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This chapter is from the book

This chapter is from the book

20.9. Sample App: RPN Calculator

In C++ Without Fear, 2nd Edition (Prentice Hall), I presented a Reverse Polish Notation (RPN) calculator as one of the more advanced examples. In this section, I present a superior version of that app.

An RPN calculator lets the user enter arbitrarily long arithmetic expressions in postfix notation. For example, to add 3 and 4, you specify not “3 + 4” but:

3 4 +

This might at first seem counterintuitive until you realize it’s an elegant notational system that does away with the need for parentheses. For example, the RPN expression:

3 4 + 10 1.5 + *

is equivalent to the following standard (infix) expression:

(3 + 4) * (10 + 1.5)

With RPN, an operator always applies to the expressions that precede it. In this case, the asterisk (*) applies to the expressions “3 4 +” and “10 1.5 +”, which produce 7 and 11.5, respectively. Multiplication is finally applied to produce 80.5. The RPN grammar can be summarized as:

expression  <=  number
expression  <=  expression expression op

Calculations: The stack mechanism, described in Section 16.3, “The stack Template,” is what powers this application. When the program reads a number, it pushes that number onto the stack. When the program reads an operator, it pops the top two values off the stack, performs a calculation, and pushes the result back onto the stack.

Lexical analysis: It’s easy enough to interpret a line of input in which spaces separate operators as well as numbers. The more challenging problem is to recognize operators as both tokens and separators so that some of the spaces are optional. For example, it would be desirable to interpret:

3 44*5  1.2+/

as if it were written as:

3 44 * 5 1.2 + /

The strtok function is inadequate for this task. So is the regex_token_iterator function. The solution is to use a regex_iterator and search for sequences of characters that constitute either of the following:

  • b-box.jpg A number, consisting of consecutive digits with or without a fractional portion, such as “3”, “44”, or “100.507”
  • b-box.jpg Any of several operators: +, -, *, or /

With this approach, it’s not necessary to have spaces on either side of an operator, although spaces are freely permitted. The following will work just fine:

3 4+ 1 2+*

The code for the application follows.

#include <iostream>
#include <string>
#include <cctype>
#include <regex>
#include <stack>

using std::cout;         // Alternatively, you can use
using std::cin;          //  using namespace std;
using std::endl;
using std::string;
using std::regex;
using std::sregex_iterator;
using std::stack;

void process_token(string s);
stack<double> st;

main() {
     string instr;
     string num_pattern("[0-9]+(\\.[0-9]*)?");
     string op_pattern("[+*/-]");
     regex re(num_pattern + "|" + op_pattern);
     while (true) {
         cout << "Enter expression (or ENTER to exit): ";
         getline(cin, instr);
         if (instr.length() == 0) { break; }
         sregex_iterator it(instr.begin(), instr.end(), re);
         sregex_iterator it_end;
         for (;it != it_end; ++it) {
         if (!st.empty()) {
              cout << "The value is: " << st.top() << endl;
     return 0;

void process_token(string s) {
     // If s contains any char that is NOT an op,
     //  consider it a number by default.
     if (s.find_first_not_of("+*/-") != s.npos) {
     } else {
          double op2 = st.top(); st.pop();
          double op1 = st.top(); st.pop();
          switch(s[0]) {
          case '+': st.push(op1 + op2); break;
          case '-': st.push(op1 - op2); break;
          case '*': st.push(op1 * op2); break;
          case '/': st.push(op1 / op2); break;

This program illustrates a couple of important features of regular-expression grammar. First, as mentioned earlier, special characters such as “*” and “+” do not need to be escaped when they occur inside brackets (although brackets themselves would need to be escaped to be treated literally, of course). Also, the minus sign (-) does not need to be escaped, because it does not occur between two other characters.

     string op_pattern("[+*/-]");

Another interesting feature is that order is potentially significant. The regex object in this application searches for a digit string first and then for an operator. This order makes Exercise 2 possible.

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