e' || s[i] == 'E') {
                cntE++;
                eIdx = i;
            }
        }
        if(cntE > 1)
            return false;
        
        if(cntE) {
            //An 'e' or 'E', shold be followed by an integer.
            if(!isInteger(s.substr(eIdx+1)))
                return false;
            //Decimal or Integer component
            s = s.substr(0, eIdx);
        }
        
        return isInteger(s) || isDecimal(s);
    }
};