The Evaluate Reverse Polish Notation problem on LeetCode challenges you to process an expression written in postfix notation (Reverse Polish Notation or RPN). This problem builds key skills in understanding stack-based algorithms, postfix evaluation, and handling arithmetic operations programmatically.
Understanding the Problem
You’re given an array of strings tokens, where each element represents either:
• An Operand: An integer (e.g., “2”, “15”).
• An Operator: One of the four basic arithmetic operators (+, -, *, /).
Your goal is to evaluate the given expression using Reverse Polish Notation (RPN) and return the final result.
What is RPN?
• In Reverse Polish Notation, operators appear after their operands.
• This differs from Infix Notation, where operators appear between operands (e.g., 2 + 1).
• RPN eliminates ambiguity and the need for parentheses because the order of operations is explicitly defined.
RPN Basics
To understand RPN, let’s first compare it with infix notation:
Infix Notation
• Operands and operators are interspersed.
• Parentheses are often needed to define precedence.
• Example: (2 + 1) x 3
Postfix (RPN) Notation
• Operators follow their operands, so no parentheses are required.
• Operands are processed before applying an operator.
• Example: 21 + 3*
Why Reverse Polish Notation (RPN) is Important: A JVM Perspective
The Java Virtual Machine (JVM) uses a stack-based execution model to process bytecode instructions. Reverse Polish Notation (RPN) plays a crucial role in this context because its structure aligns perfectly with how the JVM operates using an operand stack.
a) No Parentheses or Precedence Rules
• RPN encodes the order of operations directly in the expression.
• The JVM doesn’t need to evaluate parentheses or manage operator precedence, as RPN inherently resolves these issues.
• Example:
• Infix: (2 + 3) x 4
• RPN: 2 3 + 4 *
b) Direct Mapping to Stack Operations
• RPN aligns with the push and pop operations of the JVM stack:
• Operands are pushed onto the stack sequentially.
• Operators pop the required operands, compute the result, and push it back.
• This straightforward approach makes RPN efficient for machines to process.
c) Sequential Processing
• RPN allows the JVM to evaluate expressions in a single left-to-right pass without backtracking or additional parsing.
• This reduces computational overhead and simplifies bytecode interpretation.
Break Down the Problem
Key Concepts
1. Operand Stack:
• Use a stack to hold operands while processing the input.
• When encountering an operator, pop two operands, perform the operation, and push the result back.
2. Operators:
• Supported operations: Addition (+), Subtraction (-), Multiplication (*), Division (/).
• Division should truncate toward zero.
3. Iterative Processing:
• Evaluate the tokens from left to right.
import java.util.Stack;
public class EvaluateRPN {
public int evalRPN(String[] tokens) {
Stack<Integer> stack = new Stack<>();
for (String token : tokens) {
if (isOperator(token)) {
int b = stack.pop();
int a = stack.pop();
stack.push(applyOperator(token, a, b));
} else {
stack.push(Integer.parseInt(token));
}
}
return stack.pop();
}
private boolean isOperator(String token) {
return "+-*/".contains(token);
}
private int applyOperator(String operator, int a, int b) {
switch (operator) {
case "+": return a + b;
case "-": return a - b;
case "*": return a * b;
case "/": return a / b; // Integer division
default: throw new IllegalArgumentException("Invalid operator");
}
}
}Conclusion
The Evaluate Reverse Polish Notation problem is an excellent way to master stack-based algorithms and expression evaluation. By processing operands and operators in postfix notation, you develop key skills for solving computational challenges like expression parsing and calculator implementation. Whether using a traditional stack or an optimized array approach, this problem builds foundational knowledge for real-world systems like compilers and virtual machines.
