黑白方格画

/*
题目思路：
使用Java Stream进行解答，通过组合数学的方法计算出所有可能的涂色方案，并用Stream API来优化代码。
*/
import java.util.stream.IntStream;

public class Solution {
    public int paintingPlans(int n, int k) {
        if (k == 0) return 1;
        if (k > n * n) return 0;
        return (int) IntStream.rangeClosed(0, n)
            .boxed()
            .flatMap(rows -> IntStream.rangeClosed(0, n)
                .filter(cols -> rows * n + cols * n - rows * cols == k)
                .mapToObj(cols -> combination(n, rows) * combination(n, cols)))
            .mapToInt(Integer::intValue)
            .sum();
    }

    private int combination(int n, int k) {
        if (k == 0 || k == n) return 1;
        if (k > n) return 0;
        return IntStream.rangeClosed(1, k)
            .reduce(1, (res, i) -> res * (n - i + 1) / i);
    }

    public static void main(String[] args) {
        Solution sol = new Solution();
        System.out.println(sol.paintingPlans(2, 2));  // Output: 4
        System.out.println(sol.paintingPlans(2, 1));  // Output: 0
        System.out.println(sol.paintingPlans(2, 4));  // Output: 1
    }
}