Stack Calculator based on two stacks - c++

Question

I would like to make an algorithm based on two stacks, but my calcucator does not work well for the operator ')'. It should be on output the last of the numbers stack, but happens nothing when i add any ')'. Any suggestions?
We process further tokens until the end of the expression:
if we encounter a number, we put it back on the stack of values
if we encounter an operator, we put it on the operator stack
if we encounter an opening parenthesis, we do nothing
if we encounter a closing bracket, then:
we take off the operator and two values from the stack
we calculate the value of the expression
we put the result on the stack of values
The calculated value of the expression is on the stack
#include <iostream>
#include <string>
#include <sstream>
#include <stack>
#include <vector>
using namespace std;
int main()
{
string c;
stack<int>numbers;
stack<char>operators;
cin >> c;
string expression(c);
for(unsigned int i =0; i <expression.size(); i++)
{
if( expression[i] >= 48 && expression[i] <= 57 )
{
numbers.push(expression[i]);
}
else if(expression[i] == '(')
{
;
}
else if(expression[i] == '+')
{
operators.push(expression[i]);
}
else if(expression[i] == '-')
{
operators.push(expression[i]);
}
else if(expression[i] == '*')
{
operators.push(expression[i]);
}
else if(expression[i] == '/')
{
operators.push(expression[i]);
}
else if(expression[i] == ')' )
{
if(operators.top()== '+')
{
int a,b, score;
a = numbers.top() - '0';
numbers.pop();
b = numbers.top() - '0';
numbers.pop();
score = a+b;
numbers.push(score);
operators.pop();
}
else if(operators.top()== '-')
{
int a,b, score;
a = numbers.top() - '0';
numbers.pop();
b = numbers.top() - '0';
numbers.pop();
score = b-a;
numbers.push(score);
operators.pop();
}
else if(operators.top()== '*')
{
int a,b, score;
a = numbers.top()- '0';
numbers.pop();
b = numbers.top()- '0';
numbers.pop();
score = a*b;
numbers.push(score);
operators.pop();
}
else if(operators.top()== '/')
{
int a,b, score;
a = numbers.top()- '0';
numbers.pop();
b = numbers.top()- '0';
numbers.pop();
score = b/a;
numbers.push(score);
operators.pop();
}
}
}
cout << numbers.top()<<endl;
return 0;
}

Answer 1

The biggest issues with the code are:
This will only work for single digit numbers (you treat each character as a different number)
The fact that numbers is a char stack limits the number to the size of a char. Due to (1) that limit is not really a problem, but when you try to print it at the end the char value will be treated a string encoding. If numbers were a tack of ints instead, it would be converted to the base 10 representation we all know and love when printed.
The order of the operands is wrong (when you unstack them you get the reverse of what you stacked). This is particularly problematic for divisions and subtractions.
Moving forward you may want to have a tokenizer phase that will abstract away some of the details of the text representation to your calculator. Also, be mindful of preserving the order of the operands (eg. change score = x-y to score = y-x).