Postfix Expression Evaluation in C++

 

Postfix expression evaluation is a method of evaluating mathematical expressions in which the operators are placed after the operands. This method is also known as Reverse Polish Notation (RPN) and is used in many programming languages, including C++. The main advantage of using postfix notation is that it eliminates the need for parentheses, which can make the expressions easier to read and understand. In this article, we will discuss the concept of postfix expression evaluation in C++ and how to implement it using stack data structure.

The basic idea behind postfix notation is that the operators are applied to the operands that come before them. For example, in the expression "2 + 3 * 4", the operator "*" is applied to the operands "3" and "4" first, and then the operator "+" is applied to the result and the operand "2". In postfix notation, the same expression would be written as "2 3 4 * +".

To evaluate a postfix expression, we use a stack data structure. The stack is a last-in, first-out (LIFO) data structure that allows us to store and retrieve elements in a specific order. In our case, we use the stack to store the operands and operators of the expression.

The process of evaluating a postfix expression starts by scanning the expression from left to right. For each element, we check if it is an operand or an operator. If it is an operand, we push it onto the stack. If it is an operator, we pop the top two elements from the stack, apply the operator to them, and push the result back onto the stack. Once we have reached the end of the expression, the result will be the only element remaining on the stack.

Here is an example of how to evaluate the postfix expression "2 3 4 * +" using stack data structure in C++:

#include <iostream> 
 #include <stack> 
 using namespace std;
 int evaluatePostfix(string exp)
{
 stack<int> s;
 int i;
 for (i = 0; exp[i]; i++)
    {
 if (isdigit(exp[i]))
            s.push(exp[i] - '0');
 else 
 {
 int val1 = s.top();
 s.pop(); 
 int val2 = s.top();
 s.pop();
 switch (exp[i])
            {
 case '+':
                s.push(val2 + val1);
 break; 
 case '-':
                s.push(val2 - val1);
 break; 
 case '*':
                s.push(val2 * val1);
 break;
 case '/':
                s.push(val2 / val1); 
 break;
 } 
 } 
 } 
 return s.top(); 
} 
 int main()
{ 
 string exp = "2 3 4 * +"; 
 cout << evaluatePostfix(exp) << endl;
 return 0;
 }

In this example, we have defined a function called "evaluatePostfix" that takes a string as an argument. The function uses a stack data structure to evaluate the postfix expression. The for loop scans the expression from left to right. If the current element is a digit, it pushes it onto the stack. If the current element is an operator, it pops the top two elements from the stack,