Check if Two Chessboard Squares Have the Same Color

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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Understanding the Visualization

Input Coordinates

Two chess square coordinates like 'a1' and 'c3'

Parity Check

Convert to numbers and check if sums have same parity

Color Match

Same parity means same color (true), different parity means different colors (false)

Key Takeaway

🎯 Key Insight: Chessboard colors alternate based on coordinate sum parity - same parity means same color

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

Approach	Time	Space	Notes
✓ Mathematical Parity Formula	O(1)	O(1)	Use XOR operation to directly compare coordinate parities
Character-by-Character Analysis	O(1)	O(1)	Convert coordinates to numbers and check color pattern manually

Mathematical Parity Formula — Algorithm Steps

Convert letter and digit to integers separately
XOR all four components together
If result is 0, coordinates have same color

Visualization

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Step-by-Step Walkthrough

Convert to Indices

Convert coordinates to 0-based indices

XOR Components

XOR all four values: col1 ^ row1 ^ col2 ^ row2

Check Even

If XOR result is even, colors match

Code -

solution.c — C

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

bool solution(char* coordinate1, char* coordinate2) {
    // Use XOR to compare parities - same color if XOR of all components is even
    int col1 = coordinate1[0] - 'a';
    int row1 = coordinate1[1] - '1';
    int col2 = coordinate2[0] - 'a';
    int row2 = coordinate2[1] - '1';
    
    // XOR all components - if result is even, same color
    return (col1 ^ row1 ^ col2 ^ row2) % 2 == 0;
}

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

30.0K Views

Medium Frequency

~5 min Avg. Time

856 Likes

Ln 1, Col 1

Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Mathematical Parity Formula — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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