Check if Two Chessboard Squares Have the Same Color - Problem

Math String Easy

You are given two strings, coordinate1 and coordinate2, representing the coordinates of a square on an 8 x 8 chessboard.

Return true if these two squares have the same color and false otherwise.

The coordinate will always represent a valid chessboard square. The coordinate will always have the letter first (indicating its column), and the number second (indicating its row).

Note: On a chessboard, squares alternate between light and dark colors. Square 'a1' is dark, and colors alternate from there.

Input & Output

Example 1 — Adjacent Squares

$ Input: coordinate1 = "a1", coordinate2 = "c3"

› Output: true

💡 Note: Both squares are dark: a1 (1+1=2, even) and c3 (3+3=6, even) have same parity

Example 2 — Different Colors

$ Input: coordinate1 = "a1", coordinate2 = "h3"

› Output: false

💡 Note: a1 is dark (1+1=2, even) while h3 is light (8+3=11, odd), different colors

Example 3 — Same Row Different Color

$ Input: coordinate1 = "a1", coordinate2 = "b1"

› Output: false

💡 Note: Adjacent squares in same row: a1 (sum=2, even) vs b1 (sum=3, odd) have different colors

Constraints

coordinate1.length == 2
coordinate2.length == 2
'a' ≤ coordinate1[0], coordinate2[0] ≤ 'h'
'1' ≤ coordinate1[1], coordinate2[1] ≤ '8'

Visualization

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Asked in

Apple 15 G Google 12

The key insight is that chessboard colors follow a mathematical pattern based on coordinate sum parity. Squares with even coordinate sums (column number + row number) have one color, while odd sums have the other color. Best approach uses simple parity comparison with Time: O(1), Space: O(1).

Common Approaches

✓ Character-by-Character Analysis

⏱️ Time: O(1) Space: O(1)

Convert each coordinate's letter and number to integers, then determine color by checking if the sum is even or odd. Since chessboards alternate colors, squares with even coordinate sums have one color, odd sums have the other.

Mathematical Parity Formula

⏱️ Time: O(1) Space: O(1)

Convert coordinates to their numeric representations and use bitwise XOR to compare parities. Since chessboard colors alternate based on coordinate sum parity, we can XOR the individual coordinate components to determine if they have the same overall parity.

Character-by-Character Analysis — Algorithm Steps

Convert letter to number (a=1, b=2, etc.)
Add letter number to digit number
Check if both sums have same parity (both even or both odd)

Visualization

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Step-by-Step Walkthrough

Convert Letters

Convert column letters to numbers (a=1, b=2, etc.)

Calculate Sums

Add column number to row number for each coordinate

Compare Parity

Check if both sums are even or both are odd

Code -

solution.c — C

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

bool solution(char* coordinate1, char* coordinate2) {
    // Convert coordinates to numbers and check parity
    int sum1 = coordinate1[0] - 'a' + 1 + (coordinate1[1] - '0');
    int sum2 = coordinate2[0] - 'a' + 1 + (coordinate2[1] - '0');
    
    // Same color if both sums have same parity (both even or both odd)
    return (sum1 % 2) == (sum2 % 2);
}

int main() {
    char coordinate1[10], coordinate2[10];
    fgets(coordinate1, sizeof(coordinate1), stdin);
    coordinate1[strcspn(coordinate1, "\n")] = 0;
    fgets(coordinate2, sizeof(coordinate2), stdin);
    coordinate2[strcspn(coordinate2, "\n")] = 0;
    
    bool result = solution(coordinate1, coordinate2);
    printf(result ? "true\n" : "false\n");
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Fixed operations regardless of input size

✓ Linear Growth

Space Complexity

O(1)

Only using a few variables

✓ Linear Space

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Medium Frequency

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Check if Two Chessboard Squares Have the Same Color - Problem

Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Character-by-Character Analysis — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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