3201. Distribute Candies Among Children Ii¶

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3201. 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¶

class Solution {
    public long distributeCandies(int n, int limit) {
        return combCount(n) - 3 * combCount(n - (limit + 1)) + 3 * combCount(n - 2 * (limit + 1))- combCount(n - 3 * (limit + 1));
    }
    private long combCount(long sum) {
        if (sum < 0) return 0;
        return (sum + 2) * (sum + 1) / 2;
    }
}

Complexity Analysis¶

• Time Complexity: O(?)
• Space Complexity: O(?)

Approach¶

Detailed explanation of the approach will be added here