<p>You are given an integer array <code>cookies</code>, where <code>cookies[i]</code> denotes the number of cookies in the <code>i<sup>th</sup></code> bag. You are also given an integer <code>k</code> that denotes the number of children to distribute <strong>all</strong> the bags of cookies to. All the cookies in the same bag must go to the same child and cannot be split up.</p>

<p>The <strong>unfairness</strong> of a distribution is defined as the <strong>maximum</strong> <strong>total</strong> cookies obtained by a single child in the distribution.</p>

<p>Return <em>the <strong>minimum</strong> unfairness of all distributions</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> cookies = [8,15,10,20,8], k = 2
<strong>Output:</strong> 31
<strong>Explanation:</strong> One optimal distribution is [8,15,8] and [10,20]
- The 1<sup>st</sup> child receives [8,15,8] which has a total of 8 + 15 + 8 = 31 cookies.
- The 2<sup>nd</sup> 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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> cookies = [6,1,3,2,2,4,1,2], k = 3
<strong>Output:</strong> 7
<strong>Explanation:</strong> One optimal distribution is [6,1], [3,2,2], and [4,1,2]
- The 1<sup>st</sup> child receives [6,1] which has a total of 6 + 1 = 7 cookies.
- The 2<sup>nd</sup> child receives [3,2,2] which has a total of 3 + 2 + 2 = 7 cookies.
- The 3<sup>rd</sup> 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.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>2 &lt;= cookies.length &lt;= 8</code></li>
	<li><code>1 &lt;= cookies[i] &lt;= 10<sup>5</sup></code></li>
	<li><code>2 &lt;= k &lt;= cookies.length</code></li>
</ul>

class Solution:
    def distributeCookies(self, cookies: List[int], k: int) -> int:
        # 【太好了找了新代码 只有一个dfs() 还改成self.dfs 而且我更熟悉的逻辑】
        # 【这题老代码很tricky 2个dfs() 我给绕晕了解释不出来 还改不成self.dfs】
        # 这题要我们把饼干分给k个小孩 每个小孩拿到一整pile饼干 尽可能平均得分 要分完
        # unfairness是这么尽可能平均分后 其中一个小孩拿到的最大数量cookie 即max(pockets)
        # 那我们要这个unfairness最小 那就是min(best, max(pockets))
        self.cookies = cookies
        self.k = k
        self.best = float('inf') #要求最小 所以初始化最大
        pockets = [0]*k
        self.dfs(0, pockets) #index在cookie里跑
        return self.best

    def dfs(self, index, pockets):
        if index == len(self.cookies):
            self.best = min(self.best, max(pockets))
            return 
        if max(pockets) >= self.best:
            return
        for i in range(self.k):
            pockets[i] += self.cookies[index]  
            if self.dfs(index+1, pockets):
                return True
            else: 
                pockets[i] -= self.cookies[index]  

        
6726