# Simple C++ calculator which follows BOMDAS rules

This was my first attempt at making a C++ calculator. The user basically inputs an expression (I’ll use $1+1*(9*(11-1))$ as an example) and the program searches for and creates a vector for parentheses (which is a class I made which records its position in the string).

String:

[1][+][1][*][(][9][*][(][11][-][1][)][)]
0  1  2  3  4  5  6  7  8   9 10 11 12


Parentheses Vector:

[( position = 4][( position = 7][) position = 11][) position = 12]
0                 1               2               3


If in the parentheses vector, the parentheses’ position = n, then the corresponding closing parentheses will be vector.size()-n.

The program deals with the first parenthesis and finds its corresponding closing parenthesis using the above statement and what I call the sub expression is found between the position member variable of the selected parentheses. For the innermost set of parentheses, the sub expression will be thus: 11-1

The expression will be evaluated (10) and the result will be placed in the expression:

$1+1*(9*10)$

and the same for the other sub expression:

$1+1*90$

In terms of operator precedence, the B in BOMDAS has been followed so far, so the other operators are to be used (*,/,+,- are all supported at the moment).

Each operator has an assigned value in a map called operatorClassMap:

operatorClassMap['*']=2;
operatorClassMap['/']=2;
operatorClassMap['+']=1;
operatorClassMap['-']=1;


A little explanation on operators at this point:

1. The class operatorClass has two pointers to doubles in the expression.
2. The class records the operator’s “value” assigned above.
3. I overloaded the < operator so that the sort() function will sort the operator vector for me.
4. The vector is transferred to a stack and evaluated from the top.

To continue with the above example: $1+1*90$

The operator stack will look something like this:

[ 1 * 90]
[ 1 + 1]


The multiplication will be performed first resulting in 90. The program then decides whether or not to place the result of the multiplication to the left or right of the operator beneath it:

[1+90]


Then the final operation is performed, resulting in 91.

#include <iostream>
#include <sstream>
#include <string>
#include <stack>
#include <queue>
#include <vector>
#include <stdlib.h>
#include <map>
#include <algorithm>
#include <math.h>
#include <iomanip>
#include <limits>
using namespace std;

class operatorClass
{
public:
operatorClass(char&,int&);
void addOperands(long double&, long double&);
bool operator < (const operatorClass& str) const;
int value;
char actualoperatorClass;

long double* pointer_To_leftOperand;
long double* pointer_To_rightOperand;

};
{
}
{
//std::cout << " LEFT " << *pointer_To_leftOperand << std::endl;
//std::cout << " RIGHT " << *pointer_To_rightOperand << std::endl;
}
bool operatorClass::operator < (const operatorClass& str) const
{
return (value < str.value);
}
inline void printOperatorVector(std::vector<operatorClass> VectorToPrint)
{
for(unsigned int index = 0; index < VectorToPrint.size(); index++)
{
//std::cout << "Element #" << index <<": " << VectorToPrint[index].actualoperatorClass << std::endl;
}
}
class Parenthesis
{
public:
Parenthesis(unsigned int,char);
char typeOfParenthesis;
unsigned int position;
private:

};
Parenthesis::Parenthesis(unsigned int receivedPosition, char parenthesisType)
{
typeOfParenthesis = parenthesisType;
}
class Expression
{
public:
Expression(std::string,bool);
long double result;
private:

bool hasBrackets;
std::vector <Expression> subExpressions;
std::vector<Parenthesis> vector_parentheses; //If the position of a parenthesis in a vector
//is 'n', then the position of the closing parenthesis should be vectorSize-n in the
//same vector
void containsBrackets();//Checks to see if the expression contains parentheses
void getParentheses(); //Gets position and types of parentheses in the expression
void getSubExpressions(); //Gets the contents between each parenthesis so that they may be evaluated

long double evaluate();
std::string expressionString;
};
Expression::Expression(std::string expression, bool sub) //NOTE: being a sub means that it was surrounded
//by brackets '(' ')'
{

hasBrackets = false;
expressionString = expression;
containsBrackets();
// //std::cout << "Successfully complete 'containsBrackets' function" << std::endl;
if (hasBrackets == true)
{
getParentheses();
// //std::cout << "Successfully complete 'getParentheses()' function" << std::endl;
getSubExpressions();
// //std::cout << "Successfully complete 'getSubExpressions()' function" << std::endl;
}
evaluate();
// //std::cout << "Successfully complete 'evaluate()' function" << std::endl;

}
long double Expression::evaluate()
{
std::map<char, unsigned int> operatorClassMap;
operatorClassMap['*']=2;
operatorClassMap['/']=2;
operatorClassMap['+']=1;
operatorClassMap['-']=1;
std::vector<long double> numbers;
std::vector<operatorClass> operatorClasss;
long double number = 0;
std::string numberString = ""; //For having multi-digit numbers
// //std::cout << "Working expression: " << expressionString << std::endl;

for(unsigned int index = 0; index<=expressionString.size(); index++)
{
if(expressionString[index] != '+' && expressionString[index] != '-' && expressionString[index] != '*' && expressionString[index] != '/' && expressionString[index] != ' ')
{
numberString+= expressionString[index];
}
if (expressionString.size() == index)
{
number= strtod(numberString.c_str(), NULL);
numbers.push_back(number);
numberString = "";

}
if(expressionString[index] == '+' || expressionString[index] == '-' || expressionString[index] == '*' || expressionString[index] == '/' || expressionString[index] == ' ')
{
number= strtod(numberString.c_str(), NULL);
numbers.push_back(number);
numberString = "";

}
}
//std::cout << "SIZE" << numbers.size() << std::endl;
for(unsigned int index = 0; index < numbers.size(); index++)
{
//std::cout  << "NUMBER" << numbers[index] << std::endl;
}

for(unsigned int index = 0; index<expressionString.size(); index++)
{
//std::cout << "Index :" << index << std::endl;
if(expressionString[index] == '+' || expressionString[index] == '-' || expressionString[index] == '*' || expressionString[index] == '/' || expressionString[index] == ' ')
{
int value = operatorClassMap[expressionString[index]];
if(numbers.size() > 2)
{
operatorClass tempoperatorClass(expressionString[index],value);
operatorClasss.push_back(tempoperatorClass);
}

else
{
operatorClass tempoperatorClass(expressionString[index],value);
operatorClasss.push_back(tempoperatorClass);
}

}
else
{

}
}
for(unsigned int index = 0; index < operatorClasss.size(); index++)
{
if(numbers.size() >= 2)
else
}

std::sort(operatorClasss.begin(),operatorClasss.end());

for(unsigned int index = 0; index < numbers.size(); index++)
{
//std::cout << numbers[index] << std::endl;
}
printOperatorVector(operatorClasss);
//std::cout << 7 << std::endl;
std::stack<long double> numberStack;
std::stack<operatorClass> operatorClassStack;

for (unsigned int index = 0; index < operatorClasss.size(); index++)
{
operatorClassStack.push(operatorClasss[index]);
}
// //std::cout << "Successfully added operatorClasss and numbers to stacks" << std::endl;
long double Result = 0;
for(unsigned int index = operatorClassStack.size();index>0;index--)
{
unsigned int previousValue = operatorClassMap[operatorClassStack.top().actualoperatorClass];
if (operatorClassStack.top().actualoperatorClass == '*')
{

//std::cout << "Top number: " << *operatorClassStack.top().pointer_To_leftOperand << std::endl;

//std::cout << "operatorClass: " << operatorClassStack.top().actualoperatorClass;

//std::cout << "Other number: " << *operatorClassStack.top().pointer_To_rightOperand << std::endl;
//change stack to vector
Result = *operatorClassStack.top().pointer_To_leftOperand* *operatorClassStack.top().pointer_To_rightOperand;
numberStack.push(Result);
if(operatorClassStack.empty() == false)
operatorClassStack.pop();

//std::cout << "RESULT! : "<< Result << std::endl;
}
else if (operatorClassStack.top().actualoperatorClass == '/')
{

//std::cout << "Top number: " << *operatorClassStack.top().pointer_To_leftOperand << std::endl;

//std::cout << "operatorClass: " << operatorClassStack.top().actualoperatorClass;

//std::cout << "Other number: " << *operatorClassStack.top().pointer_To_rightOperand << std::endl;

// //std::cout << 1+1;
Result = *operatorClassStack.top().pointer_To_leftOperand/ *operatorClassStack.top().pointer_To_rightOperand;
numberStack.push(Result);
// //std::cout << Result;
if(operatorClassStack.empty() == false)
operatorClassStack.pop();

//std::cout << "RESULT! : "<< Result << std::endl;
}

else if (operatorClassStack.top().actualoperatorClass == '+')
{

//std::cout << "Top number: " << *operatorClassStack.top().pointer_To_leftOperand << std::endl;

//std::cout << "operatorClass: " << operatorClassStack.top().actualoperatorClass;

//std::cout << "Other number: " << *operatorClassStack.top().pointer_To_rightOperand << std::endl;

Result = *operatorClassStack.top().pointer_To_leftOperand + *operatorClassStack.top().pointer_To_rightOperand;
numberStack.push(Result);
if(operatorClassStack.empty() == false)
operatorClassStack.pop();

//std::cout << "RESULT! : "<< Result << std::endl;

}
else if (operatorClassStack.top().actualoperatorClass == '-')
{

//std::cout << "Top number: " << *operatorClassStack.top().pointer_To_leftOperand << std::endl;

//std::cout << "operatorClass: " << operatorClassStack.top().actualoperatorClass;

//std::cout << "Other number: " << *operatorClassStack.top().pointer_To_rightOperand << std::endl;

Result = *operatorClassStack.top().pointer_To_leftOperand- *operatorClassStack.top().pointer_To_rightOperand;
numberStack.push(Result);
if(operatorClassStack.empty() == false)
operatorClassStack.pop();

//std::cout << "RESULT! : "<< Result << std::endl;
}
if(operatorClassStack.size() > 0)
{
if(operatorClassMap[operatorClassStack.top().actualoperatorClass] > previousValue)
operatorClassStack.top().pointer_To_leftOperand =  &Result;

if(operatorClassMap[operatorClassStack.top().actualoperatorClass] <= previousValue)
operatorClassStack.top().pointer_To_rightOperand =  &Result;
}

}
// //std::cout << "Successfully evaluated expression" << std::endl;
result = numberStack.top();
// //std::cout << result;
// //std::cout << "Successfully evaluated expression" << std::endl;
}
void Expression::containsBrackets()
{
for(unsigned int index = 0; index < expressionString.size(); index++)
{
if (expressionString[index]=='(' ||expressionString[index]==')' )
{
hasBrackets = true;
}
}
}
void Expression::getParentheses() //Finds the parentheses and their positions in the expression
//so that their contents can be converted to sub expressions.
{
for (unsigned int index = 0; index < expressionString.size(); index++)
{
if (expressionString[index] == '(' || expressionString[index] == ')')
{
Parenthesis temporary(index, expressionString[index]); //Stores the position and type of the parenthesis
vector_parentheses.push_back(temporary);
}
}

/*for (unsigned int index = 0; index < vector_parentheses.size(); index++)
{
// //std::cout << vector_parentheses[index].typeOfParenthesis << std::endl;
// //std::cout << vector_parentheses[index].position << std::endl;
}
*/
}
void Expression::getSubExpressions()
{
for(unsigned int index = 0; index < vector_parentheses.size(); index++)
{
if(vector_parentheses[index].typeOfParenthesis == '(')
{
std::string subExpression = "";
// | ( | ( | ( | ) | ) | ) |
//   *   -   -   -   -   *
//  n=0                 =size-n
//in an array of parentheses, corresponding closing parenthesis for an opening bracket at position in is
// at [size-n]

unsigned int positionOfOpeningParenthesis = vector_parentheses[index].position;
// //std::cout << "Opening parenthesis: " << positionOfOpeningParenthesis << std::endl;
// //std::cout << "successfully got opening parenthesis position" << std::endl;
unsigned int positionOfClosingParenthesis = vector_parentheses[vector_parentheses.size()-1 - index].position;
// //std::cout << "Closing parenthesis: " << positionOfClosingParenthesis << std::endl;
// //std::cout << "successfully got closing parenthesis position" << std::endl;
for(unsigned int index2 = positionOfOpeningParenthesis+1; index2 < positionOfClosingParenthesis;index2++)
{
subExpression+=expressionString[index2]; //gets stuff found between each bracket
}
// //std::cout << "successfully got expression" << std::endl;
// //std::cout << "Sub expression: " << subExpression;
Expression temporaryExpression(subExpression, true); //creates a new sub expression
// //std::cout << "successfully created new expression" << std::endl;
int digits_before = 1 + (int)floor(log10(fabs(temporaryExpression.result)));
int digits_after = std::numeric_limits<long double>::digits10 - digits_before;

long double whole = floor(pow(10, digits_after) * fabs(temporaryExpression.result) + 0.5);
while (digits_after > 0 && (whole/10.0 - floor(whole/10.0)) < 0.05)
{
--digits_after;
whole = floor(whole / 10.0 + 0.5);
}
if (digits_after < 0) digits_after = 0;

std::stringstream ss;
ss << std::fixed << std::setprecision(digits_after) << temporaryExpression.result;

std::string stringResult = ss.str();
//std::cout << "successfully converted " << temporaryExpression.result <<" long double to string" << std::endl;
//std::cout << stringResult;
// //std::cout << "size of expression: " << expressionString.size() << "Position of opening parenthesis: " << positionOfOpeningParenthesis << "Position of closing parenthesis: " << positionOfClosingParenthesis << std::endl;
if(expressionString.size() <= positionOfOpeningParenthesis)
{
for (unsigned int index = expressionString.size(); index <= positionOfOpeningParenthesis+stringResult.size();index++)
{
expressionString+=' ';
}
}
else
{
expressionString.replace(positionOfOpeningParenthesis,positionOfClosingParenthesis-positionOfOpeningParenthesis +1,stringResult);
}
//GETS RESULT AND PLACES IT BACK IN THE ORIGINAL EXPRESSION //
// //std::cout << "successfully placed result of subexpression in string" << std::endl;
// //std::cout << "NEW EXPRESSION: " << expressionString;
}
evaluate(); //Evaluates new expression containing the result of the sub expression
}
}
int main() {

std::cout << "To do list: " << std::endl;
std::cout << "Validate equal bracket numbers" << std::endl;
std::cout << "Add support for negative input numbers" << std::endl;
while(true)
{
std::cout << "Please enter your expression: " ;
std::string expression;
std::cin >> expression;
if(expression == "exit")
break;
Expression expressionToEvaluate(expression, false);
std::cout << "RESULT: " << std::fixed <<  expressionToEvaluate.result<< std::endl;
}

return 0;
}


I suspect the code may be overly complex due to it being made up on the fly without any prior design planning or anything of the sort. I’d be interested in hearing what you guys have to say 🙂

If I were going to carry out this general task, I’d probably use a recursive descent parser. A simple version to handle +, -, * and / with the correct precedence can look something like this:

#include <iostream>
#include <string>
#include <cctype>

int expression();

char token() {
char ch;
std::cin >> ch;
return ch;
}

int factor() {
int val = 0;
char ch = token();
if (ch == '(') {
val = expression();
ch = token();
if (ch != ')') {
std::string error = std::string("Expected ')', got: ") + ch;
throw std::runtime_error(error.c_str());
}
}
else if (isdigit(ch)) {
std::cin.unget();
std::cin >> val;
}
else throw std::runtime_error("Unexpected character");
return val;
}

int term() {
int ch;
int val = factor();
ch = token();
if (ch == '*' || ch == '/') {
int b = term();
if (ch == '*')
val *= b;
else
val /= b;
}
else std::cin.unget();
return val;
}

int expression() {
int val = term();
char ch = token();
if (ch == '-' || ch=='+') {
int b = expression();
if (ch == '+')
val += b;
else
val -= b;
}
else std::cin.unget();
return val;
}

int main(int argc, char **argv) {
try {
std::cout << expression();
}
catch(std::exception &e) {
std::cout << e.what();
}
return 0;
}


Despite being less than one fifth the size, this already checks for balanced parentheses. Right now it’s written to take data from std::cin, but getting it to read from an arbitrary stream (including a stringstream) would be trivial. Getting it to parse input from a string would be minutely more work (the obvious way would be to create a stringstream and read from there, but you could just keep track of the current position to read from in a string as well).

The shunting-yard algorithm is also well known for this task. I don’t see a huge advantage to it myself, but some (many?) people find it somewhat simpler. Depending on how fast function calls are on your particular CPU, it may execute faster as well (but most modern CPUs make function calls pretty fast so if there’s an improvement in speed, it probably won’t be very large).