LeetCode-in-Java

2929. Distribute Candies Among Children II

Medium

You are given two positive integers n and limit.

Return the total number of ways to distribute n candies among 3 children such that no child gets more than limit candies.

Example 1:

Input: n = 5, limit = 2

Output: 3

Explanation: There are 3 ways to distribute 5 candies such that no child gets more than 2 candies: (1, 2, 2), (2, 1, 2) and (2, 2, 1).

Example 2:

Input: n = 3, limit = 3

Output: 10

Explanation: There are 10 ways to distribute 3 candies such that no child gets more than 3 candies: (0, 0, 3), (0, 1, 2), (0, 2, 1), (0, 3, 0), (1, 0, 2), (1, 1, 1), (1, 2, 0), (2, 0, 1), (2, 1, 0) and (3, 0, 0).

Constraints:

• 1 <= n <= 106
• 1 <= limit <= 106

Solution

public class Solution {
    public long distributeCandies(long n, long k) {
        if (n <= k) {
            return (n + 1) * (n + 2) / 2;
        }
        if (n <= 2 * k) {
            return (k + 1) * (k + 1)
                    - (n - k) * (n - k + 1) / 2
                    - (2 * k - n) * (2 * k - n + 1) / 2;
        }
        if (n <= 3 * k) {
            return (3 * k - n + 1) * (3 * k - n + 2) / 2;
        }
        return 0;
    }
}

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