mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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183 lines
24 KiB
JSON
183 lines
24 KiB
JSON
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"title": "Minimum Cost to Cut a Stick",
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"content": "<p>Given a wooden stick of length <code>n</code> units. The stick is labelled from <code>0</code> to <code>n</code>. For example, a stick of length <strong>6</strong> is labelled as follows:</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/07/21/statement.jpg\" style=\"width: 521px; height: 111px;\" />\n<p>Given an integer array <code>cuts</code> where <code>cuts[i]</code> denotes a position you should perform a cut at.</p>\n\n<p>You should perform the cuts in order, you can change the order of the cuts as you wish.</p>\n\n<p>The cost of one cut is the length of the stick to be cut, the total cost is the sum of costs of all cuts. When you cut a stick, it will be split into two smaller sticks (i.e. the sum of their lengths is the length of the stick before the cut). Please refer to the first example for a better explanation.</p>\n\n<p>Return <em>the minimum total cost</em> of the cuts.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/07/23/e1.jpg\" style=\"width: 350px; height: 284px;\" />\n<pre>\n<strong>Input:</strong> n = 7, cuts = [1,3,4,5]\n<strong>Output:</strong> 16\n<strong>Explanation:</strong> Using cuts order = [1, 3, 4, 5] as in the input leads to the following scenario:\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/07/21/e11.jpg\" style=\"width: 350px; height: 284px;\" />\nThe first cut is done to a rod of length 7 so the cost is 7. The second cut is done to a rod of length 6 (i.e. the second part of the first cut), the third is done to a rod of length 4 and the last cut is to a rod of length 3. The total cost is 7 + 6 + 4 + 3 = 20.\nRearranging the cuts to be [3, 5, 1, 4] for example will lead to a scenario with total cost = 16 (as shown in the example photo 7 + 4 + 3 + 2 = 16).</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 9, cuts = [5,6,1,4,2]\n<strong>Output:</strong> 22\n<strong>Explanation:</strong> If you try the given cuts ordering the cost will be 25.\nThere are much ordering with total cost <= 25, for example, the order [4, 6, 5, 2, 1] has total cost = 22 which is the minimum possible.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>2 <= n <= 10<sup>6</sup></code></li>\n\t<li><code>1 <= cuts.length <= min(n - 1, 100)</code></li>\n\t<li><code>1 <= cuts[i] <= n - 1</code></li>\n\t<li>All the integers in <code>cuts</code> array are <strong>distinct</strong>.</li>\n</ul>\n",
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"translatedTitle": "切棍子的最小成本",
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"translatedContent": "<p>有一根长度为 <code>n</code> 个单位的木棍，棍上从 <code>0</code> 到 <code>n</code> 标记了若干位置。例如，长度为 <strong>6</strong> 的棍子可以标记如下：</p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/09/statement.jpg\" style=\"height: 111px; width: 521px;\" /></p>\n\n<p>给你一个整数数组 <code>cuts</code> ，其中 <code>cuts[i]</code> 表示你需要将棍子切开的位置。</p>\n\n<p>你可以按顺序完成切割，也可以根据需要更改切割的顺序。</p>\n\n<p>每次切割的成本都是当前要切割的棍子的长度，切棍子的总成本是历次切割成本的总和。对棍子进行切割将会把一根木棍分成两根较小的木棍（这两根木棍的长度和就是切割前木棍的长度）。请参阅第一个示例以获得更直观的解释。</p>\n\n<p>返回切棍子的 <strong>最小总成本</strong> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/09/e1.jpg\" style=\"height: 284px; width: 350px;\" /></p>\n\n<pre>\n<strong>输入：</strong>n = 7, cuts = [1,3,4,5]\n<strong>输出：</strong>16\n<strong>解释：</strong>按 [1, 3, 4, 5] 的顺序切割的情况如下所示：\n<img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/08/09/e11.jpg\" style=\"height: 284px; width: 350px;\" />\n第一次切割长度为 7 的棍子，成本为 7 。第二次切割长度为 6 的棍子（即第一次切割得到的第二根棍子），第三次切割为长度 4 的棍子，最后切割长度为 3 的棍子。总成本为 7 + 6 + 4 + 3 = 20 。\n而将切割顺序重新排列为 [3, 5, 1, 4] 后，总成本 = 16（如示例图中 7 + 4 + 3 + 2 = 16）。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>n = 9, cuts = [5,6,1,4,2]\n<strong>输出：</strong>22\n<strong>解释：</strong>如果按给定的顺序切割，则总成本为 25 。总成本 <= 25 的切割顺序很多，例如，[4, 6, 5, 2, 1] 的总成本 = 22，是所有可能方案中成本最小的。</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>2 <= n <= 10^6</code></li>\n\t<li><code>1 <= cuts.length <= min(n - 1, 100)</code></li>\n\t<li><code>1 <= cuts[i] <= n - 1</code></li>\n\t<li><code>cuts</code> 数组中的所有整数都 <strong>互不相同</strong></li>\n</ul>\n",
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"When you try to get the minimum cost between i and j, try all possible cuts k between them, dp[i][j] = min(dp[i][k] + dp[k][j]) + (j - i) for all possible cuts k between them."
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