给小朋友们分糖果 I

/*
 * Problem: Given two positive integers n and limit, you need to distribute n candies among 3 children such that no child receives more than limit candies. Return the total number of ways to do so.
 * 
 * Approach: Use Java Streams to generate all possible combinations of distributing candies to three children. Filter out the combinations where any child gets more than limit candies, and then count the valid combinations.
 */
import java.util.stream.IntStream;

public class CandyDistributionStream {
    public static int countWays(int n, int limit) {
        return (int) IntStream.rangeClosed(0, Math.min(n, limit))
                .boxed()
                .flatMap(i -> IntStream.rangeClosed(0, Math.min(n - i, limit))
                        .mapToObj(j -> new int[]{i, j, n - i - j}))
                .filter(arr -> arr[2] <= limit)
                .count();
    }

    public static void main(String[] args) {
        int n = 5;
        int limit = 2;
        System.out.println(countWays(n, limit)); // Output: 3
    }
}