+ problem 1815

Author: fruit-in

Problemset/1815-Maximum Number of Groups Getting Fresh Donuts/README.md

@@ -0,0 +1,60 @@
+# 1815. Maximum Number of Groups Getting Fresh Donuts
+There is a donuts shop that bakes donuts in batches of `batchSize`. They have a rule where they must serve **all** of the donuts of a batch before serving any donuts of the next batch. You are given an integer `batchSize` and an integer array `groups`, where `groups[i]` denotes that there is a group of `groups[i]` customers that will visit the shop. Each customer will get exactly one donut.
+
+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.
+
+You can freely rearrange the ordering of the groups. Return *the **maximum** possible number of happy groups after rearranging the groups*.
+
+#### Example 1:
+<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 1st, 2nd, 4th, and 6th groups will be happy.
+</pre>
+
+#### Example 2:
+<pre>
+<strong>Input:</strong> batchSize = 4, groups = [1,3,2,5,2,2,1,6]
+<strong>Output:</strong> 4
+</pre>
+
+#### Constraints:
+* `1 <= batchSize <= 9`
+* `1 <= groups.length <= 30`
+* <code>1 <= groups[i] <= 10<sup>9</sup></code>
+
+## Solutions (Python)
+
+### 1. Solution
+```Python
+class Solution:
+ def maxHappyGroups(self, batchSize: int, groups: List[int]) -> int:
+ @cache
+ def dfs(count: Tuple[int]) -> int:
+ count = list(count)
+ remain = (total - sum(i * count[i]
+ for i in range(1, batchSize))) % batchSize
+ ret = 0
+
+ for i in range(1, batchSize):
+ if count[i] == 0:
+ continue
+
+ count[i] -= 1
+ if remain == 0:
+ ret = max(ret, 1 + dfs(tuple(count)))
+ else:
+ ret = max(ret, dfs(tuple(count)))
+ count[i] += 1
+
+ return ret
+
+ count = [0] * batchSize
+ total = 0
+
+ for x in groups:
+ count[x % batchSize] += 1
+ total += x % batchSize
+
+ return count[0] + dfs(tuple(count))
+```

Problemset/1815-Maximum Number of Groups Getting Fresh Donuts/README_CN.md

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+# 1815. 得到新鲜甜甜圈的最多组数
+有一个甜甜圈商店，每批次都烤 `batchSize` 个甜甜圈。这个店铺有个规则，就是在烤一批新的甜甜圈时，之前 **所有** 甜甜圈都必须已经全部销售完毕。给你一个整数 `batchSize` 和一个整数数组 `groups` ，数组中的每个整数都代表一批前来购买甜甜圈的顾客，其中 `groups[i]` 表示这一批顾客的人数。每一位顾客都恰好只要一个甜甜圈。
+
+当有一批顾客来到商店时，他们所有人都必须在下一批顾客来之前购买完甜甜圈。如果一批顾客中第一位顾客得到的甜甜圈不是上一组剩下的，那么这一组人都会很开心。
+
+你可以随意安排每批顾客到来的顺序。请你返回在此前提下，**最多** 有多少组人会感到开心。
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> batchSize = 3, groups = [1,2,3,4,5,6]
+<strong>输出:</strong> 4
+<strong>解释:</strong> 你可以将这些批次的顾客顺序安排为 [6,2,4,5,1,3] 。那么第 1，2，4，6 组都会感到开心。
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> batchSize = 4, groups = [1,3,2,5,2,2,1,6]
+<strong>输出:</strong> 4
+</pre>
+
+#### 提示:
+* `1 <= batchSize <= 9`
+* `1 <= groups.length <= 30`
+* <code>1 <= groups[i] <= 10<sup>9</sup></code>
+
+## 题解 (Python)
+
+### 1. 题解
+```Python
+class Solution:
+ def maxHappyGroups(self, batchSize: int, groups: List[int]) -> int:
+ @cache
+ def dfs(count: Tuple[int]) -> int:
+ count = list(count)
+ remain = (total - sum(i * count[i]
+ for i in range(1, batchSize))) % batchSize
+ ret = 0
+
+ for i in range(1, batchSize):
+ if count[i] == 0:
+ continue
+
+ count[i] -= 1
+ if remain == 0:
+ ret = max(ret, 1 + dfs(tuple(count)))
+ else:
+ ret = max(ret, dfs(tuple(count)))
+ count[i] += 1
+
+ return ret
+
+ count = [0] * batchSize
+ total = 0
+
+ for x in groups:
+ count[x % batchSize] += 1
+ total += x % batchSize
+
+ return count[0] + dfs(tuple(count))
+```

Problemset/1815-Maximum Number of Groups Getting Fresh Donuts/Solution.py

@@ -0,0 +1,30 @@
+class Solution:
+ def maxHappyGroups(self, batchSize: int, groups: List[int]) -> int:
+ @cache
+ def dfs(count: Tuple[int]) -> int:
+ count = list(count)
+ remain = (total - sum(i * count[i]
+ for i in range(1, batchSize))) % batchSize
+ ret = 0
+
+ for i in range(1, batchSize):
+ if count[i] == 0:
+ continue
+
+ count[i] -= 1
+ if remain == 0:
+ ret = max(ret, 1 + dfs(tuple(count)))
+ else:
+ ret = max(ret, dfs(tuple(count)))
+ count[i] += 1
+
+ return ret
+
+ count = [0] * batchSize
+ total = 0
+
+ for x in groups:
+ count[x % batchSize] += 1
+ total += x % batchSize
+
+ return count[0] + dfs(tuple(count))

README.md

@@ -1325,6 +1325,7 @@
 [1812][1812l]|[Determine Color of a Chessboard Square][1812] |![py]  ![rb]
 [1813][1813l]|[Sentence Similarity III][1813] |![rs]
 [1814][1814l]|[Count Nice Pairs in an Array][1814] |![rs]
+[1815][1815l]|[Maximum Number of Groups Getting Fresh Donuts][1815] |![py]
 [1816][1816l]|[Truncate Sentence][1816] |![py]
 [1817][1817l]|[Finding the Users Active Minutes][1817] |![rs]
 [1818][1818l]|[Minimum Absolute Sum Difference][1818] |![rs]
@@ -3266,6 +3267,7 @@
 [1812]:Problemset/1812-Determine%20Color%20of%20a%20Chessboard%20Square/README.md#1812-determine-color-of-a-chessboard-square
 [1813]:Problemset/1813-Sentence%20Similarity%20III/README.md#1813-sentence-similarity-iii
 [1814]:Problemset/1814-Count%20Nice%20Pairs%20in%20an%20Array/README.md#1814-count-nice-pairs-in-an-array
+[1815]:Problemset/1815-Maximum%20Number%20of%20Groups%20Getting%20Fresh%20Donuts/README.md#1815-maximum-number-of-groups-getting-fresh-donuts
 [1816]:Problemset/1816-Truncate%20Sentence/README.md#1816-truncate-sentence
 [1817]:Problemset/1817-Finding%20the%20Users%20Active%20Minutes/README.md#1817-finding-the-users-active-minutes
 [1818]:Problemset/1818-Minimum%20Absolute%20Sum%20Difference/README.md#1818-minimum-absolute-sum-difference
@@ -5201,6 +5203,7 @@
 [1812l]:https://leetcode.com/problems/determine-color-of-a-chessboard-square/
 [1813l]:https://leetcode.com/problems/sentence-similarity-iii/
 [1814l]:https://leetcode.com/problems/count-nice-pairs-in-an-array/
+[1815l]:https://leetcode.com/problems/maximum-number-of-groups-getting-fresh-donuts/
 [1816l]:https://leetcode.com/problems/truncate-sentence/
 [1817l]:https://leetcode.com/problems/finding-the-users-active-minutes/
 [1818l]:https://leetcode.com/problems/minimum-absolute-sum-difference/

README_CN.md

@@ -1325,6 +1325,7 @@
 [1812][1812l]|[判断国际象棋棋盘中一个格子的颜色][1812] |![py]  ![rb]
 [1813][1813l]|[句子相似性 III][1813] |![rs]
 [1814][1814l]|[统计一个数组中好对子的数目][1814] |![rs]
+[1815][1815l]|[得到新鲜甜甜圈的最多组数][1815] |![py]
 [1816][1816l]|[截断句子][1816] |![py]
 [1817][1817l]|[查找用户活跃分钟数][1817] |![rs]
 [1818][1818l]|[绝对差值和][1818] |![rs]
@@ -3266,6 +3267,7 @@
 [1812]:Problemset/1812-Determine%20Color%20of%20a%20Chessboard%20Square/README_CN.md#1812-判断国际象棋棋盘中一个格子的颜色
 [1813]:Problemset/1813-Sentence%20Similarity%20III/README_CN.md#1813-句子相似性-iii
 [1814]:Problemset/1814-Count%20Nice%20Pairs%20in%20an%20Array/README_CN.md#1814-统计一个数组中好对子的数目
+[1815]:Problemset/1815-Maximum%20Number%20of%20Groups%20Getting%20Fresh%20Donuts/README_CN.md#1815-得到新鲜甜甜圈的最多组数
 [1816]:Problemset/1816-Truncate%20Sentence/README_CN.md#1816-截断句子
 [1817]:Problemset/1817-Finding%20the%20Users%20Active%20Minutes/README_CN.md#1817-查找用户活跃分钟数
 [1818]:Problemset/1818-Minimum%20Absolute%20Sum%20Difference/README_CN.md#1818-绝对差值和
@@ -5201,6 +5203,7 @@
 [1812l]:https://leetcode.cn/problems/determine-color-of-a-chessboard-square/
 [1813l]:https://leetcode.cn/problems/sentence-similarity-iii/
 [1814l]:https://leetcode.cn/problems/count-nice-pairs-in-an-array/
+[1815l]:https://leetcode.cn/problems/maximum-number-of-groups-getting-fresh-donuts/
 [1816l]:https://leetcode.cn/problems/truncate-sentence/
 [1817l]:https://leetcode.cn/problems/finding-the-users-active-minutes/
 [1818l]:https://leetcode.cn/problems/minimum-absolute-sum-difference/