leetcode-problemset/leetcode/originData/selling-pieces-of-wood.json

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            "title": "Selling Pieces of Wood",
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            "content": "<p>You are given two integers <code>m</code> and <code>n</code> that represent the height and width of a rectangular piece of wood. You are also given a 2D integer array <code>prices</code>, where <code>prices[i] = [h<sub>i</sub>, w<sub>i</sub>, price<sub>i</sub>]</code> indicates you can sell a rectangular piece of wood of height <code>h<sub>i</sub></code> and width <code>w<sub>i</sub></code> for <code>price<sub>i</sub></code> dollars.</p>\n\n<p>To cut a piece of wood, you must make a vertical or horizontal cut across the <strong>entire</strong> height or width of the piece to split it into two smaller pieces. After cutting a piece of wood into some number of smaller pieces, you can sell pieces according to <code>prices</code>. You may sell multiple pieces of the same shape, and you do not have to sell all the shapes. The grain of the wood makes a difference, so you <strong>cannot</strong> rotate a piece to swap its height and width.</p>\n\n<p>Return <em>the <strong>maximum</strong> money you can earn after cutting an </em><code>m x n</code><em> piece of wood</em>.</p>\n\n<p>Note that you can cut the piece of wood as many times as you want.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/27/ex1.png\" style=\"width: 239px; height: 150px;\" />\n<pre>\n<strong>Input:</strong> m = 3, n = 5, prices = [[1,4,2],[2,2,7],[2,1,3]]\n<strong>Output:</strong> 19\n<strong>Explanation:</strong> The diagram above shows a possible scenario. It consists of:\n- 2 pieces of wood shaped 2 x 2, selling for a price of 2 * 7 = 14.\n- 1 piece of wood shaped 2 x 1, selling for a price of 1 * 3 = 3.\n- 1 piece of wood shaped 1 x 4, selling for a price of 1 * 2 = 2.\nThis obtains a total of 14 + 3 + 2 = 19 money earned.\nIt can be shown that 19 is the maximum amount of money that can be earned.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/27/ex2new.png\" style=\"width: 250px; height: 175px;\" />\n<pre>\n<strong>Input:</strong> m = 4, n = 6, prices = [[3,2,10],[1,4,2],[4,1,3]]\n<strong>Output:</strong> 32\n<strong>Explanation:</strong> The diagram above shows a possible scenario. It consists of:\n- 3 pieces of wood shaped 3 x 2, selling for a price of 3 * 10 = 30.\n- 1 piece of wood shaped 1 x 4, selling for a price of 1 * 2 = 2.\nThis obtains a total of 30 + 2 = 32 money earned.\nIt can be shown that 32 is the maximum amount of money that can be earned.\nNotice that we cannot rotate the 1 x 4 piece of wood to obtain a 4 x 1 piece of wood.</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= m, n &lt;= 200</code></li>\n\t<li><code>1 &lt;= prices.length &lt;= 2 * 10<sup>4</sup></code></li>\n\t<li><code>prices[i].length == 3</code></li>\n\t<li><code>1 &lt;= h<sub>i</sub> &lt;= m</code></li>\n\t<li><code>1 &lt;= w<sub>i</sub> &lt;= n</code></li>\n\t<li><code>1 &lt;= price<sub>i</sub> &lt;= 10<sup>6</sup></code></li>\n\t<li>All the shapes of wood <code>(h<sub>i</sub>, w<sub>i</sub>)</code> are pairwise <strong>distinct</strong>.</li>\n</ul>\n",
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                    "code": "class Solution {\npublic:\n    long long sellingWood(int m, int n, vector<vector<int>>& prices) {\n        \n    }\n};",
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                    "code": "class Solution {\n    public long sellingWood(int m, int n, int[][] prices) {\n        \n    }\n}",
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                    "code": "class Solution(object):\n    def sellingWood(self, m, n, prices):\n        \"\"\"\n        :type m: int\n        :type n: int\n        :type prices: List[List[int]]\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "class Solution:\n    def sellingWood(self, m: int, n: int, prices: List[List[int]]) -> int:\n        ",
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                    "code": "\n\nlong long sellingWood(int m, int n, int** prices, int pricesSize, int* pricesColSize){\n\n}",
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                    "lang": "C#",
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                    "code": "public class Solution {\n    public long SellingWood(int m, int n, int[][] prices) {\n        \n    }\n}",
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                    "code": "/**\n * @param {number} m\n * @param {number} n\n * @param {number[][]} prices\n * @return {number}\n */\nvar sellingWood = function(m, n, prices) {\n    \n};",
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                    "code": "# @param {Integer} m\n# @param {Integer} n\n# @param {Integer[][]} prices\n# @return {Integer}\ndef selling_wood(m, n, prices)\n    \nend",
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                    "code": "class Solution {\n    func sellingWood(_ m: Int, _ n: Int, _ prices: [[Int]]) -> Int {\n        \n    }\n}",
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                    "lang": "Go",
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                    "code": "func sellingWood(m int, n int, prices [][]int) int64 {\n    \n}",
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                    "lang": "Scala",
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                    "code": "object Solution {\n    def sellingWood(m: Int, n: Int, prices: Array[Array[Int]]): Long = {\n        \n    }\n}",
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                    "lang": "Kotlin",
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                    "code": "class Solution {\n    fun sellingWood(m: Int, n: Int, prices: Array<IntArray>): Long {\n        \n    }\n}",
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                    "lang": "Rust",
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                    "code": "impl Solution {\n    pub fn selling_wood(m: i32, n: i32, prices: Vec<Vec<i32>>) -> i64 {\n        \n    }\n}",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer $m\n     * @param Integer $n\n     * @param Integer[][] $prices\n     * @return Integer\n     */\n    function sellingWood($m, $n, $prices) {\n        \n    }\n}",
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                    "lang": "TypeScript",
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                    "code": "function sellingWood(m: number, n: number, prices: number[][]): number {\n\n};",
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                    "code": "(define/contract (selling-wood m n prices)\n  (-> exact-integer? exact-integer? (listof (listof exact-integer?)) exact-integer?)\n\n  )",
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                    "lang": "Erlang",
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                    "code": "-spec selling_wood(M :: integer(), N :: integer(), Prices :: [[integer()]]) -> integer().\nselling_wood(M, N, Prices) ->\n  .",
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                    "lang": "Elixir",
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                    "code": "defmodule Solution do\n  @spec selling_wood(m :: integer, n :: integer, prices :: [[integer]]) :: integer\n  def selling_wood(m, n, prices) do\n\n  end\nend",
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            "hints": [
                "Note down the different actions that can be done on a piece of wood with dimensions m x n. What do you notice?",
                "If possible, we could sell the m x n piece. We could also cut the piece vertically creating two pieces of size m x n1 and m x n2 where n1 + n2 = n, or horizontally creating two pieces of size m1 x n and m2 x n where m1 + m2 = m.",
                "Notice that cutting a piece breaks the problem down into smaller subproblems, and selling the piece when available is also a case that terminates the process. Thus, we can use DP to efficiently solve this."
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