distribute-candies-among-children-ii

java

python

python3

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cangjie

Algorithms

You are given two positive integers <code>n</code> and <code>limit</code>.

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

&nbsp;
Example 1:

<pre>
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).
</pre>

Example 2:

<pre>
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).
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= n &lt;= 106</code></li>
	<li><code>1 &lt;= limit &lt;= 106</code></li>
</ul>

distributeCandies

Distribute Candies Among Children II

Count Ways to Distribute Candies

count-ways-to-distribute-candies

计算分配糖果的不同方式

Math

Combinatorics

Enumeration

给你两个正整数&nbsp;<code>n</code> 和&nbsp;<code>limit</code>&nbsp;。

请你将 <code>n</code>&nbsp;颗糖果分给 <code>3</code>&nbsp;位小朋友，确保没有任何小朋友得到超过 <code>limit</code>&nbsp;颗糖果，请你返回满足此条件下的&nbsp;总方案数&nbsp;。

&nbsp;

示例 1：

<pre>
输入：n = 5, limit = 2
输出：3
解释：总共有 3 种方法分配 5 颗糖果，且每位小朋友的糖果数不超过 2 ：(1, 2, 2) ，(2, 1, 2) 和 (2, 2, 1) 。
</pre>

示例 2：

<pre>
输入：n = 3, limit = 3
输出：10
解释：总共有 10 种方法分配 3 颗糖果，且每位小朋友的糖果数不超过 3 ：(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) 和 (3, 0, 0) 。
</pre>

&nbsp;

提示：

<ul>
	<li><code>1 &lt;= n &lt;= 106</code></li>
	<li><code>1 &lt;= limit &lt;= 106</code></li>
</ul>