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3274. Check if Two Chessboard Squares Have the Same Color

Description

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

Below is the chessboard for reference.

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).

 

Example 1:

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

Output: true

Explanation:

Both squares are black.

Example 2:

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

Output: false

Explanation:

Square "a1" is black and "h3" is white.

 

Constraints:

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

Solutions

Solution 1: Mathematics

Thinking

A chessboard alternates colors; the color of \((c,r)\) is the parity of column plus row. Two squares match iff those parities match.

If the sum of the file difference and the rank difference is even, the colors are the same. Two characters minus, then modulo \(2\), in constant time.

We calculate the differences in the x-coordinates and y-coordinates of the two points. If the sum of these differences is even, then the colors of the squares at these two coordinates are the same; otherwise, they are different.

The time complexity is \(O(1)\), and the space complexity is \(O(1)\).

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class Solution:
    def checkTwoChessboards(self, coordinate1: str, coordinate2: str) -> bool:
        x = ord(coordinate1[0]) - ord(coordinate2[0])
        y = int(coordinate1[1]) - int(coordinate2[1])
        return (x + y) % 2 == 0

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class Solution {
    public boolean checkTwoChessboards(String coordinate1, String coordinate2) {
        int x = coordinate1.charAt(0) - coordinate2.charAt(0);
        int y = coordinate1.charAt(1) - coordinate2.charAt(1);
        return (x + y) % 2 == 0;
    }
}

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class Solution {
public:
    bool checkTwoChessboards(string coordinate1, string coordinate2) {
        int x = coordinate1[0] - coordinate2[0];
        int y = coordinate1[1] - coordinate2[1];
        return (x + y) % 2 == 0;
    }
};

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func checkTwoChessboards(coordinate1 string, coordinate2 string) bool {
    x := coordinate1[0] - coordinate2[0]
    y := coordinate1[1] - coordinate2[1]
    return (x+y)%2 == 0
}

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function checkTwoChessboards(coordinate1: string, coordinate2: string): boolean {
    const x = coordinate1.charCodeAt(0) - coordinate2.charCodeAt(0);
    const y = coordinate1.charCodeAt(1) - coordinate2.charCodeAt(1);
    return (x + y) % 2 === 0;
}

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