+ problem 756

Author: fruit-in

Problemset/0756-Pyramid Transition Matrix/README.md

@@ -0,0 +1,67 @@
+# 756. Pyramid Transition Matrix
+You are stacking blocks to form a pyramid. Each block has a color, which is represented by a single letter. Each row of blocks contains **one less block** than the row beneath it and is centered on top.
+
+To make the pyramid aesthetically pleasing, there are only specific **triangular patterns** that are allowed. A triangular pattern consists of a **single block** stacked on top of **two blocks**. The patterns are given as a list of three-letter strings `allowed`, where the first two characters of a pattern represent the left and right bottom blocks respectively, and the third character is the top block.
+
+* For example, `"ABC"` represents a triangular pattern with a `'C'` block stacked on top of an `'A'` (left) and `'B'` (right) block. Note that this is different from `"BAC"` where `'B'` is on the left bottom and `'A'` is on the right bottom.
+
+You start with a bottom row of blocks `bottom`, given as a single string, that you **must** use as the base of the pyramid.
+
+Given `bottom` and `allowed`, return `true` *if you can build the pyramid all the way to the top such that **every triangular pattern** in the pyramid is in* `allowed`*, or* `false` *otherwise*.
+
+#### Example 1:
+![](https://assets.leetcode.com/uploads/2021/08/26/pyramid1-grid.jpg)
+<pre>
+<strong>Input:</strong> bottom = "BCD", allowed = ["BCC","CDE","CEA","FFF"]
+<strong>Output:</strong> true
+<strong>Explanation:</strong> The allowed triangular patterns are shown on the right.
+Starting from the bottom (level 3), we can build "CE" on level 2 and then build "A" on level 1.
+There are three triangular patterns in the pyramid, which are "BCC", "CDE", and "CEA". All are allowed.
+</pre>
+
+#### Example 2:
+![](https://assets.leetcode.com/uploads/2021/08/26/pyramid2-grid.jpg)
+<pre>
+<strong>Input:</strong> bottom = "AAAA", allowed = ["AAB","AAC","BCD","BBE","DEF"]
+<strong>Output:</strong> false
+<strong>Explanation:</strong> The allowed triangular patterns are shown on the right.
+Starting from the bottom (level 4), there are multiple ways to build level 3, but trying all the possibilites, you will get always stuck before building level 1.
+</pre>
+
+#### Constraints:
+* `2 <= bottom.length <= 6`
+* `0 <= allowed.length <= 216`
+* `allowed[i].length == 3`
+* The letters in all input strings are from the set `{'A', 'B', 'C', 'D', 'E', 'F'}`.
+* All the values of `allowed` are **unique**.
+
+## Solutions (Python)
+
+### 1. Solution
+```Python
+class Solution:
+ def pyramidTransition(self, bottom: str, allowed: List[str]) -> bool:
+ @cache
+ def buildFromBottom(bottom: str) -> bool:
+ if len(bottom) == 1:
+ return True
+
+ top = [''] * (len(bottom) - 1)
+
+ def buildTop(i: int) -> bool:
+ if i >= len(top):
+ return buildFromBottom(''.join(top))
+
+ for pattern in allowed:
+ if bottom[i:i + 2] == pattern[:2]:
+ top[i] = pattern[2]
+ if buildTop(i + 1):
+ return True
+ top[i] = ''
+
+ return False
+
+ return buildTop(0)
+
+ return buildFromBottom(bottom)
+```

Problemset/0756-Pyramid Transition Matrix/README_CN.md

@@ -0,0 +1,67 @@
+# 756. 金字塔转换矩阵
+你正在把积木堆成金字塔。每个块都有一个颜色，用一个字母表示。每一行的块比它下面的行 **少一个块** ，并且居中。
+
+为了使金字塔美观，只有特定的 **三角形图案** 是允许的。一个三角形的图案由 **两个块** 和叠在上面的 **单个块** 组成。模式是以三个字母字符串的列表形式 `allowed` 给出的，其中模式的前两个字符分别表示左右底部块，第三个字符表示顶部块。
+
+* 例如，`"ABC"` 表示一个三角形图案，其中一个 `“C”` 块堆叠在一个 `'A'` 块(左)和一个 `'B'` 块(右)之上。请注意，这与 `"BAC"` 不同，`"B"` 在左下角，`"A"` 在右下角。
+
+你从作为单个字符串给出的底部的一排积木 `bottom` 开始，**必须** 将其作为金字塔的底部。
+
+在给定 `bottom` 和 `allowed` 的情况下，如果你能一直构建到金字塔顶部，使金字塔中的 **每个三角形图案** 都是在 `allowed` 中的，则返回 `true` ，否则返回 `false` 。
+
+#### 示例 1:
+![](https://assets.leetcode.com/uploads/2021/08/26/pyramid1-grid.jpg)
+<pre>
+<strong>输入:</strong> bottom = "BCD", allowed = ["BCC","CDE","CEA","FFF"]
+<strong>输出:</strong> true
+<strong>解释:</strong> 允许的三角形图案显示在右边。
+从最底层(第 3 层)开始，我们可以在第 2 层构建“CE”，然后在第 1 层构建“E”。
+金字塔中有三种三角形图案，分别是 “BCC”、“CDE” 和 “CEA”。都是允许的。
+</pre>
+
+#### 示例 2:
+![](https://assets.leetcode.com/uploads/2021/08/26/pyramid2-grid.jpg)
+<pre>
+<strong>输入:</strong> bottom = "AAAA", allowed = ["AAB","AAC","BCD","BBE","DEF"]
+<strong>输出:</strong> false
+<strong>解释:</strong> 允许的三角形图案显示在右边。
+从最底层(即第 4 层)开始，创造第 3 层有多种方法，但如果尝试所有可能性，你便会在创造第 1 层前陷入困境。
+</pre>
+
+#### 提示:
+* `2 <= bottom.length <= 6`
+* `0 <= allowed.length <= 216`
+* `allowed[i].length == 3`
+* 所有输入字符串中的字母来自集合 `{'A', 'B', 'C', 'D', 'E', 'F'}`。
+* `allowed` 中所有值都是 **唯一的**
+
+## 题解 (Python)
+
+### 1. 题解
+```Python
+class Solution:
+ def pyramidTransition(self, bottom: str, allowed: List[str]) -> bool:
+ @cache
+ def buildFromBottom(bottom: str) -> bool:
+ if len(bottom) == 1:
+ return True
+
+ top = [''] * (len(bottom) - 1)
+
+ def buildTop(i: int) -> bool:
+ if i >= len(top):
+ return buildFromBottom(''.join(top))
+
+ for pattern in allowed:
+ if bottom[i:i + 2] == pattern[:2]:
+ top[i] = pattern[2]
+ if buildTop(i + 1):
+ return True
+ top[i] = ''
+
+ return False
+
+ return buildTop(0)
+
+ return buildFromBottom(bottom)
+```

Problemset/0756-Pyramid Transition Matrix/Solution.py

@@ -0,0 +1,25 @@
+class Solution:
+ def pyramidTransition(self, bottom: str, allowed: List[str]) -> bool:
+ @cache
+ def buildFromBottom(bottom: str) -> bool:
+ if len(bottom) == 1:
+ return True
+
+ top = [''] * (len(bottom) - 1)
+
+ def buildTop(i: int) -> bool:
+ if i >= len(top):
+ return buildFromBottom(''.join(top))
+
+ for pattern in allowed:
+ if bottom[i:i + 2] == pattern[:2]:
+ top[i] = pattern[2]
+ if buildTop(i + 1):
+ return True
+ top[i] = ''
+
+ return False
+
+ return buildTop(0)
+
+ return buildFromBottom(bottom)

README.md

@@ -546,6 +546,7 @@
 [752][752l] |[Open the Lock][752] |![rb]  ![rs]
 [753][753l] |[Cracking the Safe][753] |![py]
 [754][754l] |[Reach a Number][754] |![rs]
+[756][756l] |[Pyramid Transition Matrix][756] |![py]
 [757][757l] |[Set Intersection Size At Least Two][757] |![py]
 [762][762l] |[Prime Number of Set Bits in Binary Representation][762] |![py]
 [763][763l] |[Partition Labels][763] |![rs]
@@ -2475,6 +2476,7 @@
 [752]:Problemset/0752-Open%20the%20Lock/README.md#752-open-the-lock
 [753]:Problemset/0753-Cracking%20the%20Safe/README.md#753-cracking-the-safe
 [754]:Problemset/0754-Reach%20a%20Number/README.md#754-reach-a-number
+[756]:Problemset/0756-Pyramid%20Transition%20Matrix/README.md#756-pyramid-transition-matrix
 [757]:Problemset/0757-Set%20Intersection%20Size%20At%20Least%20Two/README.md#757-set-intersection-size-at-least-two
 [762]:Problemset/0762-Prime%20Number%20of%20Set%20Bits%20in%20Binary%20Representation/README.md#762-prime-number-of-set-bits-in-binary-representation
 [763]:Problemset/0763-Partition%20Labels/README.md#763-partition-labels
@@ -4398,6 +4400,7 @@
 [752l]:https://leetcode.com/problems/open-the-lock/
 [753l]:https://leetcode.com/problems/cracking-the-safe/
 [754l]:https://leetcode.com/problems/reach-a-number/
+[756l]:https://leetcode.com/problems/pyramid-transition-matrix/
 [757l]:https://leetcode.com/problems/set-intersection-size-at-least-two/
 [762l]:https://leetcode.com/problems/prime-number-of-set-bits-in-binary-representation/
 [763l]:https://leetcode.com/problems/partition-labels/

README_CN.md

@@ -546,6 +546,7 @@
 [752][752l] |[打开转盘锁][752] |![rb]  ![rs]|
 [753][753l] |[破解保险箱][753] |![py]
 [754][754l] |[到达终点数字][754] |![rs]
+[756][756l] |[金字塔转换矩阵][756] |![py]
 [757][757l] |[设置交集大小至少为2][757] |![py]
 [762][762l] |[二进制表示中质数个计算置位][762] |![py]
 [763][763l] |[划分字母区间][763] |![rs]
@@ -2475,6 +2476,7 @@
 [752]:Problemset/0752-Open%20the%20Lock/README_CN.md#752-打开转盘锁
 [753]:Problemset/0753-Cracking%20the%20Safe/README_CN.md#753-破解保险箱
 [754]:Problemset/0754-Reach%20a%20Number/README_CN.md#754-到达终点数字
+[756]:Problemset/0756-Pyramid%20Transition%20Matrix/README_CN.md#756-金字塔转换矩阵
 [757]:Problemset/0757-Set%20Intersection%20Size%20At%20Least%20Two/README_CN.md#757-设置交集大小至少为2
 [762]:Problemset/0762-Prime%20Number%20of%20Set%20Bits%20in%20Binary%20Representation/README_CN.md#762-二进制表示中质数个计算置位
 [763]:Problemset/0763-Partition%20Labels/README_CN.md#763-划分字母区间
@@ -4398,6 +4400,7 @@
 [752l]:https://leetcode.cn/problems/open-the-lock/
 [753l]:https://leetcode.cn/problems/cracking-the-safe/
 [754l]:https://leetcode.cn/problems/reach-a-number/
+[756l]:https://leetcode.cn/problems/pyramid-transition-matrix/
 [757l]:https://leetcode.cn/problems/set-intersection-size-at-least-two/
 [762l]:https://leetcode.cn/problems/prime-number-of-set-bits-in-binary-representation/
 [763l]:https://leetcode.cn/problems/partition-labels/