{ "data": { "question": { "questionId": "1376", "questionFrontendId": "2312", "categoryTitle": "Algorithms", "boundTopicId": 1607257, "title": "Selling Pieces of Wood", "titleSlug": "selling-pieces-of-wood", "content": "

You are given two integers m and n that represent the height and width of a rectangular piece of wood. You are also given a 2D integer array prices, where prices[i] = [hi, wi, pricei] indicates you can sell a rectangular piece of wood of height hi and width wi for pricei dollars.

\n\n

To cut a piece of wood, you must make a vertical or horizontal cut across the entire 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 prices. 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 cannot rotate a piece to swap its height and width.

\n\n

Return the maximum money you can earn after cutting an m x n piece of wood.

\n\n

Note that you can cut the piece of wood as many times as you want.

\n\n

 

\n

Example 1:

\n\"\"\n
\nInput: m = 3, n = 5, prices = [[1,4,2],[2,2,7],[2,1,3]]\nOutput: 19\nExplanation: 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
\n\n

Example 2:

\n\"\"\n
\nInput: m = 4, n = 6, prices = [[3,2,10],[1,4,2],[4,1,3]]\nOutput: 32\nExplanation: 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.
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "卖木头块", "translatedContent": "

给你两个整数 m 和 n ，分别表示一块矩形木块的高和宽。同时给你一个二维整数数组 prices ，其中 prices[i] = [hi, wi, pricei] 表示你可以以 pricei 元的价格卖一块高为 hi 宽为 wi 的矩形木块。

\n\n

每一次操作中，你必须按下述方式之一执行切割操作，以得到两块更小的矩形木块：

\n\n\n\n

在将一块木块切成若干小木块后，你可以根据 prices 卖木块。你可以卖多块同样尺寸的木块。你不需要将所有小木块都卖出去。你 不能 旋转切好后木块的高和宽。

\n\n

请你返回切割一块大小为 m x n 的木块后，能得到的 最多 钱数。

\n\n

注意你可以切割木块任意次。

\n\n

 

\n\n

示例 1：

\n\n

\"\"

\n\n
\n输入：m = 3, n = 5, prices = [[1,4,2],[2,2,7],[2,1,3]]\n输出：19\n解释：上图展示了一个可行的方案。包括：\n- 2 块 2 x 2 的小木块，售出 2 * 7 = 14 元。\n- 1 块 2 x 1 的小木块，售出 1 * 3 = 3 元。\n- 1 块 1 x 4 的小木块，售出 1 * 2 = 2 元。\n总共售出 14 + 3 + 2 = 19 元。\n19 元是最多能得到的钱数。\n
\n\n

示例 2：

\n\n

\"\"

\n\n
\n输入：m = 4, n = 6, prices = [[3,2,10],[1,4,2],[4,1,3]]\n输出：32\n解释：上图展示了一个可行的方案。包括：\n- 3 块 3 x 2 的小木块，售出 3 * 10 = 30 元。\n- 1 块 1 x 4 的小木块，售出 1 * 2 = 2 元。\n总共售出 30 + 2 = 32 元。\n32 元是最多能得到的钱数。\n注意我们不能旋转 1 x 4 的木块来得到 4 x 1 的木块。
\n\n

 

\n\n

提示：

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