+ problem 887

Author: fruit-in

Problemset/0887-Super Egg Drop/README.md

@@ -0,0 +1,56 @@
+# 887. Super Egg Drop
+You are given `k` identical eggs and you have access to a building with `n` floors labeled from `1` to `n`.
+
+You know that there exists a floor `f` where `0 <= f <= n` such that any egg dropped at a floor **higher** than `f` will **break**, and any egg dropped **at or below** floor `f` will **not break**.
+
+Each move, you may take an unbroken egg and drop it from any floor `x` (where `1 <= x <= n`). If the egg breaks, you can no longer use it. However, if the egg does not break, you may **reuse** it in future moves.
+
+Return *the **minimum number of moves** that you need to determine **with certainty** what the value of* `f` is.
+
+#### Example 1:
+<pre>
+<strong>Input:</strong> k = 1, n = 2
+<strong>Output:</strong> 2
+<strong>Explanation:</strong>
+Drop the egg from floor 1. If it breaks, we know that f = 0.
+Otherwise, drop the egg from floor 2. If it breaks, we know that f = 1.
+If it does not break, then we know f = 2.
+Hence, we need at minimum 2 moves to determine with certainty what the value of f is.
+</pre>
+
+#### Example 2:
+<pre>
+<strong>Input:</strong> k = 2, n = 6
+<strong>Output:</strong> 3
+</pre>
+
+#### Example 3:
+<pre>
+<strong>Input:</strong> k = 3, n = 14
+<strong>Output:</strong> 4
+</pre>
+
+#### Constraints:
+* `1 <= k <= 100`
+* <code>1 <= n <= 10<sup>4</sup></code>
+
+## Solutions (Python)
+
+### 1. Solution
+```Python
+class Solution:
+ @cache
+ def superEggDrop(self, k: int, n: int) -> int:
+ if n == 0:
+ return 0
+ if k == 1:
+ return n
+
+ x = bisect_right(range(1, n + 1), 0, key=lambda x: self.superEggDrop(k -
+ 1, x - 1) - self.superEggDrop(k, n - x)) + 1
+ ret = 1 + self.superEggDrop(k - 1, x - 1)
+ if x > 0:
+ ret = min(ret, 1 + self.superEggDrop(k, n - x + 1))
+
+ return ret
+```

Problemset/0887-Super Egg Drop/README_CN.md

@@ -0,0 +1,56 @@
+# 887. 鸡蛋掉落
+给你 `k` 枚相同的鸡蛋，并可以使用一栋从第 `1` 层到第 `n` 层共有 `n` 层楼的建筑。
+
+已知存在楼层 `f` ，满足 `0 <= f <= n` ，任何从 **高于** `f` 的楼层落下的鸡蛋都会碎，从 `f` 楼层或比它低的楼层落下的鸡蛋都不会破。
+
+每次操作，你可以取一枚没有碎的鸡蛋并把它从任一楼层 `x` 扔下（满足 `1 <= x <= n`）。如果鸡蛋碎了，你就不能再次使用它。如果某枚鸡蛋扔下后没有摔碎，则可以在之后的操作中 **重复使用** 这枚鸡蛋。
+
+请你计算并返回要确定 `f` **确切的值** 的 **最小操作次数** 是多少？
+
+#### 示例 1:
+<pre>
+<strong>输入:</strong> k = 1, n = 2
+<strong>输出:</strong> 2
+<strong>解释:</strong>
+鸡蛋从 1 楼掉落。如果它碎了，肯定能得出 f = 0 。
+否则，鸡蛋从 2 楼掉落。如果它碎了，肯定能得出 f = 1 。
+如果它没碎，那么肯定能得出 f = 2 。
+因此，在最坏的情况下我们需要移动 2 次以确定 f 是多少。
+</pre>
+
+#### 示例 2:
+<pre>
+<strong>输入:</strong> k = 2, n = 6
+<strong>输出:</strong> 3
+</pre>
+
+#### 示例 3:
+<pre>
+<strong>输入:</strong> k = 3, n = 14
+<strong>输出:</strong> 4
+</pre>
+
+#### 提示:
+* `1 <= k <= 100`
+* <code>1 <= n <= 10<sup>4</sup></code>
+
+## 题解 (Python)
+
+### 1. 题解
+```Python
+class Solution:
+ @cache
+ def superEggDrop(self, k: int, n: int) -> int:
+ if n == 0:
+ return 0
+ if k == 1:
+ return n
+
+ x = bisect_right(range(1, n + 1), 0, key=lambda x: self.superEggDrop(k -
+ 1, x - 1) - self.superEggDrop(k, n - x)) + 1
+ ret = 1 + self.superEggDrop(k - 1, x - 1)
+ if x > 0:
+ ret = min(ret, 1 + self.superEggDrop(k, n - x + 1))
+
+ return ret
+```

Problemset/0887-Super Egg Drop/Solution.py

@@ -0,0 +1,15 @@
+class Solution:
+ @cache
+ def superEggDrop(self, k: int, n: int) -> int:
+ if n == 0:
+ return 0
+ if k == 1:
+ return n
+
+ x = bisect_right(range(1, n + 1), 0, key=lambda x: self.superEggDrop(k -
+ 1, x - 1) - self.superEggDrop(k, n - x)) + 1
+ ret = 1 + self.superEggDrop(k - 1, x - 1)
+ if x > 0:
+ ret = min(ret, 1 + self.superEggDrop(k, n - x + 1))
+
+ return ret

README.md

@@ -668,6 +668,7 @@
 [884][884l] |[Uncommon Words from Two Sentences][884] |![py]
 [885][885l] |[Spiral Matrix III][885] |![rs]
 [886][886l] |[Possible Bipartition][886] |![rs]
+[887][887l] |[Super Egg Drop][887] |![py]
 [888][888l] |[Fair Candy Swap][888] |![rs]
 [889][889l] |[Construct Binary Tree from Preorder and Postorder Traversal][889] |![py]
 [890][890l] |[Find and Replace Pattern][890] |![py]
@@ -2605,6 +2606,7 @@
 [884]:Problemset/0884-Uncommon%20Words%20from%20Two%20Sentences/README.md#884-uncommon-words-from-two-sentences
 [885]:Problemset/0885-Spiral%20Matrix%20III/README.md#885-spiral-matrix-iii
 [886]:Problemset/0886-Possible%20Bipartition/README.md#886-possible-bipartition
+[887]:Problemset/0887-Super%20Egg%20Drop/README.md#887-super-egg-drop
 [888]:Problemset/0888-Fair%20Candy%20Swap/README.md#888-fair-candy-swap
 [889]:Problemset/0889-Construct%20Binary%20Tree%20from%20Preorder%20and%20Postorder%20Traversal/README.md#889-construct-binary-tree-from-preorder-and-postorder-traversal
 [890]:Problemset/0890-Find%20and%20Replace%20Pattern/README.md#890-find-and-replace-pattern
@@ -4536,6 +4538,7 @@
 [884l]:https://leetcode.com/problems/uncommon-words-from-two-sentences/
 [885l]:https://leetcode.com/problems/spiral-matrix-iii/
 [886l]:https://leetcode.com/problems/possible-bipartition/
+[887l]:https://leetcode.com/problems/super-egg-drop/
 [888l]:https://leetcode.com/problems/fair-candy-swap/
 [889l]:https://leetcode.com/problems/construct-binary-tree-from-preorder-and-postorder-traversal/
 [890l]:https://leetcode.com/problems/find-and-replace-pattern/

README_CN.md

@@ -668,6 +668,7 @@
 [884][884l] |[两句话中的不常见单词][884] |![py]
 [885][885l] |[螺旋矩阵 III][885] |![rs]
 [886][886l] |[可能的二分法][886] |![rs]
+[887][887l] |[鸡蛋掉落][887] |![py]
 [888][888l] |[公平的糖果交换][888] |![rs]
 [889][889l] |[根据前序和后序遍历构造二叉树][889] |![py]
 [890][890l] |[查找和替换模式][890] |![py]
@@ -2605,6 +2606,7 @@
 [884]:Problemset/0884-Uncommon%20Words%20from%20Two%20Sentences/README_CN.md#884-两句话中的不常见单词
 [885]:Problemset/0885-Spiral%20Matrix%20III/README_CN.md#885-螺旋矩阵-iii
 [886]:Problemset/0886-Possible%20Bipartition/README_CN.md#886-可能的二分法
+[887]:Problemset/0887-Super%20Egg%20Drop/README_CN.md#887-鸡蛋掉落
 [888]:Problemset/0888-Fair%20Candy%20Swap/README_CN.md#888-公平的糖果交换
 [889]:Problemset/0889-Construct%20Binary%20Tree%20from%20Preorder%20and%20Postorder%20Traversal/README_CN.md#889-根据前序和后序遍历构造二叉树
 [890]:Problemset/0890-Find%20and%20Replace%20Pattern/README_CN.md#890-查找和替换模式
@@ -4536,6 +4538,7 @@
 [884l]:https://leetcode.cn/problems/uncommon-words-from-two-sentences/
 [885l]:https://leetcode.cn/problems/spiral-matrix-iii/
 [886l]:https://leetcode.cn/problems/possible-bipartition/
+[887l]:https://leetcode.cn/problems/super-egg-drop/
 [888l]:https://leetcode.cn/problems/fair-candy-swap/
 [889l]:https://leetcode.cn/problems/construct-binary-tree-from-preorder-and-postorder-traversal/
 [890l]:https://leetcode.cn/problems/find-and-replace-pattern/