"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> </p>\n<p><strong class=\"example\">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 class=\"example\">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> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= m, n <= 200</code></li>\n\t<li><code>1 <= prices.length <= 2 * 10<sup>4</sup></code></li>\n\t<li><code>prices[i].length == 3</code></li>\n\t<li><code>1 <= h<sub>i</sub> <= m</code></li>\n\t<li><code>1 <= w<sub>i</sub> <= n</code></li>\n\t<li><code>1 <= price<sub>i</sub> <= 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",
"similarQuestions":"[{\"title\": \"Tiling a Rectangle with the Fewest Squares\", \"titleSlug\": \"tiling-a-rectangle-with-the-fewest-squares\", \"difficulty\": \"Hard\", \"translatedTitle\": null}, {\"title\": \"Number of Ways of Cutting a Pizza\", \"titleSlug\": \"number-of-ways-of-cutting-a-pizza\", \"difficulty\": \"Hard\", \"translatedTitle\": null}]",
"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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