2929. Distribute Candies Among Children II

Problem Link

Description

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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

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Python3

class Solution:
    def distributeCandies(self, n: int, limit: int) -> int:
        firstMin = max(0, n - 2 * limit)
        firstMax = min(limit, n)
        res = 0
        
        for first in range(firstMin, firstMax + 1):
            secondMin = max(0, n - first - limit)
            secondMax = min(limit, n - first)
            res += secondMax - secondMin + 1
        
        return res