h.cpp

// Problem H: Reverse Roman Notation
// Author: Christopher Vo

#include <iostream>
#include <stack>
#include <string>
using namespace std;
stack<int> sys;

// exceptions
class Underflow {};
class DivByZero {};
class OutOfRange {};
class IllegalChar {};

// roman number digits
const string d[] = {"M","CM","D","CD","C","XC",
                    "L","XL","X","IX","V","IV","I"};
const int v[]={1000,900,500,400,100,90,50,40,10,9,5,4,1};

// get num at top of stack
int top() {
    if(sys.empty()) throw Underflow();
    return sys.top();
}

// get two arguments from the stack
void pop_args(int & a1, int & a2) {
    if(sys.size()<2) throw Underflow();
    a1 = sys.top();
    sys.pop();
    a2 = sys.top();
    sys.pop();
}

// convert integer to roman
string ator(int a) {
    int i; string r;
    for(i=0;a>0&&i<13;i++) {
        while(v[i]<=a) {
            r+=d[i];
            a-=v[i];
        }
    }
    return r;
}

// get index of roman string
int get_index(string x) {
    for(int i=0;i<13;i++)
       if(d[i]==x) return i;
    return -1;
}

// convert roman to integer
int rtoa(string r) {
    int i,res=0,last=0,n=r.length();
    for(i=n-1;i>=0;--i) {
       int p = get_index(r.substr(i,1));
       if(p==-1) throw IllegalChar();
       // add bigger numbers, subtract smaller numbers
       v[p]>=last?res+=v[p]:res-=v[p];
       last=v[p];
    }
    return res;
}

// perform an arithmetic operation
int perform(char op, int & a1, int & a2) {
    int res(0);
    switch(op) {
    case '+': res=a1+a2; break;
    case '-': res=a2-a1; break;
    case '*': res=a2*a1; break;
    case '/':
         if(a1==0) throw DivByZero();
         res=a2/a1;
         break;
    }
    return res;
}

// perform an operation on the input
void do_op(string op) {
     int arg1, arg2, res;
     try {
         switch(op[0]) {
         case '=':
              if(top()<0||top()>4999) throw OutOfRange();
              cout << ator(top()) << endl;
              break;
         case '+': case '-': case '/': case '*':
              pop_args(arg1,arg2);
              sys.push(perform(op[0],arg1,arg2));
              break;
         default:
              sys.push(rtoa(op));
         }
     } catch(Underflow) {
       cout << "stack underflow" << endl;
     } catch(DivByZero) {
       cout << "division by zero exception" << endl;
       sys.push(arg2);
     } catch(OutOfRange) {
       cout << "out of range exception" << endl;
     } catch(IllegalChar) {
       cout << "illegal character in roman string" << endl;
     }
}

int main()
{
    string op;
    while(cin>>op) do_op(op);
    return 0;
}