What is the time complexity of Determine Color of a Chessboard Square?

The optimal solution has a time complexity of O(1).

What data structures are used to solve Determine Color of a Chessboard Square?

This problem uses Math, String. Understanding these concepts is essential for solving this Easy problem efficiently.

What are the key insights for solving Determine Color of a Chessboard Square?

Insight 1: Recognizing that the color of a square alternates. Squares on the same diagonal have the same color. Insight 2: The use of modular arithmetic (`%`) to efficiently determine the color based on the row and column numbers.

Which companies ask LeetCode 1812. Determine Color of a Chessboard Square in interviews?

This problem is frequently asked at J.P. Morgan.

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Determine Color of a Chessboard Square - LeetCode 1812 Solution

Determine Color of a Chessboard Square - Complete Solution Guide

Determine Color of a Chessboard Square is LeetCode problem 1812, 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 coordinates , a string that represents the coordinates of a square of the chessboard. Below is a chessboard for your reference. Return true if the square is white, and false if the square is black . The coordinate will always represent a valid chessboard square. The coordinate will always have the letter first, and the number second. Example 1: Input: coordinates = "a1" Output: false Explanation: From the chessboard above, the square with coordinates "a1" is black, so return false.

Detailed Explanation

The problem asks you to determine the color (white or black) of a square on a standard 8x8 chessboard given its coordinates as a string. The input string `coordinates` is in the format "[letter][number]", where the letter represents the column (a-h) and the number represents the row (1-8). The output is a boolean: `true` if the square is white, and `false` if it's black.

Solution Approach

The provided solutions leverage the pattern of alternating colors on the chessboard. They convert the letter (column) and number (row) coordinates into numerical values and then use the sum of these values modulo 2 to determine the color. If the sum is even, it's one color; if it's odd, it's the other. The choice of which color corresponds to even/odd can be adjusted, as long as it's consistent.

Step-by-Step Algorithm

Step 1: Extract the column letter and row number from the input string `coordinates`.
Step 2: Convert the column letter to its numerical equivalent (a=1, b=2, ..., h=8). This is typically done using ASCII character arithmetic (e.g., subtracting the ASCII value of 'a').
Step 3: Convert the row number (which is already a number) from string to an integer.
Step 4: Add the numerical representations of the column and row.
Step 5: Calculate the remainder when the sum is divided by 2 (using the modulo operator, %).
Step 6: Return `true` (white) if the remainder is 1 (odd), and `false` (black) if the remainder is 0 (even). This mapping (odd=white, even=black) can be reversed as long as it's consistent.

Key Insights

Insight 1: Recognizing that the color of a square alternates. Squares on the same diagonal have the same color.
Insight 2: The use of modular arithmetic (`%`) to efficiently determine the color based on the row and column numbers.
Insight 3: Converting the letter coordinate to a numerical representation simplifies the color determination logic.

Complexity Analysis

Time Complexity: O(1)

Space Complexity: O(1)

Topics

This problem involves: Math, String.

Companies

Asked at: J.P. Morgan.

Determine Color of a Chessboard Square | LeetCode 1812

Easy

Math String

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

Solution Code

Available in:

class Solution {
    public boolean squareIsWhite(String coordinates) {
        char file = coordinates.charAt(0);
        char rank = coordinates.charAt(1);

        if ((file - 'a') % 2 == 0) {
            return (rank - '1') % 2 != 0;
        } else {
            return (rank - '1') % 2 == 0;
        }
    }
}

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Problem Info

Description

Problem 1812: Determine Color of a Chessboard Square - Detailed explanation and solution approaches.

Topics

Math String

Companies

J.P. Morgan

Stats

Difficulty:Easy

Languages:4

Companies:1

Problem #:1812

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

6 steps

1
Step 1: Extract the column letter and row number from the input string `coordinates`.
2
Step 2: Convert the column letter to its numerical equivalent (a=1, b=2, ..., h=8). This is typically done using ASCII character arithmetic (e.g., subtracting the ASCII value of 'a').
3
Step 3: Convert the row number (which is already a number) from string to an integer.
4
Step 4: Add the numerical representations of the column and row.
5
Step 5: Calculate the remainder when the sum is divided by 2 (using the modulo operator, %).
6
Step 6: Return `true` (white) if the remainder is 1 (odd), and `false` (black) if the remainder is 0 (even). This mapping (odd=white, even=black) can be reversed as long as it's consistent.

💡

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(1)

⚡ Constant time - Super fast! Same speed regardless of input size.

💾

Space Complexity

O(1)

💪 Constant space - Uses same memory regardless of input!

📝

Why?

The algorithm performs a fixed number of arithmetic operations regardless of the input coordinates. It does not use any data structures that grow with the input size. Therefore, both time and space complexity are constant.

📖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

Lookup Table

Pre-compute a 2D array (or map) representing the chessboard, where each element stores the color (true/false) of the corresponding square. Use the coordinates to directly access the color in the table.

Time: O(1)Space: O(64)

Trade-offs: This approach is simpler to read and understand but uses a small, fixed amount of space to store the entire chessboard. This is a good solution if speed is a priority and space is not a major constraint.

Bit Manipulation

Represent the chessboard as a bitmask. Each bit corresponds to a square, with 0 representing black and 1 representing white. Calculate the bit position based on the coordinates and then check if the bit is set or not.

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

Trade-offs: This approach is efficient in terms of both time and space, but is harder to understand and implement than simpler arithmetic based solutions. It might be preferred for performance-critical applications.

✨

Key Insights

1Insight 1: Recognizing that the color of a square alternates. Squares on the same diagonal have the same color.
2Insight 2: The use of modular arithmetic (`%`) to efficiently determine the color based on the row and column numbers.
3Insight 3: Converting the letter coordinate to a numerical representation simplifies the color determination logic.

📚

Key Terms Explained

For Students

String

A sequence of characters. Like a word or sentence in programming!

Edge Cases

Edge case 1: Input coordinates are at the edges of the board (a1, h8, etc.). The solution handles these correctly using the modular arithmetic approach, because the same logic applies to all coordinates.
Edge case 2: Invalid input (not 'a' to 'h' and '1' to '8'). While the problem statement specifies that only valid coordinates will be given, robust solutions could check the input's validity before proceeding with the calculations.

⚠️

Common Mistakes to Avoid

✗Common mistake 1: Incorrectly mapping the column letter to a numerical value (off-by-one errors are common).

✗Common mistake 2: Using the wrong modulo operator or incorrectly interpreting the remainder when performing modular arithmetic (e.g., mixing up even and odd results).

✅

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: This problem showcases a simple, elegant solution to problems involving patterns and coordinate systems, which can be found in various applications such as game development (board games, simulations), image processing (coordinate mapping), or any problem involving a grid structure.

🏦Real-world scenario 2: The underlying concept of modular arithmetic and pattern recognition can be applied to various computational tasks where periodic behavior or cyclical patterns are involved. For example, it is useful in calculating the day of the week for a given date, or other cyclic phenomena.

💡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

Even for easy problems, discuss time and space complexity. Interviewers want to see you think analytically.

⚠️ Watch Out

Always test your solution with edge cases: empty input, single element, and boundary values.

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: June 13, 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.

@InterviewProJul 14

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

@CodeNinjaJul 7

❓

Frequently Asked Questions

How do I handle string manipulation efficiently?

In languages with immutable strings (Java, Python, C#), use StringBuilder/list to avoid O(n) concatenation cost. Consider using character arrays for in-place modifications. For pattern matching, consider KMP or Rabin-Karp for O(n+m) 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 Color of a Chessboard Square"?

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

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