Determine Color of a Chessboard Square - Practice Coding Problems

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

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Understanding the Visualization

Input

Chessboard coordinates as string (e.g., "a1")

Process

Convert to numbers and check sum parity

Output

Boolean indicating if square is white

Key Takeaway

🎯 Key Insight: The sum of column number and row number determines the square color through parity check

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

Approach	Time	Space	Notes
✓ Direct Pattern Recognition	O(1)	O(1)	Manually check the coordinate pattern
Mathematical Formula	O(1)	O(1)	Use modular arithmetic to determine color
XOR Bit Manipulation	O(1)	O(1)	Use XOR operation to check if coordinates have same parity

Direct Pattern Recognition — Algorithm Steps

Extract column letter and row number
Convert column letter to number (a=1, b=2, etc.)
Calculate sum of column number and row number
If sum is even, square is black; if odd, square is white

Visualization

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Step-by-Step Walkthrough

Parse Coordinates

Extract column letter and row number

Calculate Sum

Convert column to number and add to row

Check Parity

Even sum = black, odd sum = white

Code -

solution.c — C

#include <stdio.h>
#include <string.h>

int solution(char* coordinates) {
    int col = coordinates[0] - 'a' + 1;
    int row = coordinates[1] - '0';
    return (col + row) % 2 == 1;
}

int main() {
    char coordinates[10];
    fgets(coordinates, sizeof(coordinates), stdin);
    coordinates[strcspn(coordinates, "\n")] = 0;
    int result = solution(coordinates);
    printf(result ? "true\n" : "false\n");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Only performs constant operations regardless of input

✓ Linear Growth

Space Complexity

O(1)

Uses only a few variables for calculations

✓ Linear Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Direct Pattern Recognition — Algorithm Steps

Visualization

Code -

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