Stone Game IX
<p>Alice and Bob continue their games with stones. There is a row of n stones, and each stone has an associated value. You are given an integer array <code>stones</code>, where <code>stones[i]</code> is the <strong>value</strong> of the <code>i<sup>th</sup></code> stone.</p>

<p>Alice and Bob take turns, with <strong>Alice</strong> starting first. On each turn, the player may remove any stone from <code>stones</code>. The player who removes a stone <strong>loses</strong> if the <strong>sum</strong> of the values of <strong>all removed stones</strong> is divisible by <code>3</code>. Bob will win automatically if there are no remaining stones (even if it is Alice&#39;s turn).</p>

<p>Assuming both players play <strong>optimally</strong>, return <code>true</code> <em>if Alice wins and</em> <code>false</code> <em>if Bob wins</em>.</p>

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

<pre>
<strong>Input:</strong> stones = [2,1]
<strong>Output:</strong> true
<strong>Explanation:</strong>&nbsp;The game will be played as follows:
- Turn 1: Alice can remove either stone.
- Turn 2: Bob removes the remaining stone. 
The sum of the removed stones is 1 + 2 = 3 and is divisible by 3. Therefore, Bob loses and Alice wins the game.
</pre>

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

<pre>
<strong>Input:</strong> stones = [2]
<strong>Output:</strong> false
<strong>Explanation:</strong>&nbsp;Alice will remove the only stone, and the sum of the values on the removed stones is 2. 
Since all the stones are removed and the sum of values is not divisible by 3, Bob wins the game.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> stones = [5,1,2,4,3]
<strong>Output:</strong> false
<strong>Explanation:</strong> Bob will always win. One possible way for Bob to win is shown below:
- Turn 1: Alice can remove the second stone with value 1. Sum of removed stones = 1.
- Turn 2: Bob removes the fifth stone with value 3. Sum of removed stones = 1 + 3 = 4.
- Turn 3: Alices removes the fourth stone with value 4. Sum of removed stones = 1 + 3 + 4 = 8.
- Turn 4: Bob removes the third stone with value 2. Sum of removed stones = 1 + 3 + 4 + 2 = 10.
- Turn 5: Alice removes the first stone with value 5. Sum of removed stones = 1 + 3 + 4 + 2 + 5 = 15.
Alice loses the game because the sum of the removed stones (15) is divisible by 3. Bob wins the game.
</pre>

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

<ul>
	<li><code>1 &lt;= stones.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= stones[i] &lt;= 10<sup>4</sup></code></li>
</ul>

['stone-game', 'stone-game-ii', 'stone-game-iii', 'stone-game-iv', 'stone-game-v', 'stone-game-vi', 'stone-game-vii', 'stone-game-viii', 'stone-game-ix']
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    bool stoneGameIX(vector<int>& stones) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public boolean stoneGameIX(int[] stones) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def stoneGameIX(self, stones):\n        \"\"\"\n        :type stones: List[int]\n        :rtype: bool\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def stoneGameIX(self, stones: List[int]) -> bool:\n        "}, {"value": "c", "text": "C", "defaultCode": "bool stoneGameIX(int* stones, int stonesSize) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public bool StoneGameIX(int[] stones) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number[]} stones\n * @return {boolean}\n */\nvar stoneGameIX = function(stones) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function stoneGameIX(stones: number[]): boolean {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param Integer[] $stones\n     * @return Boolean\n     */\n    function stoneGameIX($stones) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func stoneGameIX(_ stones: [Int]) -> Bool {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun stoneGameIX(stones: IntArray): Boolean {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  bool stoneGameIX(List<int> stones) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func stoneGameIX(stones []int) bool {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {Integer[]} stones\n# @return {Boolean}\ndef stone_game_ix(stones)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def stoneGameIX(stones: Array[Int]): Boolean = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn stone_game_ix(stones: Vec<i32>) -> bool {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (stone-game-ix stones)\n  (-> (listof exact-integer?) boolean?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec stone_game_ix(Stones :: [integer()]) -> boolean().\nstone_game_ix(Stones) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec stone_game_ix(stones :: [integer]) :: boolean\n  def stone_game_ix(stones) do\n    \n  end\nend"}]
{
  "name": "stoneGameIX",
  "params": [
    {
      "name": "stones",
      "type": "integer[]"
    }
  ],
  "return": {
    "type": "boolean"
  }
}
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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>"]}
['Array', 'Math', 'Greedy', 'Counting', 'Game Theory']