Pyramid Transition Matrix
<p>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 <strong>one less block</strong> than the row beneath it and is centered on top.</p>

<p>To make the pyramid aesthetically pleasing, there are only specific <strong>triangular patterns</strong> that are allowed. A triangular pattern consists of a <strong>single block</strong> stacked on top of <strong>two blocks</strong>. The patterns are given&nbsp;as a list of&nbsp;three-letter strings <code>allowed</code>, where the first two characters of a pattern represent the left and right bottom blocks respectively, and the third character is the top block.</p>

<ul>
	<li>For example, <code>&quot;ABC&quot;</code> represents a triangular pattern with a <code>&#39;C&#39;</code> block stacked on top of an <code>&#39;A&#39;</code> (left) and <code>&#39;B&#39;</code> (right) block. Note that this is different from <code>&quot;BAC&quot;</code> where <code>&#39;B&#39;</code> is on the left bottom and <code>&#39;A&#39;</code> is on the right bottom.</li>
</ul>

<p>You start with a bottom row of blocks <code>bottom</code>, given as a single string, that you <strong>must</strong> use as the base of the pyramid.</p>

<p>Given <code>bottom</code> and <code>allowed</code>, return <code>true</code><em> if you can build the pyramid all the way to the top such that <strong>every triangular pattern</strong> in the pyramid is in </em><code>allowed</code><em>, or </em><code>false</code><em> otherwise</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/26/pyramid1-grid.jpg" style="width: 600px; height: 232px;" />
<pre>
<strong>Input:</strong> bottom = &quot;BCD&quot;, allowed = [&quot;BCC&quot;,&quot;CDE&quot;,&quot;CEA&quot;,&quot;FFF&quot;]
<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 &quot;CE&quot; on level 2 and then build &quot;A&quot; on level 1.
There are three triangular patterns in the pyramid, which are &quot;BCC&quot;, &quot;CDE&quot;, and &quot;CEA&quot;. All are allowed.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/26/pyramid2-grid.jpg" style="width: 600px; height: 359px;" />
<pre>
<strong>Input:</strong> bottom = &quot;AAAA&quot;, allowed = [&quot;AAB&quot;,&quot;AAC&quot;,&quot;BCD&quot;,&quot;BBE&quot;,&quot;DEF&quot;]
<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>

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

<ul>
	<li><code>2 &lt;= bottom.length &lt;= 6</code></li>
	<li><code>0 &lt;= allowed.length &lt;= 216</code></li>
	<li><code>allowed[i].length == 3</code></li>
	<li>The letters in all input strings are from the set <code>{&#39;A&#39;, &#39;B&#39;, &#39;C&#39;, &#39;D&#39;, &#39;E&#39;, &#39;F&#39;}</code>.</li>
	<li>All the values of <code>allowed</code> are <strong>unique</strong>.</li>
</ul>

[]
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    bool pyramidTransition(string bottom, vector<string>& allowed) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public boolean pyramidTransition(String bottom, List<String> allowed) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def pyramidTransition(self, bottom, allowed):\n        \"\"\"\n        :type bottom: str\n        :type allowed: List[str]\n        :rtype: bool\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def pyramidTransition(self, bottom: str, allowed: List[str]) -> bool:\n        "}, {"value": "c", "text": "C", "defaultCode": "bool pyramidTransition(char* bottom, char** allowed, int allowedSize) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public bool PyramidTransition(string bottom, IList<string> allowed) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {string} bottom\n * @param {string[]} allowed\n * @return {boolean}\n */\nvar pyramidTransition = function(bottom, allowed) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function pyramidTransition(bottom: string, allowed: string[]): boolean {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param String $bottom\n     * @param String[] $allowed\n     * @return Boolean\n     */\n    function pyramidTransition($bottom, $allowed) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func pyramidTransition(_ bottom: String, _ allowed: [String]) -> Bool {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun pyramidTransition(bottom: String, allowed: List<String>): Boolean {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  bool pyramidTransition(String bottom, List<String> allowed) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func pyramidTransition(bottom string, allowed []string) bool {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {String} bottom\n# @param {String[]} allowed\n# @return {Boolean}\ndef pyramid_transition(bottom, allowed)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def pyramidTransition(bottom: String, allowed: List[String]): Boolean = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn pyramid_transition(bottom: String, allowed: Vec<String>) -> bool {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (pyramid-transition bottom allowed)\n  (-> string? (listof string?) boolean?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec pyramid_transition(Bottom :: unicode:unicode_binary(), Allowed :: [unicode:unicode_binary()]) -> boolean().\npyramid_transition(Bottom, Allowed) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec pyramid_transition(bottom :: String.t, allowed :: [String.t]) :: boolean\n  def pyramid_transition(bottom, allowed) do\n    \n  end\nend"}]
{
  "name": "pyramidTransition",
  "params": [
    {
      "name": "bottom",
      "type": "string"
    },
    {
      "name": "allowed",
      "type": "list<string>"
    }
  ],
  "return": {
    "type": "boolean"
  }
}

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Using compile arguments: <code>--enable-preview --release 21</code></p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>"], "python": ["Python", "<p><code>Python 2.7.18</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/2/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/2/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/2/library/collections.html\" target=\"_blank\">collections</a>. If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>\r\n\r\n<p>Note that Python 2.7 <a href=\"https://www.python.org/dev/peps/pep-0373/\" target=\"_blank\">is not maintained anymore</a>. For the latest Python, please choose Python3 instead.</p>"], "c": ["C", "<p>Compiled with <code>gcc 14</code> using the gnu11 standard.</p>\r\n\r\n<p>Your code is compiled with level one optimization (<code>-O2</code>). <a href=\"https://github.com/google/sanitizers/wiki/AddressSanitizer\" target=\"_blank\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\r\n\r\n<p>Most standard library headers are already included automatically for your convenience.</p>\r\n\r\n<p>For hash table operations, you may use <a href=\"https://troydhanson.github.io/uthash/\" target=\"_blank\">uthash</a>. \"uthash.h\" is included by default. Below are some examples:</p>\r\n\r\n<p><b>1. Adding an item to a hash.</b>\r\n<pre>\r\nstruct hash_entry {\r\n    int id;            /* we'll use this field as the key */\r\n    char name[10];\r\n    UT_hash_handle hh; /* makes this structure hashable */\r\n};\r\n\r\nstruct hash_entry *users = NULL;\r\n\r\nvoid add_user(struct hash_entry *s) {\r\n    HASH_ADD_INT(users, id, s);\r\n}\r\n</pre>\r\n</p>\r\n\r\n<p><b>2. Looking up an item in a hash:</b>\r\n<pre>\r\nstruct hash_entry *find_user(int user_id) {\r\n    struct hash_entry *s;\r\n    HASH_FIND_INT(users, &user_id, s);\r\n    return s;\r\n}\r\n</pre>\r\n</p>\r\n\r\n<p><b>3. Deleting an item in a hash:</b>\r\n<pre>\r\nvoid delete_user(struct hash_entry *user) {\r\n    HASH_DEL(users, user);  \r\n}\r\n</pre>\r\n</p>"], "csharp": ["C#", "<p><a href=\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-13\" target=\"_blank\">C# 13</a> with .NET 9 runtime</p>"], "javascript": ["JavaScript", "<p><code>Node.js 22.14.0</code>.</p>\r\n\r\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\"http://node.green/\" target=\"_blank\">new ES6 features</a>.</p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "ruby": ["Ruby", "<p><code>Ruby 3.2</code></p>\r\n\r\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>"], "swift": ["Swift", "<p><code>Swift 6.0</code>.</p>\r\n\r\n<p>You may use the following packages:<br/>\r\n<a href=\"https://github.com/apple/swift-algorithms/tree/1.2.0\" target=\"_blank\">swift-algorithms 1.2.0</a><br/>\r\n<a href=\"https://github.com/apple/swift-collections/tree/1.1.4\" target=\"_blank\">swift-collections 1.1.4</a><br/>\r\n<a href=\"https://github.com/apple/swift-numerics/tree/1.0.2\" target=\"_blank\">swift-numerics 1.0.2</a></p>"], "golang": ["Go", "<p><code>Go 1.23</code></p>\r\n<p>Support <a href=\"https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods@v1.18.1</a> and <a href=\"https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha\" target=\"_blank\">https://pkg.go.dev/github.com/emirpasic/gods/v2@v2.0.0-alpha</a> library.</p>"], "python3": ["Python3", "<p><code>Python 3.11</code>.</p>\r\n\r\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\"https://docs.python.org/3/library/array.html\" target=\"_blank\">array</a>, <a href=\"https://docs.python.org/3/library/bisect.html\" target=\"_blank\">bisect</a>, <a href=\"https://docs.python.org/3/library/collections.html\" target=\"_blank\">collections</a>. If you need more libraries, you can import it yourself.</p>\r\n\r\n<p>For Map/TreeMap data structure, you may use <a href=\"http://www.grantjenks.com/docs/sortedcontainers/\" target=\"_blank\">sortedcontainers</a> library.</p>"], "scala": ["Scala", "<p><code>Scala 3.3.1</code>.</p>"], "kotlin": ["Kotlin", "<p><code>Kotlin 2.1.10</code>.</p>"], "rust": ["Rust", "<p><code>Rust 1.85.0</code>. Your code will be compiled with <code>opt-level</code> 2.</p>\r\n\r\n<p>Supports <a href=\"https://crates.io/crates/rand\" target=\"_blank\">rand v0.8</a> and <a href=\"https://crates.io/crates/regex\" target=\"_blank\">regex\u00a0v1</a> and <a href=\"https://crates.io/crates/itertools\" target=\"_blank\">itertools\u00a0v0.14</a> from crates.io</p>"], "php": ["PHP", "<p><code>PHP 8.2</code>.</p>\r\n<p>With bcmath module</p>"], "typescript": ["Typescript", "<p><code>TypeScript 5.7.3, Node.js 22.14.0</code>.</p>\r\n\r\n<p>Compile Options: <code>--alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2024</code></p>\r\n\r\n<p><a href=\"https://lodash.com\" target=\"_blank\">lodash.js</a> library is included by default.</p>\r\n\r\n<p>For Priority Queue / Queue data structures, you may use 6.3.2 version of <a href=\"https://github.com/datastructures-js/priority-queue/tree/v6.3.2\" target=\"_blank\">datastructures-js/priority-queue</a> and 4.2.3 version of <a href=\"https://github.com/datastructures-js/queue/tree/v4.2.3\" target=\"_blank\">datastructures-js/queue</a> and 1.0.4 version of <a href=\"https://github.com/datastructures-js/deque/tree/v1.0.4\" target=\"_blank\">datastructures-js/deque</a>.</p>"], "racket": ["Racket", "<p><a href=\"https://docs.racket-lang.org/guide/performance.html#%28tech._c%29\" target=\"_blank\">Racket CS</a> v8.15</p>\r\n\r\n<p>Using <code>#lang racket</code></p>\r\n\r\n<p>Required <code>data/gvector data/queue data/order data/heap</code> automatically for your convenience</p>"], "erlang": ["Erlang", "Erlang/OTP 26"], "elixir": ["Elixir", "Elixir 1.17 with Erlang/OTP 26"], "dart": ["Dart", "<p>Dart 3.2. You may use package <a href=\"https://pub.dev/packages/collection/versions/1.18.0\" target=\"_blank\">collection</a></p>\r\n\r\n<p>Your code will be run directly without compiling</p>"]}
['Bit Manipulation', 'Depth-First Search', 'Breadth-First Search']