#include <iostream>
#include <math.h>
#include <stdlib.h>
#include <string>
#include <cstdio>

using namespace std;
bool checkInput(string input);
double computeFirst(int valx,int valn);
double computeMid(int valx,int valn);
double computeLast(int valx,int valn);
double factorial(int value);
int conValues(double input); //convert double value to integer
void displayRules();

int main()
{
    string inputx, inputn, confirm, name,rules;
    int n,x,error,ignore=1;
    long double First,Middle,Last,Final;
    bool contd,digitx, digitn;
    
    cout << "***************************" << endl;
    cout << "*      Assignement 2      *" << endl;
    cout << "***************************" << endl;
    
    cout << "Do you look at the rules? (Y/N) " << endl;
    cin >> rules;
    cin.ignore();
    if(rules == "y" || rules == "Y")
        displayRules();     
    
    do{ //ask whether the user continue playing or not
    do{
        error = 1; //reset & default
        cout << endl;
        cout << "Please enter the value of x" << endl;
        getline(cin,inputx);
        cout << "Please enter the value of n" << endl;
        getline(cin,inputn);
        
        if(inputn == "" || inputx == "")
                error = 5; //null inputs
        else{
                digitx = checkInput(inputx);
                digitn = checkInput(inputn);}
        
        if(error == 5){
                cout << "No inputs are entered, please enter again.\n";
                contd = false;}
        else  if(digitx && digitn){
                x = atoi(inputx.c_str()); //convert x
                n = atoi(inputn.c_str()); //convert n
                if(n<1)
                    error = 2; // n must be greater than 1
                else if (x == 0)
                    error = 3; // x cannot equal to 0
                else 
                    error = 1;} //everything fine when contd = 1
        else{
                x = atoi(inputx.c_str()); //convert x
                n = atoi(inputn.c_str()); //convert n
                error = 4;} //input contain invalid char
        
        if(error == 1){ // no errors
                cout << "The converted value of x is " << x << endl;
                cout << "The converted value of n is " << n << endl;
                contd = true;
                
                if(x>200 || n>200){
                    cout << "Input values are too big.This might affect the accuracy of the answers.\n";
                    cout << "It is recommended to input the values smaller than 100." <<endl;}
                
                //confirmation by users
                cout << "\nAre you confirm with the values entered? (Y/N) " << endl;
                do{ //prompt user either enter yes or n
                   cin >> confirm;
                   cin.ignore();
                   if(confirm == "y" || confirm == "Y")
                       contd = true; //cofirm values
                   else if (confirm == "N" ||confirm == "n")
                       contd = false; //not confirm values
                   else //user enter invalid values
                       cout << "Invalid input.Please enter again" <<endl;
                }while(!(confirm == "y" || confirm == "Y"||confirm == "N" ||confirm == "n"));}
                
        else if(error == 2){
                cout << "The converted value of x is " << x << endl;
                cout << "The converted value of n is " << n << endl;
                cout << "Value n must be greater than 1, please enter again." << endl;
                contd = false;}
                
        else if(error == 3){
                cout << "The converted value of x is " << x << endl;
                cout << "The converted value of n is " << n << endl;
                cout << "Value x cannot equal to 0, please enter again." << endl;
                contd = false;}
                
        else if(error == 4){
                cout << "The converted value of x is " << x << endl;
                cout << "The converted value of n is " << n << endl;
                cout << "Inputs contain invalid characters, please enter again." << endl;
                contd = false;}
    }while(contd == false);                       
    
    //start computing the values of First, Middle, Last, Final
      First = computeFirst(x,n);
      Middle = computeMid(x,n);
      Last = computeLast(x,n);
    
    //compute Final value
      if(Last == 0){
            cout << "The answer is UNDEFINED!\n";
            cout << "Please run the program again using another values or exit\n";}
      else{
            Final = (First/Last) + Middle;
            cout << "\nFirst: " << First << "\n";
            cout << "Middle: " << Middle << "\n";
            cout << "Last: " << Last << "\n";
            cout << "Final: " << Final <<endl;} //end else
            
      cout << "Do you still want to play? (Y/N)" << "\n";
    
      do{ //prompt user either enter yes or no
        cin >> confirm;
        cin.ignore();
        if(confirm == "y" || confirm == "Y")
                contd = true;
        else if (confirm == "N" ||confirm == "n")
                contd = false;
        else //user enter invalid values
                cout << "Invalid input.Please enter again" <<endl;
                
        }while(!(confirm == "y" || confirm == "Y"||confirm == "N" ||confirm == "n"));
        
    } while(contd);
    
    cout << "\nPlease enter your name" << endl;
    cin >> name;
    cout << "\n-------------------------- THE END --------------------------" << endl;  
    cout << "\nThank you, Mr/Ms " << name << " for spending time on this program" << endl <<endl;  
    getchar();
    return 0;
}

//check the input type user entered
bool checkInput(string input)
{
    bool state;
    state = true;
    for(int i=0;i<=input.length()-1;i++)
    {
        if(isalpha(input[i])|| isspace(input[i]))
                state = false; 
    }
    return state;
}

double computeFirst(int valx,int valn) //compute value First
{
    bool add; double dbx,sum,result,answer;
    add = true; sum = 0; dbx = valx;
    for(int i=1;i<=valn;i+=2) //i == firstCounter
    {
            result = factorial(i);  //result of factorial
            answer = pow(dbx,i)/result; //perform power function 
            if(add){
               sum += answer;
               add = false;}
            else {
               sum -= answer;
               add = true;}
    }
    return sum;
}

double computeMid(int valx,int valn) //compute value Middle
{
       double root, sum;
       sum = 0;
       for(int i=1;i<=valn;i++){ //i == midcounter
               root = i;
               sum += (sqrt(root))/valx;}
       return sum;
}

double computeLast(int valx,int valn) //compute value Last
{
       bool add; double dbx,sum,result,answer;
       add = false; sum = 1; dbx = valx;
       for(int i=2;i<=valn;i+=2) //i == lastcounter
       { 
               result = factorial(i); //i as the argument to control the factorial number
               answer = pow(dbx,i)/result;
               if(add){
                       sum += answer;
                       add = false;}
               else {
                    sum -= answer;
                    add = true;}
       }
       return sum;
}

double factorial(int value) //calculate the factorial number
{
       double result = 1;
       for(int i=1;i<=value;i++){
               result *= i;}
       return result;
}

void displayRules()
{   
    cout << "1.All the inputs must be numeric values." <<endl;
    cout << "2.All the inputs must be integers, any decimal numbers will be rounded to integer." <<endl;
    cout << "3.Alphabets and punctuations are considered as invalid inputs." <<endl;
    cout << "4.Inputs must be entered and cannot be null." << endl;
    cout << "5.The value of n and x must not be too large to maintain the accuracy the answers." <<endl;
    cout << "Thank you" << endl;
}