Evaluate the Value of an Arithmetic Expression in Reverse Polish Notation in Python

Reverse Polish Notation (RPN), also called postfix notation, places operators after operands. It removes the need for parentheses and operator-precedence rules, making it efficient for stack-based evaluation.

Given a valid RPN expression containing integers and the operators +, -, *, /, compute its final value. Where:

• Operands may be positive or negative integers
• Division truncates toward zero
• No division by zero will occur
• The expression always evaluates to an integer result

For Example:

Input: ["10", "6", "9", "3", "+", "-11", "*", "/", "*", "17", "+", "5", "+"]
Output: 22
Explanation: ((10 * (6 / ((9 + 3) * -11))) + 17) + 5 = ((10 * (6 / (12 * -11))) + 17) + 5
= ((10 * (6 / -132)) + 17) + 5
= ((10 * 0) + 17) + 5
= (0 + 17) + 5
= 17 + 5
= 22

Python Implementation

A stack is used to evaluate the RPN expression by processing tokens one by one. Operands are stored, and operators compute results using the last two values.

tokens = ["10", "6", "9", "3", "+", "-11", "*", "/", "*", "17", "+", "5", "+"]
stack = []

for token in tokens:
    if token not in {"+", "-", "*", "/"}:
        stack.append(int(token))
    else:
        right = stack.pop()
        left = stack.pop()

        if token == "+":
            stack.append(left + right)
        elif token == "-":
            stack.append(left - right)
        elif token == "*":
            stack.append(left * right)
        elif token == "/":
            stack.append(int(left / right))

print("Value of the expression =", stack.pop())

Value of the expression = 22

Explanation:

• stack stores operands during evaluation.
• for token in tokens: iterates through each element of the RPN expression.
• if token not in {"+", "-", "*", "/"} checks whether the token is an operand.
• stack.append(int(token)) pushes the operand onto the stack.
• right = stack.pop() and left = stack.pop() retrieve the last two operands.
• Arithmetic operations (+, -, *, /) are applied based on the operator.
• int(left / right) ensures division truncates toward zero.
• stack.pop() at the end gives the final evaluated result.