What is the time complexity of Baseball Game?

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

What data structures are used to solve Baseball Game?

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

What are the key insights for solving Baseball Game?

Insight 1: The problem is essentially a stack manipulation task. The operations directly correspond to pushing, popping, and peeking at the top elements of a stack. Insight 2: Using a stack (or a dynamically sized array like a list in Python or a vector in C++) is crucial for efficiently managing the scores and applying the 'C', 'D', and '+' operations in the correct order.

Which companies ask LeetCode 682. Baseball Game in interviews?

This problem is frequently asked at Turing.

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Baseball Game - LeetCode 682 Solution

Baseball Game - Complete Solution Guide

Baseball Game is LeetCode problem 682, a Easy 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 keeping the scores for a baseball game with strange rules. At the beginning of the game, you start with an empty record. You are given a list of strings operations , where operations[i] is the i th operation you must apply to the record and is one of the following: An integer x . Record a new score of x . '+' . Record a new score that is the sum of the previous two scores. 'D' . Record a new score that is the double of the previous score. 'C' . Invalidate the previous score, removing it

Detailed Explanation

The "Baseball Game" problem requires you to simulate a baseball game with specific rules for scoring. You are given a list of operations, where each operation can be an integer (representing a new score), or one of the special commands: '+', 'D', or 'C'. '+' means to add the previous two scores together, 'D' means to double the previous score, and 'C' means to invalidate (remove) the previous score. The goal is to calculate the final sum of all valid scores after applying all the operations.

Solution Approach

The solution utilizes a stack (implemented as a list in Python or a Stack data structure in Java). It iterates through the list of operations. If the operation is an integer, it's pushed onto the stack. If the operation is '+', the sum of the top two elements is calculated and pushed onto the stack. If the operation is 'D', the top element is doubled and pushed onto the stack. If the operation is 'C', the top element is popped from the stack. Finally, the sum of the remaining elements in the stack is calculated and returned.

Step-by-Step Algorithm

Step 1: Initialize an empty stack (or list/vector) to store the scores.
Step 2: Iterate through the input array of operations.
Step 3: For each operation, perform the following:
Step 4: If the operation is an integer, convert it to an integer and push it onto the stack.
Step 5: If the operation is '+', pop the top two elements from the stack, add them together, push the first element back onto the stack and then push the sum of the two elements.
Step 6: If the operation is 'D', peek at the top element of the stack, double it, and push the result onto the stack.
Step 7: If the operation is 'C', pop the top element from the stack.
Step 8: After processing all operations, calculate the sum of the remaining elements in the stack.
Step 9: Return the sum.

Key Insights

Insight 1: The problem is essentially a stack manipulation task. The operations directly correspond to pushing, popping, and peeking at the top elements of a stack.
Insight 2: Using a stack (or a dynamically sized array like a list in Python or a vector in C++) is crucial for efficiently managing the scores and applying the 'C', 'D', and '+' operations in the correct order.
Insight 3: The input constraints guarantee the validity of the operations, specifically that '+' will always have at least two previous scores, and 'C' and 'D' will always have at least one.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(n)

Topics

This problem involves: Array, Stack, Simulation.

Companies

Asked at: Turing.

Baseball Game | LeetCode 682

Easy

Array Stack Simulation

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

Solution Code

Available in:

class Solution {
    public int calPoints(String[] operations) {
        Stack<Integer> stack = new Stack<>();
        for (String op : operations) {
            if (op.equals("+")) {
                int top = stack.pop();
                int secondTop = stack.peek();
                stack.push(top);
                stack.push(top + secondTop);
            } else if (op.equals("C")) {
                stack.pop();
            } else if (op.equals("D")) {
                stack.push(stack.peek() * 2);
            } else {
                stack.push(Integer.parseInt(op));
            }
        }
        int sum = 0;
        while (!stack.isEmpty()) {
            sum += stack.pop();
        }
        return sum;
    }
}

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Problem Info

Description

Problem 682: Baseball Game - Detailed explanation and solution approaches.

Topics

Array Stack Simulation

Companies

Turing

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:682

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

9 steps

1
Step 1: Initialize an empty stack (or list/vector) to store the scores.
2
Step 2: Iterate through the input array of operations.
3
Step 3: For each operation, perform the following:
4
Step 4: If the operation is an integer, convert it to an integer and push it onto the stack.
5
Step 5: If the operation is '+', pop the top two elements from the stack, add them together, push the first element back onto the stack and then push the sum of the two elements.
6
Step 6: If the operation is 'D', peek at the top element of the stack, double it, and push the result onto the stack.
7
Step 7: If the operation is 'C', pop the top element from the stack.
8
Step 8: After processing all operations, calculate the sum of the remaining elements in the stack.
9
Step 9: Return the sum.

💡

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 derived from the single loop that iterates through the 'operations' array. Each operation within the loop takes constant time. The space complexity arises from the use of a stack/list to store the scores. In the worst case, the stack/list could hold all the scores, leading to a space complexity of O(n).

📖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

Using a Queue

While a stack is the most natural data structure for this problem, a queue could technically be used with a lot of extra overhead by enqueuing, dequeuing, and temporarily storing elements to undo the queue's FIFO order. This approach would be significantly more complex and less efficient.

Time: O(n^2) in worst case, due to re-ordering queue when 'C', 'D' or '+' is encountered.Space: O(n)

Trade-offs: This is highly inefficient and not recommended.

Using a fixed-size array (without dynamic resizing)

If the problem statement included a maximum bound for how many *valid* scores can be stored at any time (as opposed to the number of *operations*), a fixed size array could be used. However, you would need careful index management to simulate the stack operations. This could be more efficient than dynamically resizing lists/stacks, especially in languages with less efficient dynamic memory management.

Time: O(n)Space: O(k), where k is the maximum number of valid scores

Trade-offs: Only usable if a hard limit on *valid* scores is defined. Otherwise requires guessing a size beforehand or over-allocating, which could be wasteful.

✨

Key Insights

1Insight 1: The problem is essentially a stack manipulation task. The operations directly correspond to pushing, popping, and peeking at the top elements of a stack.
2Insight 2: Using a stack (or a dynamically sized array like a list in Python or a vector in C++) is crucial for efficiently managing the scores and applying the 'C', 'D', and '+' operations in the correct order.
3Insight 3: The input constraints guarantee the validity of the operations, specifically that '+' will always have at least two previous scores, and 'C' and 'D' will always have at least one.

📚

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: Empty input array. The code correctly handles this implicitly as the loop will not execute, and the sum will be 0.
Edge case 2: Only 'C' operations. The stack will eventually be empty and the final sum will be 0, which is the expected behavior.
Edge case 3: Large numbers of 'D' operations. As long as intermediate calculations and the final answer fit within the 32-bit integer limit, the code will function correctly. The problem statement guarantees this condition.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Not handling integer parsing correctly. Remember to convert the string representation of numbers to integers before performing calculations.

✗Common mistake 2: Incorrectly implementing the '+' operation. It's important to remember the stack order and add the last two valid scores correctly.

✗Common mistake 3: Forgetting the data structure (stack or array) and trying to track the valid numbers using individual variables, which leads to errors in undoing steps (the 'C' operation) and performing calculations ('+' and 'D' operations).

✅

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: Undo/Redo functionality in software. The 'C' operation simulates an undo, and the stack is used to maintain the history of actions.

🏦Real-world scenario 2: Backtracking algorithms. Many backtracking problems use a stack (implicitly or explicitly) to keep track of the current state and revert to previous states when necessary.

🎮Real-world scenario 3: Evaluating Reverse Polish Notation (RPN) expressions, where operators are applied to the previous operands on the stack.

💡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

Use this problem to demonstrate clean code practices. Variable naming and code organization matter.

⚠️ Watch Out

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

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 21, 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

I was asked this exact problem at my Google interview. The interviewer wanted me to optimize space complexity.

@InterviewProJun 15

Try solving this without using extra space first. It's a great exercise for understanding the underlying pattern.

@CodeNinjaJun 8

❓

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 problems are best solved with a stack?

Stacks excel at: matching problems (parentheses validation), next greater/smaller element, expression evaluation, backtracking, and undo operations. The key pattern is LIFO (Last In, First Out) - when you need to access the most recently added element.

How should I approach easy-level algorithm problems?

Easy problems build foundational skills. Focus on: 1) Understanding the problem completely before coding, 2) Writing clean, readable code, 3) Handling all edge cases (empty input, single element, etc.), 4) Analyzing time and space complexity. Don't skip complexity analysis even for simple solutions.

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 "Baseball Game"?

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

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