Question

2. Write a C++ program that reads string expressions from input file “expressions.txt”. The program should check if the given postfix expression is valid

Answer 1

It is not necessary to solve the string, and you can use a counter, not a stack.

The counter tracks the number of values that would be on the stack if you would have solved the expression.

let's consider you have only operands and binary operators.

This algorithm uses a special decreament operation: if when you decrement, the counter goes below zero, the string is invalid:

1. Initialize the counter to 0.
2. When you see a literal, increment the counter.
3. When you see a binary operator, decrement the counter twice, then increment it.
4. At the end of the string, if the counter is 1, and if it never went below 0, the string is valid.

C++ code:-

#include<iostream>
using namespace std;

//this utility function checks if count < 0, then return true
bool checkCount(int count)
{
   if(count < 0)
   {
       cout << "\nPostfix expression in Invalid" << endl;
       true;
   }
   return false;
}
int main()
{
   //redding postfix expression
   string postfix;
   cout << "Enter Postfix expression: ";
   cin >> postfix;

   //initialis the counter
   int count = 0;
  
   //looping through each character in exp
   for(int i = 0 ; i < postfix.size() ; i++)
   {
       //if we find a binary operator
       if(postfix[i] == '+' || postfix[i] == '-' ||
               postfix[i] == '*' || postfix[i] == '/' || postfix[i] == '^')
       {
           //decreament the cound
           //this simulates popping from the stack.
           //while solving we pop twixw from stack if an operator is found
           count--;
           count--;
           if(checkCount(count))
           {
               cout << "\nPostfix expression in Invalid" << endl;
               return 0;
           }
           //now increasing
           //after popping in prevoius step, we need to evaluate the exp
           //and the result is pushed in stack
           //so we increament
           count ++;
       }
       //if any upper case or lower case character
       //that is we have an english letter
       //considering that as an operand
       else if( isupper(postfix[i]) || islower(postfix[i]))
       {
           count++;
       }
       else
       {
           cout << "\nPostfix expression in Invalid" << endl;
           return 2;
       }
         
      
   }
  
   //if count == 1
   //the stack only has a single value
   //the result
   if(count == 1)
       cout <<"\nPostfix Expression is valid.";
   else
       cout << "\nPostfix expression in Invalid" << endl;  
   return 0;
}