Filling Bookcase Shelves
<p>You are given an array <code>books</code> where <code>books[i] = [thickness<sub>i</sub>, height<sub>i</sub>]</code> indicates the thickness and height of the <code>i<sup>th</sup></code> book. You are also given an integer <code>shelfWidth</code>.</p>

<p>We want to place these books in order onto bookcase shelves that have a total width <code>shelfWidth</code>.</p>

<p>We choose some of the books to place on this shelf such that the sum of their thickness is less than or equal to <code>shelfWidth</code>, then build another level of the shelf of the bookcase so that the total height of the bookcase has increased by the maximum height of the books we just put down. We repeat this process until there are no more books to place.</p>

<p>Note that at each step of the above process, the order of the books we place is the same order as the given sequence of books.</p>

<ul>
	<li>For example, if we have an ordered list of <code>5</code> books, we might place the first and second book onto the first shelf, the third book on the second shelf, and the fourth and fifth book on the last shelf.</li>
</ul>

<p>Return <em>the minimum possible height that the total bookshelf can be after placing shelves in this manner</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/06/24/shelves.png" style="height: 500px; width: 337px;" />
<pre>
<strong>Input:</strong> books = [[1,1],[2,3],[2,3],[1,1],[1,1],[1,1],[1,2]], shelfWidth = 4
<strong>Output:</strong> 6
<strong>Explanation:</strong>
The sum of the heights of the 3 shelves is 1 + 3 + 2 = 6.
Notice that book number 2 does not have to be on the first shelf.
</pre>

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

<pre>
<strong>Input:</strong> books = [[1,3],[2,4],[3,2]], shelfWidth = 6
<strong>Output:</strong> 4
</pre>

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

<ul>
	<li><code>1 &lt;= books.length &lt;= 1000</code></li>
	<li><code>1 &lt;= thickness<sub>i</sub> &lt;= shelfWidth &lt;= 1000</code></li>
	<li><code>1 &lt;= height<sub>i</sub> &lt;= 1000</code></li>
</ul>

[]
[]
[{"value": "cpp", "text": "C++", "defaultCode": "class Solution {\npublic:\n    int minHeightShelves(vector<vector<int>>& books, int shelfWidth) {\n        \n    }\n};"}, {"value": "java", "text": "Java", "defaultCode": "class Solution {\n    public int minHeightShelves(int[][] books, int shelfWidth) {\n        \n    }\n}"}, {"value": "python", "text": "Python", "defaultCode": "class Solution(object):\n    def minHeightShelves(self, books, shelfWidth):\n        \"\"\"\n        :type books: List[List[int]]\n        :type shelfWidth: int\n        :rtype: int\n        \"\"\"\n        "}, {"value": "python3", "text": "Python3", "defaultCode": "class Solution:\n    def minHeightShelves(self, books: List[List[int]], shelfWidth: int) -> int:\n        "}, {"value": "c", "text": "C", "defaultCode": "int minHeightShelves(int** books, int booksSize, int* booksColSize, int shelfWidth) {\n    \n}"}, {"value": "csharp", "text": "C#", "defaultCode": "public class Solution {\n    public int MinHeightShelves(int[][] books, int shelfWidth) {\n        \n    }\n}"}, {"value": "javascript", "text": "JavaScript", "defaultCode": "/**\n * @param {number[][]} books\n * @param {number} shelfWidth\n * @return {number}\n */\nvar minHeightShelves = function(books, shelfWidth) {\n    \n};"}, {"value": "typescript", "text": "TypeScript", "defaultCode": "function minHeightShelves(books: number[][], shelfWidth: number): number {\n    \n};"}, {"value": "php", "text": "PHP", "defaultCode": "class Solution {\n\n    /**\n     * @param Integer[][] $books\n     * @param Integer $shelfWidth\n     * @return Integer\n     */\n    function minHeightShelves($books, $shelfWidth) {\n        \n    }\n}"}, {"value": "swift", "text": "Swift", "defaultCode": "class Solution {\n    func minHeightShelves(_ books: [[Int]], _ shelfWidth: Int) -> Int {\n        \n    }\n}"}, {"value": "kotlin", "text": "Kotlin", "defaultCode": "class Solution {\n    fun minHeightShelves(books: Array<IntArray>, shelfWidth: Int): Int {\n        \n    }\n}"}, {"value": "dart", "text": "Dart", "defaultCode": "class Solution {\n  int minHeightShelves(List<List<int>> books, int shelfWidth) {\n    \n  }\n}"}, {"value": "golang", "text": "Go", "defaultCode": "func minHeightShelves(books [][]int, shelfWidth int) int {\n    \n}"}, {"value": "ruby", "text": "Ruby", "defaultCode": "# @param {Integer[][]} books\n# @param {Integer} shelf_width\n# @return {Integer}\ndef min_height_shelves(books, shelf_width)\n    \nend"}, {"value": "scala", "text": "Scala", "defaultCode": "object Solution {\n    def minHeightShelves(books: Array[Array[Int]], shelfWidth: Int): Int = {\n        \n    }\n}"}, {"value": "rust", "text": "Rust", "defaultCode": "impl Solution {\n    pub fn min_height_shelves(books: Vec<Vec<i32>>, shelf_width: i32) -> i32 {\n        \n    }\n}"}, {"value": "racket", "text": "Racket", "defaultCode": "(define/contract (min-height-shelves books shelfWidth)\n  (-> (listof (listof exact-integer?)) exact-integer? exact-integer?)\n  )"}, {"value": "erlang", "text": "Erlang", "defaultCode": "-spec min_height_shelves(Books :: [[integer()]], ShelfWidth :: integer()) -> integer().\nmin_height_shelves(Books, ShelfWidth) ->\n  ."}, {"value": "elixir", "text": "Elixir", "defaultCode": "defmodule Solution do\n  @spec min_height_shelves(books :: [[integer]], shelf_width :: integer) :: integer\n  def min_height_shelves(books, shelf_width) do\n    \n  end\nend"}]
{
  "name": "minHeightShelves",
  "params": [
    {
      "name": "books",
      "type": "integer[][]"
    },
    {
      "type": "integer",
      "name": "shelfWidth"
    }
  ],
  "return": {
    "type": "integer"
  }
}
{"cpp": ["C++", "<p>Compiled with <code> clang 19 </code> using the latest C++ 23 standard, and <code>libstdc++</code> provided by GCC 14.</p>\r\n\r\n<p>Your code is compiled with level two 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>"], "java": ["Java", "<p><code>OpenJDK 21</code>. 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>"]}
['Array', 'Dynamic Programming']