// Prog: calculator_l.cpp
// evaluate arithmetic expressions involving +, -, *, /, (, )
// over double operands, with left-to-right evaluation order

// Syntax in BNF:
// ---------------
// expression = term | term "+" expression | term "-" expression.
// term = factor | factor "*" term | factor "/" term.
// factor = "(" expression ")" | "-" factor | unsigned double.

#include<iostream>
#include<istream>
#include<sstream>
#include<cassert>

// declarations
// ------------

// PRE: is = expression...
// POST: expression e is extracted from is, and
//       its value Sigma (0, +, e) is returned
double expression (double v, char sign, std::istream& is);
double expression (std::istream& is);

// PRE: is = term...
// POST: term S is extracted from is, and
//       the value Pi (1, *, t) is returned
double term (double v, char sign, std::istream& is);
double term (std::istream& is);

// PRE: is = factor...
// POST: factor f is extracted from is, and
//       its value is returned
double factor (std::istream& is);

// definitions
// -----------

// POST: leading whitespace characters are extracted
//       from is, and the first non-whitespace character
//       is returned (0 if there is no such character)
char lookahead (std::istream& is)
{
  is >> std::ws;         // skip whitespaces
  if (is.eof())
    return 0;            // end of stream
  else
    return is.peek();    // next character in is
}

// expression = term | term "+" expression | term "-" expression.
double expression (double v, char sign, std::istream& is){
  if (sign == '+')
    v += term(is);
  else if (sign == '-')
    v -= term(is);
  char c = lookahead (is);
  if (c == '+' || c == '-')
    return expression (v, c, is >> c);
  return v;
}

double expression(std::istream & is){
  return expression (0.0, '+', is);
}

// term = factor | factor "*" term | factor "/" term.
double term (double v, char sign, std::istream& is){
  if (sign == '*')
    v *= factor(is);
  else if (sign == '/')
    v /= factor(is);
  char c = lookahead (is);
  if (c == '*' || c == '/')
    return term (v, c, is >> c);
  return v;
}

double term (std::istream & is){
  return term (1.0,'*',is);
}


// factor = "(" expression ")" | "-" factor | unsigned double.
double factor (std::istream& is)
{
  double v;
  char c = lookahead (is);
  if (c == '(') {
    v = expression (is >> c);
    is >> c;
    assert (c == ')');
  }
  else if (c == '-') {
    v = -factor(is >> c);
  }
  else {
    double d;
    is >> d;
    assert (!is.fail());
    v = d;
  }
  return v;
}

int main()
{
  std::stringstream input1 ("-(3-(4-5))*(3+4*5)/6"); // -15.33333
  std::stringstream input2 ("3-4-5");                // -6
  std::cout << expression (input1) << "\n";
  std::cout << expression (input2) << "\n";
  return 0;
}