+ problem 2312

Author: fruit-in

Problemset/2312-Selling Pieces of Wood/README.md

@@ -0,0 +1,68 @@
+# 2312. Selling Pieces of Wood
+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 <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.
+
+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.
+
+Return *the **maximum** money you can earn after cutting an* `m x n` *piece of wood*.
+
+Note that you can cut the piece of wood as many times as you want.
+
+#### Example 1:
+![](https://assets.leetcode.com/uploads/2022/04/27/ex1.png)
+<pre>
+<strong>Input:</strong> m = 3, n = 5, prices = [[1,4,2],[2,2,7],[2,1,3]]
+<strong>Output:</strong> 19
+<strong>Explanation:</strong> The diagram above shows a possible scenario. It consists of:
+- 2 pieces of wood shaped 2 x 2, selling for a price of 2 * 7 = 14.
+- 1 piece of wood shaped 2 x 1, selling for a price of 1 * 3 = 3.
+- 1 piece of wood shaped 1 x 4, selling for a price of 1 * 2 = 2.
+This obtains a total of 14 + 3 + 2 = 19 money earned.
+It can be shown that 19 is the maximum amount of money that can be earned.
+</pre>
+
+#### Example 2:
+![](https://assets.leetcode.com/uploads/2022/04/27/ex2new.png)
+<pre>
+<strong>Input:</strong> m = 4, n = 6, prices = [[3,2,10],[1,4,2],[4,1,3]]
+<strong>Output:</strong> 32
+<strong>Explanation:</strong> The diagram above shows a possible scenario. It consists of:
+- 3 pieces of wood shaped 3 x 2, selling for a price of 3 * 10 = 30.
+- 1 piece of wood shaped 1 x 4, selling for a price of 1 * 2 = 2.
+This obtains a total of 30 + 2 = 32 money earned.
+It can be shown that 32 is the maximum amount of money that can be earned.
+Notice that we cannot rotate the 1 x 4 piece of wood to obtain a 4 x 1 piece of wood.
+</pre>
+
+#### Constraints:
+* `1 <= m, n <= 200`
+* <code>1 <= prices.length <= 2 * 10<sup>4</sup></code>
+* `prices[i].length == 3`
+* <code>1 <= h<sub>i</sub> <= m</code>
+* <code>1 <= w<sub>i</sub> <= n</code>
+* <code>1 <= price<sub>i</sub> <= 10<sup>6</sup></code>
+* All the shapes of wood <code>(h<sub>i</sub>, w<sub>i</sub>)</code> are pairwise **distinct**.
+
+## Solutions (Python)
+
+### 1. Solution
+```Python
+from functools import cache
+
+
+class Solution:
+    def sellingWood(self, m: int, n: int, prices: List[List[int]]) -> int:
+        prices = {(h, w): price for h, w, price in prices}
+
+        @cache
+        def maxSelling(m: int, n: int) -> int:
+            ret = prices.get((m, n), 0)
+
+            for h in range(1, m):
+                ret = max(ret, maxSelling(h, n) + maxSelling(m - h, n))
+            for w in range(1, n):
+                ret = max(ret, maxSelling(m, w) + maxSelling(m, n - w))
+
+            return ret
+
+        return maxSelling(m, n)
+```

Problemset/2312-Selling Pieces of Wood/README_CN.md

@@ -0,0 +1,73 @@
+# 2312. 卖木头块
+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 <code>prices[i] = [h<sub>i</sub>, w<sub>i</sub>, price<sub>i</sub>]</code> 表示你可以以 <code>price<sub>i</sub></code> 元的价格卖一块高为 <code>h<sub>i</sub></code> 宽为 <code>w<sub>i</sub></code> 的矩形木块。
+
+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：
+
+* 沿垂直方向按高度 **完全** 切割木块，或
+* 沿水平方向按宽度 **完全** 切割木块
+
+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** 旋转切好后木块来交换它的高度值和宽度值。
+
+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。
+
+注意你可以切割木块任意次。
+
+#### 示例 1:
+![](https://assets.leetcode.com/uploads/2022/04/27/ex1.png)
+<pre>
+<strong>输入:</strong> m = 3, n = 5, prices = [[1,4,2],[2,2,7],[2,1,3]]
+<strong>输出:</strong> 19
+<strong>解释:</strong> 上图展示了一个可行的方案。包括：
+- 2 块 2 x 2 的小木块，售出 2 * 7 = 14 元。
+- 1 块 2 x 1 的小木块，售出 1 * 3 = 3 元。
+- 1 块 1 x 4 的小木块，售出 1 * 2 = 2 元。
+总共售出 14 + 3 + 2 = 19 元。
+19 元是最多能得到的钱数。
+</pre>
+
+#### 示例 2:
+![](https://assets.leetcode.com/uploads/2022/04/27/ex2new.png)
+<pre>
+<strong>输入:</strong> m = 4, n = 6, prices = [[3,2,10],[1,4,2],[4,1,3]]
+<strong>输出:</strong> 32
+<strong>解释:</strong> 上图展示了一个可行的方案。包括：
+- 3 块 3 x 2 的小木块，售出 3 * 10 = 30 元。
+- 1 块 1 x 4 的小木块，售出 1 * 2 = 2 元。
+总共售出 30 + 2 = 32 元。
+32 元是最多能得到的钱数。
+注意我们不能旋转 1 x 4 的木块来得到 4 x 1 的木块。
+</pre>
+
+#### 提示:
+* `1 <= m, n <= 200`
+* <code>1 <= prices.length <= 2 * 10<sup>4</sup></code>
+* `prices[i].length == 3`
+* <code>1 <= h<sub>i</sub> <= m</code>
+* <code>1 <= w<sub>i</sub> <= n</code>
+* <code>1 <= price<sub>i</sub> <= 10<sup>6</sup></code>
+* 所有 <code>(h<sub>i</sub>, w<sub>i</sub>)</code> 互不相同 。
+
+## 题解 (Python)
+
+### 1. 题解
+```Python
+from functools import cache
+
+
+class Solution:
+    def sellingWood(self, m: int, n: int, prices: List[List[int]]) -> int:
+        prices = {(h, w): price for h, w, price in prices}
+
+        @cache
+        def maxSelling(m: int, n: int) -> int:
+            ret = prices.get((m, n), 0)
+
+            for h in range(1, m):
+                ret = max(ret, maxSelling(h, n) + maxSelling(m - h, n))
+            for w in range(1, n):
+                ret = max(ret, maxSelling(m, w) + maxSelling(m, n - w))
+
+            return ret
+
+        return maxSelling(m, n)
+```

Problemset/2312-Selling Pieces of Wood/Solution.py

@@ -0,0 +1,19 @@
+from functools import cache
+
+
+class Solution:
+    def sellingWood(self, m: int, n: int, prices: List[List[int]]) -> int:
+        prices = {(h, w): price for h, w, price in prices}
+
+        @cache
+        def maxSelling(m: int, n: int) -> int:
+            ret = prices.get((m, n), 0)
+
+            for h in range(1, m):
+                ret = max(ret, maxSelling(h, n) + maxSelling(m - h, n))
+            for w in range(1, n):
+                ret = max(ret, maxSelling(m, w) + maxSelling(m, n - w))
+
+            return ret
+
+        return maxSelling(m, n)

README.md

@@ -1369,6 +1369,7 @@
 [2306][2306l]|[Naming a Company][2306]                                                              |![py]
 [2309][2309l]|[Greatest English Letter in Upper and Lower Case][2309]                               |![rs]
 [2310][2310l]|[Sum of Numbers With Units Digit K][2310]                                             |![rs]
+[2312][2312l]|[Selling Pieces of Wood][2312]                                                        |![py]
 [2315][2315l]|[Count Asterisks][2315]                                                               |![rs]
 [2317][2317l]|[Maximum XOR After Operations][2317]                                                  |![rs]
 [2319][2319l]|[Check if Matrix Is X-Matrix][2319]                                                   |![py]
@@ -2880,6 +2881,7 @@
 [2306]:Problemset/2306-Naming%20a%20Company/README.md#2306-naming-a-company
 [2309]:Problemset/2309-Greatest%20English%20Letter%20in%20Upper%20and%20Lower%20Case/README.md#2309-greatest-english-letter-in-upper-and-lower-case
 [2310]:Problemset/2310-Sum%20of%20Numbers%20With%20Units%20Digit%20K/README.md#2310-sum-of-numbers-with-units-digit-k
+[2312]:Problemset/2312-Selling%20Pieces%20of%20Wood/README.md#2312-selling-pieces-of-wood
 [2315]:Problemset/2315-Count%20Asterisks/README.md#2315-count-asterisks
 [2317]:Problemset/2317-Maximum%20XOR%20After%20Operations/README.md#2317-maximum-xor-after-operations
 [2319]:Problemset/2319-Check%20if%20Matrix%20Is%20X-Matrix/README.md#2319-check-if-matrix-is-x-matrix
@@ -4390,6 +4392,7 @@
 [2306l]:https://leetcode.com/problems/naming-a-company/
 [2309l]:https://leetcode.com/problems/greatest-english-letter-in-upper-and-lower-case/
 [2310l]:https://leetcode.com/problems/sum-of-numbers-with-units-digit-k/
+[2312l]:https://leetcode.com/problems/selling-pieces-of-wood/
 [2315l]:https://leetcode.com/problems/count-asterisks/
 [2317l]:https://leetcode.com/problems/maximum-xor-after-operations/
 [2319l]:https://leetcode.com/problems/check-if-matrix-is-x-matrix/

README_CN.md

@@ -1369,6 +1369,7 @@
 [2306][2306l]|[公司命名][2306]                                          |![py]
 [2309][2309l]|[兼具大小写的最好英文字母][2309]                          |![rs]
 [2310][2310l]|[个位数字为 K 的整数之和][2310]                           |![rs]
+[2312][2312l]|[卖木头块][2312]                                          |![py]
 [2315][2315l]|[统计星号][2315]                                          |![rs]
 [2317][2317l]|[操作后的最大异或和][2317]                                |![rs]
 [2319][2319l]|[判断矩阵是否是一个 X 矩阵][2319]                         |![py]
@@ -2880,6 +2881,7 @@
 [2306]:Problemset/2306-Naming%20a%20Company/README_CN.md#2306-公司命名
 [2309]:Problemset/2309-Greatest%20English%20Letter%20in%20Upper%20and%20Lower%20Case/README_CN.md#2309-兼具大小写的最好英文字母
 [2310]:Problemset/2310-Sum%20of%20Numbers%20With%20Units%20Digit%20K/README_CN.md#2310-个位数字为-k-的整数之和
+[2312]:Problemset/2312-Selling%20Pieces%20of%20Wood/README_CN.md#2312-卖木头块
 [2315]:Problemset/2315-Count%20Asterisks/README_CN.md#2315-统计星号
 [2317]:Problemset/2317-Maximum%20XOR%20After%20Operations/README_CN.md#2317-操作后的最大异或和
 [2319]:Problemset/2319-Check%20if%20Matrix%20Is%20X-Matrix/README_CN.md#2319-判断矩阵是否是一个-x-矩阵
@@ -4390,6 +4392,7 @@
 [2306l]:https://leetcode.cn/problems/naming-a-company/
 [2309l]:https://leetcode.cn/problems/greatest-english-letter-in-upper-and-lower-case/
 [2310l]:https://leetcode.cn/problems/sum-of-numbers-with-units-digit-k/
+[2312l]:https://leetcode.cn/problems/selling-pieces-of-wood/
 [2315l]:https://leetcode.cn/problems/count-asterisks/
 [2317l]:https://leetcode.cn/problems/maximum-xor-after-operations/
 [2319l]:https://leetcode.cn/problems/check-if-matrix-is-x-matrix/