Expression parsing in C++ with Dijkstra's Shunting-yard algorithm.
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C++ expression parsing

A simple form of mathematical expression parsing can take a string such as -pi+1 on input and output -2.14. This post presents a C++ library to parse a character sequence as an expression using Dijkstra's Shunting-yard algorithm, which modifies Jesse Brown's code. The library is available on biicode.Build Status The biicode block has been automatically published via AppVeyor from the forked github repo. It includes a CMakeListst.txt and a biicode.conf files added to the original repository: bamos/cpp-expression-parser in order to work properly with biicode.

To use it in biicode include:

  #include "amalulla/cpp-expression-parser/shunting-yard.h"

Check out an example on how to use cpp-expression-parser. Or a more detailed guide on biicode docs

Using AppVeyor CI and Deploy for Windows

master branch automatically publishes to biicode via Appveyor.

  • Win Visual Studio 12: Build status

Minimal example.

#include <iostream>
#include "shunting-yard.h"

int main() {
  std::map<std::string, double> vars;
  vars["pi"] = 3.14;
  std::cout << calculator::calculate("-pi+1", &vars) << std::endl;
  return 0;

More examples.

  • See test-shunting-yard.cpp.


  • Unary operators. +, -
  • Binary operators. +, -, /, +, <<, >>
  • Map of variable names.

Adding a binary operator.

To add a binary operator,

  1. Update the operator precedence map in calculator::calculate.
  2. Add the computation to calculator::consume.

Implementation Details

The main steps of the calculate method are:

  1. Create the operator precedence map.
  2. Convert to RPN with Dijkstra's Shunting-yard algorithm.
  3. Evaluate the expression in RPN form.

Converting to RPN.

Most of the Shunting-yard algorithm resides here. The idea is to do everything in one pass for elegance. Please see the source code for implementation-specific details, and refer to the pruned code below for a summary.

TokenQueue_t calculator::toRPN(const char* expr,
    std::map<std::string, double>* vars,
    std::map<std::string, int> opPrecedence) {
  TokenQueue_t rpnQueue; std::stack<std::string> operatorStack;

  while (*expr ) {
    if (isdigit(*expr )) {
      // If the token is a number, add it to the output queue.
    } else if (isvariablechar(*expr )) {
      // If the function is a variable, resolve it and
      // add the parsed number to the output queue.
    } else {
      // Otherwise, the variable is an operator or parenthesis.
      switch (*expr) {
        case '(':
        case ')':
          while ("(")) {
            rpnQueue.push(new Token<std::string>(;
            // The token is an operator.
            // Let p(o) denote the precedence of an operator o.
            // If the token is an operator, o1, then
            //   While there is an operator token, o2, at the top
            //       and p(o1) <= p(o2), then
            //     pop o2 off the stack onto the output queue.
            //   Push o1 on the stack.
  while (!operatorStack.empty()) {
    rpnQueue.push(new Token<std::string>(;
  return rpnQueue;

Evaluating RPN form.

The RPN is represented as tokens in a stack. To evaluate this, pop all of the elements off and handle operations when encountered.

std::stack<double> evaluation;
while (!rpn.empty()) {
  TokenBase* base = rpn.front();

  Token<std::string>* strTok = dynamic_cast<Token<std::string>*>(base);
  Token<double>* doubleTok = dynamic_cast<Token<double>*>(base);
  if (strTok) {
    std::string str = strTok->val;
    if (evaluation.size() < 2) {
      throw std::domain_error("Invalid equation.");
    double right =; evaluation.pop();
    double left  =; evaluation.pop();
    if (!"+")) {
      evaluation.push(left + right);
    } else if (!"*")) {
      evaluation.push(left * right);
    } else if (!"-")) {
      evaluation.push(left - right);
    } else if (!"/")) {
      evaluation.push(left / right);
    } else if (!"<<")) {
      evaluation.push((int) left << (int) right);
    } else if (!">>")) {
      evaluation.push((int) left >> (int) right);
    } else {
      throw std::domain_error("Unknown operator: '" + str + "'.");
  } else if (doubleTok) {
  } else {
    throw std::domain_error("Invalid token.");
  delete base;

The evaluated value resides in of type double.

Future work.

See the issues on GitHub for work to be done. I'm currently not actively working on additional features, so please contribute if you add additional functionality or bug fixes.