This program evaluates postfix expressions using a stack. Postfix notation, also known as Reverse Polish notation, is a mathematical notation in which each operator follows all of its operands. It does not need any parentheses as long as each operator has a fixed number of operands.

Program Structure

The program uses a stack to keep track of operands. When an operator is encountered in the expression, the program:

• Pops the requisite number of operands from the stack,
• Applies the operator,
• And pushes the result back onto the stack.

The final value remaining in the stack after processing the entire expression is the result.

Python Code

def evaluate_postfix(expression):
    stack = []
    for char in expression.split():
        if char.isdigit():
            stack.append(int(char))
        else:
            right = stack.pop()
            left = stack.pop()
            if char == '+':
                stack.append(left + right)
            elif char == '-':
                stack.append(left - right)
            elif char == '*':
                stack.append(left * right)
            elif char == '/':
                stack.append(int(left / right))  # use int to perform floor division

# Example Usage
expression = "3 4 + 2 * 7 /"
print(f"Result of '{expression}':", evaluate_postfix(expression))

Explanation of the Code

• Function evaluate_postfix: Takes a string expression and initializes an empty stack. It processes each token separated by space:
• Operands: Are directly pushed onto the stack.
• Operators: Cause the last two operands to be popped from the stack, the operation to be performed, and the result to be pushed back onto the stack.
• Result: At the end of the expression, the stack contains one element, the result of the postfix expression.

Usage

This function can be used in applications that need to evaluate expressions stored in postfix notation, such as certain calculators and algorithm implementations that benefit from this notation’s elimination of the need for parentheses and precedence rules.