/**
 * Get two polynomials from the user and output the summation
 * 
 * @Author		Mario Lopez
 * @Version		1.0
 * @Date		   Feb 23 2007
 */

#include <iostream>
#include <list>
#include <string>
using namespace std;

// Class to hold data for each element
// e.g. +4.9x^7
// where + is held in "sign"
//     4.9 is held in "coefficient"
//       7 is held in "exponent"
class Component{
      char sign; 
      float coefficient;
      float exponent;
   public:
      Component(char s, float c, float e){sign = s; coefficient = c; exponent = e;};
      void printComponent();
      float getExponent();
      void getComponentArgs(char &s, float &c, float &e);
};

// Method to print out a component (e.g. "+4.9x^7")
void Component::printComponent() {
	cout << sign << coefficient << "x^" << exponent;
};

// Method to return the exponent of a certain component
float Component::getExponent() {
   return exponent;
};

// Copy component variables
void Component::getComponentArgs(char &s, float &c, float &e) {
   s = sign;
   c = coefficient;
   e = exponent;
};

// To get input and parse it into a component
int readComponent(char &s, float &c, float &e){
   char l;

   l = cin.get();
   if( l == '+' || l == '-') {
	   s = l;                  // Get sign
      cin >> c;               // Get coefficient
	   cin.get();cin.get();    // Ignore x and ^ chars
      cin >> e;               // Get exponent
   }
   else if (l == '\n') return 0;
   return 1;
}

int main()
{
   list<Component> L1, L2, summedList;
   float c,e, c2;
   char s, s2;
   
   cout << "Please input the first polynomial:" << endl;
   while( readComponent(s,c,e) ) {
      Component component(s,c,e);
      L1.push_back(component);
   }
   
   cout << "Please input the second polynomial:" << endl;
   while( readComponent(s,c,e) ) {
      Component component(s,c,e);
      L2.push_back(component);
   }
   
   list<Component>::iterator element1, element2;
   element1 = L1.begin();
   element2 = L2.begin();
   
   // Start adding the two polynomials
   while( element1 != L1.end() && element2 != L2.end() ) {
      // If List2 has a component with an exponent List1 doesn't have
      if( (*element1).getExponent() < (*element2).getExponent() ) {
         (*element2).getComponentArgs(s,c,e);
         Component component(s,c,e);
         summedList.push_back(component);
         element2++;
      }
      // If List1 has a component with an exponent List2 doesn't have
      else if( (*element1).getExponent() > (*element2).getExponent() ) {
         (*element1).getComponentArgs(s,c,e);
         Component component(s,c,e);
         summedList.push_back(component);
         element1++;
      }
      // If List1 and List2 both have a component with the same exponent
      else {
         (*element1).getComponentArgs(s,c,e);
         (*element2).getComponentArgs(s2, c2, e);
         
         // Deal with the signs
         if( s == s2 ) {   // Same sign, either + or -
            c += c2;
         }
         else {            // Different sign
            if( c > c2 )
               c -= c2;
            else {
               c = c2 - c;
               s = s2;
            }
         }
         
         Component component(s,c,e);
         summedList.push_back(component);
         element2++;
         element1++;
      }
   }
   
   // Finish up L1 if need be
   while( element1 != L1.end() ) {
      (*element1).getComponentArgs(s,c,e);
      Component component(s,c,e);
      summedList.push_back(component);
      element1++;
   }
   
   // Finish up L2 if need be
   while( element2 != L2.end() ) {
      (*element2).getComponentArgs(s,c,e);
      Component component(s,c,e);
      summedList.push_back(component);
      element2++;
   }
   
   cout << "The summation of these two polynomials are:" << endl;
   
   // Reusing the variable "element1"
   // Going through the "summedList" to print the output
   for( element1 = summedList.begin(); element1 != summedList.end(); element1++ ) 
	   (*element1).printComponent();
   cout << endl;

   return 0;
}