Determine Color of a Chessboard Square - Problem

Math String Easy

You are given coordinates, a string that represents the coordinates of a square on a chessboard.

A chessboard is an 8x8 grid where squares alternate between white and black colors. The bottom-left square a1 is a dark (black) square.

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.

Input & Output

Example 1 — Corner Square

$ Input: coordinates = "a1"

› Output: false

💡 Note: Square a1 is at column 1, row 1. Sum = 1 + 1 = 2 (even), so it's black. Return false.

Example 2 — White Square

$ Input: coordinates = "h3"

› Output: true

💡 Note: Square h3 is at column 8, row 3. Sum = 8 + 3 = 11 (odd), so it's white. Return true.

Example 3 — Adjacent Square

$ Input: coordinates = "c7"

› Output: false

💡 Note: Square c7 is at column 3, row 7. Sum = 3 + 7 = 10 (even), so it's black. Return false.

Constraints

coordinates.length == 2
coordinates[0] is a letter from 'a' to 'h'
coordinates[1] is a digit from '1' to '8'

Visualization

Tap to expand

Asked in

G Google 15 M Microsoft 12 a Amazon 8

The key insight is that chessboard colors follow a mathematical pattern based on coordinate sum parity. Best approach uses sum modulo 2 to determine if a square is white (odd sum) or black (even sum). Time: O(1), Space: O(1)

Common Approaches

✓ Memoization

⏱️ Time: N/A Space: N/A

Direct Pattern Recognition

⏱️ Time: O(1) Space: O(1)

Since a1 is black, we can determine that squares where the sum of column index and row number is even are black, and odd sums are white.

Mathematical Formula

⏱️ Time: O(1) Space: O(1)

Since chessboard colors alternate, we can use the mathematical property that adjacent squares have different colors. The sum of coordinates modulo 2 gives us the color pattern.

XOR Bit Manipulation

⏱️ Time: O(1) Space: O(1)

Instead of addition and modulo, we can use XOR operation. Since XOR returns 1 when bits are different, we can directly check if column and row parities differ.

Algorithm Steps — Algorithm Steps

Code -

solution.c — C

#include <stdio.h>
#include <stdbool.h>

int main() {
    char coordinates[3];
    
    // Read coordinates from stdin
    if (scanf("%s", coordinates) != 1) {
        return 1;
    }
    
    // Extract column and row
    char col = coordinates[0];  // 'a' to 'h'
    char row = coordinates[1];  // '1' to '8'
    
    // Convert to numbers (a=1, b=2, ..., h=8)
    int colNum = col - 'a' + 1;
    int rowNum = row - '0';
    
    // A square is white if sum of column and row is even
    // (since a1 is black and has sum 1+1=2, but we need to consider 0-based logic)
    // Actually, a1 is black, so sum=2 should be black
    // Let's think: a1=black, a2=white, b1=white, b2=black
    // Pattern: (col+row) is even -> white, odd -> black
    // But a1: col=1, row=1, sum=2 (even) but should be black
    // So it's inverted: (col+row) is odd -> white, even -> black
    
    bool isWhite = ((colNum + rowNum) % 2) == 1;
    
    // Output result
    if (isWhite) {
        printf("true");
    } else {
        printf("false");
    }
    
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

✓ Linear Growth

Space Complexity

✓ Linear Space

25.0K Views

Medium Frequency

~5 min Avg. Time

890 Likes

Ln 1, Col 1

Smart Actions

💡 Explanation

AI Ready

💡 Suggestion Tab to accept Esc to dismiss

// Output will appear here after running code

Code Editor Closed

Click the red button to reopen

Determine Color of a Chessboard Square - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Algorithm Steps — Algorithm Steps

Code -

Time & Space Complexity

Select Compiler