What is the time complexity of Evaluate Reverse Polish Notation?

The optimal solution has a time complexity of O(n).

What data structures are used to solve Evaluate Reverse Polish Notation?

This problem uses Array, Math, Stack. Understanding these concepts is essential for solving this Medium problem efficiently.

What are the key insights for solving Evaluate Reverse Polish Notation?

Insight 1: The core idea is to use a stack to keep track of operands. When an operator is encountered, pop the necessary number of operands from the stack (two in this case), perform the operation, and push the result back onto the stack. Insight 2: The order of operands is crucial for subtraction and division. The first operand popped from the stack is the second operand in the operation, and the second operand popped is the first operand.

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Evaluate Reverse Polish Notation - LeetCode 150 Solution

Q: Which companies ask LeetCode 150. Evaluate Reverse Polish Notation in interviews?

This problem is frequently asked at Apollo.io, Attentive, Canonical, Citadel, Grammarly and 4 more companies.

Evaluate Reverse Polish Notation - Complete Solution Guide

Evaluate Reverse Polish Notation is LeetCode problem 150, a Medium level challenge. This complete guide provides step-by-step explanations, multiple solution approaches, and optimized code in python3, java, cpp, c.

Problem Statement

You are given an array of strings tokens that represents an arithmetic expression in a Reverse Polish Notation . Evaluate the expression. Return an integer that represents the value of the expression . Note that: The valid operators are '+' , '-' , '*' , and '/' . Each operand may be an integer or another expression. The division between two integers always truncates toward zero . There will not be any division by zero. The input represents a valid arithmetic expression in a reverse polish notat

Detailed Explanation

The problem asks us to evaluate an arithmetic expression given in Reverse Polish Notation (RPN), also known as postfix notation. In RPN, operators follow their operands. For instance, "2 1 +" means "2 + 1". We need to parse the given array of strings, which contains numbers and operators ('+', '-', '*', '/'), and return the integer result of the entire expression. Integer division should truncate towards zero. The expression is guaranteed to be valid and the result will fit in a 32-bit integer.

Solution Approach

The provided code implements the stack-based approach to evaluate the RPN expression. It iterates through the input `tokens` array. If a token is an operand (a number), it's converted to an integer and pushed onto the stack. If a token is an operator, the top two operands are popped from the stack, the operation is performed, and the result is pushed back onto the stack. Finally, after processing all tokens, the stack will contain a single element, which is the result of the entire expression.

Step-by-Step Algorithm

Step 1: Initialize an empty stack to store operands.
Step 2: Iterate through the `tokens` array.
Step 3: If the current token is a number (operand), convert it to an integer and push it onto the stack.
Step 4: If the current token is an operator ('+', '-', '*', '/'):
Step 4.1: Pop the top two elements from the stack (operand2, operand1).
Step 4.2: Perform the corresponding operation (operand1 + operand2, operand1 - operand2, operand1 * operand2, or operand1 / operand2). Note that the division is integer division.
Step 4.3: Push the result back onto the stack.
Step 5: After processing all tokens, the stack will contain the final result. Return the top element of the stack.

Key Insights

Insight 1: The core idea is to use a stack to keep track of operands. When an operator is encountered, pop the necessary number of operands from the stack (two in this case), perform the operation, and push the result back onto the stack.
Insight 2: The order of operands is crucial for subtraction and division. The first operand popped from the stack is the second operand in the operation, and the second operand popped is the first operand.
Insight 3: Integer division needs to be handled carefully to ensure truncation towards zero, as specified in the problem.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Math, Stack.

Companies

Asked at: Apollo.io, Attentive, Canonical, Citadel, Grammarly, LinkedIn, Odoo, Yandex, Zendesk.

Evaluate Reverse Polish Notation | LeetCode 150

Medium

Array Math Stack

Time: O(n)Space: O(n)

Solution Code

Available in:

import java.util.Stack;

class Solution {
    public int evalRPN(String[] tokens) {
        Stack<Integer> stack = new Stack<>();
        for (String token : tokens) {
            if (token.equals("+")) {
                int op2 = stack.pop();
                int op1 = stack.pop();
                stack.push(op1 + op2);
            } else if (token.equals("-")) {
                int op2 = stack.pop();
                int op1 = stack.pop();
                stack.push(op1 - op2);
            } else if (token.equals("*")) {
                int op2 = stack.pop();
                int op1 = stack.pop();
                stack.push(op1 * op2);
            } else if (token.equals("/")) {
                int op2 = stack.pop();
                int op1 = stack.pop();
                stack.push(op1 / op2);
            } else {
                stack.push(Integer.parseInt(token));
            }
        }
        
        return stack.get(0);
    }
}

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Problem Info

Description

Problem 150: Evaluate Reverse Polish Notation - Detailed explanation and solution approaches.

Topics

Array Math Stack

Companies

Apollo.ioAttentiveCanonicalCitadelGrammarlyLinkedInOdooYandex

Stats

Difficulty:Medium

Languages:4

Companies:9

Problem #:150

Problem Explanation

💡

Think Before You Code

🤔 Ask Yourself

→What is the input? What output do I need?
→Can I solve a smaller version of this problem first?
→What patterns have I seen in similar problems?

✏️ Try This First

Before looking at the solution, try to solve it on paper with a simple example!

🚀 Try on LeetCode

Solution Approach

📋

Step-by-Step Solution

8 steps

1
Step 1: Initialize an empty stack to store operands.
2
Step 2: Iterate through the `tokens` array.
3
Step 3: If the current token is a number (operand), convert it to an integer and push it onto the stack.
4
Step 4: If the current token is an operator ('+', '-', '*', '/'):
5
Step 4.1: Pop the top two elements from the stack (operand2, operand1).
6
Step 4.2: Perform the corresponding operation (operand1 + operand2, operand1 - operand2, operand1 * operand2, or operand1 / operand2). Note that the division is integer division.
7
Step 4.3: Push the result back onto the stack.
8
Step 5: After processing all tokens, the stack will contain the final result. Return the top element of the stack.

💡

Pro Tip for Students

Try tracing through each step with a small example on paper before coding. Understanding "why" each step happens is more important than memorizing the code!

⚡

Complexity Analysis

⏱️

Time Complexity

O(n)

👍 Linear - Good! Visits each element once.

💾

Space Complexity

O(n)

📦 Linear space - Memory grows with input size.

📝

Why?

The time complexity is linear because we iterate through the `tokens` array once. The space complexity depends on the maximum size of the stack, which is proportional to the number of operands in the expression. In the worst case, the expression will have only operands, causing the stack to have n elements.

📖New to Big O? Click to learn more

Big O Notation - Quick Guide

O(1)Best - Instant

O(log n)Excellent - Binary Search

O(n)Good - One loop

O(n log n)OK - Sorting

O(n²)Slow - Nested loops

O(2ⁿ)Very Slow - Recursion

Alternative Approaches

Recursive Approach

A recursive approach could be used to parse the RPN expression, but it's generally less efficient than the iterative stack-based approach due to the overhead of function calls and the potential for stack overflow with very large expressions.

Time: O(n)Space: O(n) due to the recursion depth in the worst case

Trade-offs: Less efficient and more prone to stack overflow errors compared to the iterative approach. Primarily useful for educational purposes to understand the recursive nature of evaluating RPN expressions.

✨

Key Insights

1Insight 1: The core idea is to use a stack to keep track of operands. When an operator is encountered, pop the necessary number of operands from the stack (two in this case), perform the operation, and push the result back onto the stack.
2Insight 2: The order of operands is crucial for subtraction and division. The first operand popped from the stack is the second operand in the operation, and the second operand popped is the first operand.
3Insight 3: Integer division needs to be handled carefully to ensure truncation towards zero, as specified in the problem.

📚

Key Terms Explained

For Students

Array

A collection of items stored at contiguous memory locations. Like a row of boxes.

Stack

LIFO structure - Last In, First Out. Like a stack of plates!

Edge Cases

Edge case 1: Single operand. If the input contains only a single number (e.g., tokens = ['5']), the algorithm still works correctly because the number is pushed onto the stack, and the algorithm returns that number.
Edge case 2: Division by zero. The problem statement explicitly mentions that there will not be any division by zero, so we don't need to handle this case.
Edge case 3: Large intermediate results. The problem guarantees that all intermediate calculations can be represented in a 32-bit integer, so overflow is not a concern.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrect order of operands during subtraction or division. Remember to pop the operands in the correct order (operand2, then operand1) and perform the operation as operand1 - operand2 or operand1 / operand2.

✗Common mistake 2: Not handling integer division correctly. Remember to truncate towards zero, which is the default behavior in most languages when performing integer division.

✗Common mistake 3: Failing to convert string operands to integers before pushing them onto the stack.

✅

Learning Tip

Every mistake is a learning opportunity! When you make an error, understand why it happened before moving on.

🌍

Where is This Used in Real Life?

💼Real-world scenario 1: Compiler design. RPN is commonly used in compilers and interpreters to represent arithmetic expressions because it simplifies the evaluation process.

🏦Real-world scenario 2: Scientific calculators. Many scientific calculators use RPN as their input method due to its efficiency and lack of need for parentheses.

💡Understanding real-world applications helps you see the "why" behind algorithms. It's not just about passing interviews—these concepts power the apps and websites you use every day!

Author's Notes

💡 Key Insight

When dealing with arrays, always consider if sorting would simplify the problem. Many array problems have O(n) solutions using hash maps or two-pointer technique.

🎯 Interview Tip

Medium problems are the bread and butter of technical interviews. Practice explaining your approach before coding.

⚠️ Watch Out

Off-by-one errors are the most common mistake. Double-check your loop bounds and array indices.

👨‍💻 From Experience

This problem pattern appears frequently in real codebases. I've used similar logic when building production systems.

Written by Saswata Mondal

Software Engineer • Algorithms Enthusiast • Interview Coach

👨‍💻

About the Author

👨‍💻

Saswata MondalAuthor400+ LC Problems

B.Tech CSE, IEM Kolkata | LeetCode Rating: 1672 (Top 15%)

Certified: IBM Java Developer, NPTEL Programming in Java

Last updated: October 29, 2024LeetCode Profile GitHub

This solution has been crafted based on my experience solving 400+ LeetCode problems. Each explanation is designed to help you understand the underlying concepts, not just memorize the code.

Community Tips & Insights

Don't forget to handle the edge case when the input is empty. Many candidates miss this in interviews.

@DevExpert92Jul 13

The key insight here is recognizing the pattern. Once you see it, the solution becomes straightforward.

@AlgoMasterJul 6

❓

Frequently Asked Questions

What is the most efficient way to solve array problems?

Most array problems can be solved efficiently using techniques like two-pointer approach, sliding window, or hash maps. The key is identifying whether the array is sorted (enabling binary search) or if tracking seen elements (using hash maps) can help achieve O(n) time complexity.

What techniques are commonly tested in medium-difficulty problems?

Medium problems often require combining multiple techniques: two-pointer with hash maps, BFS/DFS with state tracking, dynamic programming with optimization, or divide-and-conquer approaches. They test your ability to recognize patterns and choose the right combination of techniques.

How should I practice algorithm problems effectively?

Focus on understanding patterns rather than memorizing solutions. After solving a problem, review optimal solutions and understand the intuition. Group similar problems to recognize patterns. Practice explaining your approach out loud. Review problems after a few days to test retention.

What is the optimal approach for "Evaluate Reverse Polish Notation"?

For this medium-level Array problem, the key is to identify the core pattern. Analyze the input constraints to determine acceptable time complexity. Consider whether math techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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