Problem of The Day: Determine Color of a Chessboard Square

3 min read 607 words

Problem Statement

leetcode problem link

Solution [Accepted]

class Solution:
    def squareIsWhite(self, coordinates: str) -> bool:
        n = 8
        WHITE = 0
        BLACK = 1
        matrix = [[0] * n for _ in range(n)]
        isWhite = True
        for row in range(n):
            for col in range(n):
                if isWhite:
                    matrix[row][col] = WHITE
                else:
                    matrix[row][col] = BLACK
                isWhite = not isWhite
            isWhite = not isWhite

        row = ord(coordinates[0]) - ord('a')
        col = n - int(coordinates[1])

        return matrix[row][col] == WHITE

public class Solution {
    public bool SquareIsWhite(string coordinates) {
        int n = 8;
        int[][] matrix = new int[8][];
        for (int i = 0; i < 8; i++)
        {
            matrix[i] = new int[8];
        }
        for (int i = 0; i < 8; i++) {
            for (int j = 0; j < 8; j++) {
                if (i % 2 == 0) {
                    if (j % 2 != 0) {
                        matrix[i][j] = 1;
                    }
                } else {
                    if (j % 2 == 0) {
                        matrix[i][j] = 1;
                    }
                }
            }
        }
        int row = coordinates[0] - 'a';
        int col = n - (coordinates[1] - '0');
        return matrix[row][col] == 0;
    }
}

• time: O(n^2)
• space: O(n^2)

Optimize Solution

class Solution:
    def squareIsWhite(self, coordinates: str) -> bool:
        # Convert column letter to 0-based index (a=0, b=1, ..., h=7)
        col = ord(coordinates[0]) - ord('a')
        # Convert row number to 0-based index (1=0, 2=1, ..., 8=7)
        row = int(coordinates[1]) - 1
        # Chessboard pattern: square is white when sum of indices is odd
        return (col + row) % 2 == 1