# 1812. Determine Color of a Chessboard Square

## Description

You are given coordinates, a string that represents the coordinates of a square of the chessboard. Below is a chessboard for your reference.

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.

Example 1:

Input: coordinates = "a1"
Output: false
Explanation: From the chessboard above, the square with coordinates "a1" is black, so return false.


Example 2:

Input: coordinates = "h3"
Output: true
Explanation: From the chessboard above, the square with coordinates "h3" is white, so return true.


Example 3:

Input: coordinates = "c7"
Output: false


Constraints:

• coordinates.length == 2
• 'a' <= coordinates[0] <= 'h'
• '1' <= coordinates[1] <= '8'

## Solutions

Solution 1: Find the Pattern

By observing the chessboard, we find that two squares $(x_1, y_1)$ and $(x_2, y_2)$ with the same color satisfy that both $x_1 + y_1$ and $x_2 + y_2$ are either odd or even.

Therefore, we can get the corresponding coordinates $(x, y)$ from coordinates. If $x + y$ is odd, then the square is white, return true, otherwise return false.

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

• class Solution {
public boolean squareIsWhite(String coordinates) {
return (coordinates.charAt(0) + coordinates.charAt(1)) % 2 == 1;
}
}

• class Solution {
public:
bool squareIsWhite(string coordinates) {
return (coordinates[0] + coordinates[1]) % 2;
}
};

• class Solution:
def squareIsWhite(self, coordinates: str) -> bool:
return (ord(coordinates[0]) + ord(coordinates[1])) % 2 == 1


• func squareIsWhite(coordinates string) bool {
return (coordinates[0]+coordinates[1])%2 == 1
}

• function squareIsWhite(coordinates: string): boolean {
return ((coordinates.charCodeAt(0) + coordinates.charCodeAt(1)) & 1) === 1;
}


• /**
* @param {string} coordinates
* @return {boolean}
*/
var squareIsWhite = function (coordinates) {
const x = coordinates.charAt(0).charCodeAt();
const y = coordinates.charAt(1).charCodeAt();
return (x + y) % 2 == 1;
};


• impl Solution {
pub fn square_is_white(coordinates: String) -> bool {
let s = coordinates.as_bytes();
((s[0] + s[1]) & 1) == 1
}
}