Maximum Number of Groups Getting Fresh Donuts
<p>There is a donuts shop that bakes donuts in batches of <code>batchSize</code>. They have a rule where they must serve <strong>all</strong> of the donuts of a batch before serving any donuts of the next batch. You are given an integer <code>batchSize</code> and an integer array <code>groups</code>, where <code>groups[i]</code> denotes that there is a group of <code>groups[i]</code> customers that will visit the shop. Each customer will get exactly one donut.</p>

<p>When a group visits the shop, all customers of the group must be served before serving any of the following groups. A group will be happy if they all get fresh donuts. That is, the first customer of the group does not receive a donut that was left over from the previous group.</p>

<p>You can freely rearrange the ordering of the groups. Return <em>the <strong>maximum</strong> possible number of happy groups after rearranging the groups.</em></p>

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

<pre>
<strong>Input:</strong> batchSize = 3, groups = [1,2,3,4,5,6]
<strong>Output:</strong> 4
<strong>Explanation:</strong> You can arrange the groups as [6,2,4,5,1,3]. Then the 1<sup>st</sup>, 2<sup>nd</sup>, 4<sup>th</sup>, and 6<sup>th</sup> groups will be happy.
</pre>

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

<pre>
<strong>Input:</strong> batchSize = 4, groups = [1,3,2,5,2,2,1,6]
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>1 &lt;= batchSize &lt;= 9</code></li>
	<li><code>1 &lt;= groups.length &lt;= 30</code></li>
	<li><code>1 &lt;= groups[i] &lt;= 10<sup>9</sup></code></li>
</ul>
Bit Manipulation; Memoization; Array; Dynamic Programming; Bitmask
func maxHappyGroups(batchSize int, groups []int) (ans int) {
	state := 0
	for _, v := range groups {
		i := v % batchSize
		if i == 0 {
			ans++
		} else {
			state += 1 << (i * 5)
		}
	}
	f := map[int]int{}
	var dfs func(int, int) int
	dfs = func(state, mod int) int {
		if v, ok := f[state]; ok {
			return v
		}
		res := 0
		x := 0
		if mod == 0 {
			x = 1
		}
		for i := 1; i < batchSize; i++ {
			if state>>(i*5)&31 != 0 {
				t := dfs(state-1<<(i*5), (mod+i)%batchSize)
				res = max(res, t+x)
			}
		}
		f[state] = res
		return res
	}
	ans += dfs(state, 0)
	return
}