Shopping Offers
<p>In LeetCode Store, there are <code>n</code> items to sell. Each item has a price. However, there are some special offers, and a special offer consists of one or more different kinds of items with a sale price.</p>

<p>You are given an integer array <code>price</code> where <code>price[i]</code> is the price of the <code>i<sup>th</sup></code> item, and an integer array <code>needs</code> where <code>needs[i]</code> is the number of pieces of the <code>i<sup>th</sup></code> item you want to buy.</p>

<p>You are also given an array <code>special</code> where <code>special[i]</code> is of size <code>n + 1</code> where <code>special[i][j]</code> is the number of pieces of the <code>j<sup>th</sup></code> item in the <code>i<sup>th</sup></code> offer and <code>special[i][n]</code> (i.e., the last integer in the array) is the price of the <code>i<sup>th</sup></code> offer.</p>

<p>Return <em>the lowest price you have to pay for exactly certain items as given, where you could make optimal use of the special offers</em>. You are not allowed to buy more items than you want, even if that would lower the overall price. You could use any of the special offers as many times as you want.</p>

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

<pre>
<strong>Input:</strong> price = [2,5], special = [[3,0,5],[1,2,10]], needs = [3,2]
<strong>Output:</strong> 14
<strong>Explanation:</strong> There are two kinds of items, A and B. Their prices are $2 and $5 respectively. 
In special offer 1, you can pay $5 for 3A and 0B
In special offer 2, you can pay $10 for 1A and 2B. 
You need to buy 3A and 2B, so you may pay $10 for 1A and 2B (special offer #2), and $4 for 2A.
</pre>

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

<pre>
<strong>Input:</strong> price = [2,3,4], special = [[1,1,0,4],[2,2,1,9]], needs = [1,2,1]
<strong>Output:</strong> 11
<strong>Explanation:</strong> The price of A is $2, and $3 for B, $4 for C. 
You may pay $4 for 1A and 1B, and $9 for 2A ,2B and 1C. 
You need to buy 1A ,2B and 1C, so you may pay $4 for 1A and 1B (special offer #1), and $3 for 1B, $4 for 1C. 
You cannot add more items, though only $9 for 2A ,2B and 1C.
</pre>

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

<ul>
	<li><code>n == price.length == needs.length</code></li>
	<li><code>1 &lt;= n &lt;= 6</code></li>
	<li><code>0 &lt;= price[i], needs[i] &lt;= 10</code></li>
	<li><code>1 &lt;= special.length &lt;= 100</code></li>
	<li><code>special[i].length == n + 1</code></li>
	<li><code>0 &lt;= special[i][j] &lt;= 50</code></li>
	<li>The input is generated that at least one of <code>special[i][j]</code> is non-zero for <code>0 &lt;= j &lt;= n - 1</code>.</li>
</ul>

[]
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    int shoppingOffers(vector<int>& price, vector<vector<int>>& special, vector<int>& needs) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public int shoppingOffers(List<Integer> price, List<List<Integer>> special, List<Integer> needs) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def shoppingOffers(self, price, special, needs):\n        \"\"\"\n        :type price: List[int]\n        :type special: List[List[int]]\n        :type needs: List[int]\n        :rtype: int\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def shoppingOffers(self, price: List[int], special: List[List[int]], needs: List[int]) -> int:\n        "}, {"value": "c", "text": "C", "defaultCode": "int shoppingOffers(int* price, int priceSize, int** special, int specialSize, int* specialColSize, int* needs, int needsSize) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public int ShoppingOffers(IList<int> price, IList<IList<int>> special, IList<int> needs) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number[]} price\n * @param {number[][]} special\n * @param {number[]} needs\n * @return {number}\n */\nvar shoppingOffers = function(price, special, needs) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function shoppingOffers(price: number[], special: number[][], needs: number[]): number {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param Integer[] $price\n     * @param Integer[][] $special\n     * @param Integer[] $needs\n     * @return Integer\n     */\n    function shoppingOffers($price, $special, $needs) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func shoppingOffers(_ price: [Int], _ special: [[Int]], _ needs: [Int]) -> Int {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun shoppingOffers(price: List<Int>, special: List<List<Int>>, needs: List<Int>): Int {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  int shoppingOffers(List<int> price, List<List<int>> special, List<int> needs) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func shoppingOffers(price []int, special [][]int, needs []int) int {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {Integer[]} price\n# @param {Integer[][]} special\n# @param {Integer[]} needs\n# @return {Integer}\ndef shopping_offers(price, special, needs)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def shoppingOffers(price: List[Int], special: List[List[Int]], needs: List[Int]): Int = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn shopping_offers(price: Vec<i32>, special: Vec<Vec<i32>>, needs: Vec<i32>) -> i32 {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (shopping-offers price special needs)\n  (-> (listof exact-integer?) (listof (listof exact-integer?)) (listof exact-integer?) exact-integer?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec shopping_offers(Price :: [integer()], Special :: [[integer()]], Needs :: [integer()]) -> integer().\nshopping_offers(Price, Special, Needs) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec shopping_offers(price :: [integer], special :: [[integer]], needs :: [integer]) :: integer\n  def shopping_offers(price, special, needs) do\n    \n  end\nend"}]
{
  "name": "shoppingOffers",
  "params": [
    {
      "name": "price",
      "type": "list<integer>"
    },
    {
      "name": "special",
      "type": "list<list<integer>>"
    },
    {
      "name": "needs",
      "type": "list<integer>"
    }
  ],
  "return": {
    "type": "integer"
  }
}

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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>\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>. 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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', 'Dynamic Programming', 'Backtracking', 'Bit Manipulation', 'Memoization', 'Bitmask']