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Java-based LeetCode algorithm problem solutions, regularly updated
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2305\. Fair Distribution of Cookies
Medium
You are given an integer array `cookies`, where `cookies[i]` denotes the number of cookies in the ith
bag. You are also given an integer `k` that denotes the number of children to distribute **all** the bags of cookies to. All the cookies in the same bag must go to the same child and cannot be split up.
The **unfairness** of a distribution is defined as the **maximum** **total** cookies obtained by a single child in the distribution.
Return _the **minimum** unfairness of all distributions_.
**Example 1:**
**Input:** cookies = [8,15,10,20,8], k = 2
**Output:** 31
**Explanation:** One optimal distribution is [8,15,8] and [10,20]
- The 1st child receives [8,15,8] which has a total of 8 + 15 + 8 = 31 cookies.
- The 2nd child receives [10,20] which has a total of 10 + 20 = 30 cookies.
The unfairness of the distribution is max(31,30) = 31.
It can be shown that there is no distribution with an unfairness less than 31.
**Example 2:**
**Input:** cookies = [6,1,3,2,2,4,1,2], k = 3
**Output:** 7
**Explanation:** One optimal distribution is [6,1], [3,2,2], and [4,1,2]
- The 1st child receives [6,1] which has a total of 6 + 1 = 7 cookies.
- The 2nd child receives [3,2,2] which has a total of 3 + 2 + 2 = 7 cookies.
- The 3rd child receives [4,1,2] which has a total of 4 + 1 + 2 = 7 cookies.
The unfairness of the distribution is max(7,7,7) = 7.
It can be shown that there is no distribution with an unfairness less than 7.
**Constraints:**
* `2 <= cookies.length <= 8`
* 1 <= cookies[i] <= 105
* `2 <= k <= cookies.length`
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