What is the time complexity of Determine the Winner of a Bowling Game?

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

What data structures are used to solve Determine the Winner of a Bowling Game?

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

What are the key insights for solving Determine the Winner of a Bowling Game?

Insight 1: The scoring system requires iterating through the player's scores, considering the previous two turns to determine score multipliers. Insight 2: A simple iterative approach is sufficient to calculate the total score for each player. No complex data structures are needed.

Which companies ask LeetCode 2660. Determine the Winner of a Bowling Game in interviews?

This problem is frequently asked at DE Shaw.

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Determine the Winner of a Bowling Game - LeetCode 2660 Solution

Determine the Winner of a Bowling Game - Complete Solution Guide

Determine the Winner of a Bowling Game is LeetCode problem 2660, 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 given two 0-indexed integer arrays player1 and player2 , representing the number of pins that player 1 and player 2 hit in a bowling game, respectively. The bowling game consists of n turns, and the number of pins in each turn is exactly 10. Assume a player hits x i pins in the i th turn. The value of the i th turn for the player is: 2x i if the player hits 10 pins in either (i - 1) th or (i - 2) th turn . Otherwise, it is x i . The score of the player is the sum of the values of their n

Detailed Explanation

The problem simulates a simplified bowling game between two players. Each player's performance is represented by an array where each element indicates the number of pins knocked down in a turn. The scoring system is unique: if a player knocks down 10 pins in either the previous or the turn before the previous, their score for the current turn is doubled. The goal is to determine the winner (player 1, player 2, or a draw) based on their total scores.

Solution Approach

The solution uses a straightforward iterative approach. For each player, it iterates through their score array. It checks if the previous one or two turns resulted in a score of 10. If so, the current turn's score is doubled before being added to the running total. Finally, it compares the total scores of both players to determine the winner.

Step-by-Step Algorithm

Step 1: Initialize the scores for player 1 and player 2 to 0.
Step 2: Iterate through the `player1` array. For each element (score), check if the previous two scores (if they exist) are equal to 10. If either is 10, double the current score. Add the (possibly doubled) score to `score1`.
Step 3: Repeat Step 2 for `player2`, calculating `score2`.
Step 4: Compare `score1` and `score2`. Return 1 if `score1 > score2`, 2 if `score2 > score1`, and 0 if they are equal.

Key Insights

Insight 1: The scoring system requires iterating through the player's scores, considering the previous two turns to determine score multipliers.
Insight 2: A simple iterative approach is sufficient to calculate the total score for each player. No complex data structures are needed.
Insight 3: Edge cases must be handled, specifically the first two turns where there are no previous turns to check for a bonus.

Complexity Analysis

Time Complexity: O(n)

Space Complexity: O(1)

Topics

This problem involves: Array, Simulation.

Companies

Asked at: DE Shaw.

Determine the Winner of a Bowling Game | LeetCode 2660

Easy

Array Simulation

Time: O(n)Space: O(1)

Solution Code

Available in:

class Solution {
    public int isWinner(int[] player1, int[] player2) {
        int score1 = 0;
        int score2 = 0;
        for (int i = 0; i < player1.length; i++) {
            int val1 = player1[i];
            int val2 = player2[i];
            if (i > 1) {
                if (player1[i - 1] == 10 || player1[i - 2] == 10) {
                    val1 *= 2;
                }
                if (player2[i - 1] == 10 || player2[i - 2] == 10) {
                    val2 *= 2;
                }
            }
            score1 += val1;
            score2 += val2;
        }
        if (score1 > score2) {
            return 1;
        } else if (score2 > score1) {
            return 2;
        } else {
            return 0;
        }
    }
}

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Problem Info

Description

Problem 2660: Determine the Winner of a Bowling Game - Detailed explanation and solution approaches.

Topics

Array Simulation

Companies

DE Shaw

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:2660

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

4 steps

1
Step 1: Initialize the scores for player 1 and player 2 to 0.
2
Step 2: Iterate through the `player1` array. For each element (score), check if the previous two scores (if they exist) are equal to 10. If either is 10, double the current score. Add the (possibly doubled) score to `score1`.
3
Step 3: Repeat Step 2 for `player2`, calculating `score2`.
4
Step 4: Compare `score1` and `score2`. Return 1 if `score1 > score2`, 2 if `score2 > score1`, and 0 if they are equal.

💡

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(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The solution iterates through the input arrays once for each player. The number of operations is directly proportional to the length of the arrays (n). It uses a fixed number of variables to store the scores, regardless of the input size, hence O(1) space complexity.

📖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

Functional Approach

Using a functional programming paradigm, the score calculation could be implemented using a recursive function or map/reduce operations. This approach might be more concise but potentially less efficient for very large inputs.

Time: O(n)Space: O(n) (Potentially higher due to recursive call stack or intermediate data structures)

Trade-offs: Functional approaches can enhance readability but may sacrifice some performance compared to the iterative approach. Suitable for smaller datasets where code clarity is prioritized.

✨

Key Insights

1Insight 1: The scoring system requires iterating through the player's scores, considering the previous two turns to determine score multipliers.
2Insight 2: A simple iterative approach is sufficient to calculate the total score for each player. No complex data structures are needed.
3Insight 3: Edge cases must be handled, specifically the first two turns where there are no previous turns to check for a bonus.

📚

Key Terms Explained

For Students

Array

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

Edge Cases

Edge case 1: The first one or two turns. The code correctly handles this by only checking previous scores if `i > 1`.
Edge case 2: Empty input arrays. While the problem statement implies non-empty arrays, robust code should ideally check for this and return 0 or handle it appropriately.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly handling the bonus condition. Forgetting to check both the (i-1)th and (i-2)th scores or applying the bonus incorrectly can lead to inaccurate scores.

✗Common mistake 2: Off-by-one errors in indexing the arrays. Accessing elements beyond the array bounds when checking previous scores can cause runtime errors.

✅

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: Scoring systems in various sports or games can benefit from this type of scoring algorithm where bonus points depend on previous events (e.g., bonus points for consecutive successful shots).

🏦Real-world scenario 2: Implementing customized reward systems in applications or games where actions build upon each other and can trigger special bonuses.

💡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

Don't rush. Explain your thought process clearly. Easy problems are often about communication.

⚠️ Watch Out

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

👨‍💻 From Experience

This is one of the first problems I solved when learning Array. It's a great foundation for more complex problems.

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 19, 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 14

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

@AlgoMasterJul 7

❓

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.

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 "Determine the Winner of a Bowling 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 simulation techniques can optimize the solution. Always handle edge cases and validate your approach with examples before coding.

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