Distribute Candies Among Children I — LeetCode 2928 Python Solution

The problem

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

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).

Python solution

class Solution:
    def distributeCandies(self, n: int, limit: int) -> int:
        if n > 3 * limit:
            return 0
        ans = comb(n + 2, 2)
        if n > limit:
            ans -= 3 * comb(n - limit + 1, 2)
        if n - 2 >= 2 * limit:
            ans += 3 * comb(n - 2 * limit, 2)
        return ans

Complexity

Pattern: Math and Number Theory

Find the closed form, the invariant, or the modular identity — and skip the loop entirely. LeetCode 2928. Distribute Candies Among Children I is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Math and Combinatorics.

The math and number theory guide has the Python template for the pattern and the 485 LeetCode problems that use it.

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