leetcode-problemset/leetcode-cn/originData/minimum-path-cost-in-a-grid.json

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        "question": {
            "questionId": "1394",
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            "categoryTitle": "Algorithms",
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            "title": "Minimum Path Cost in a Grid",
            "titleSlug": "minimum-path-cost-in-a-grid",
            "content": "<p>You are given a <strong>0-indexed</strong> <code>m x n</code> integer matrix <code>grid</code> consisting of <strong>distinct</strong> integers from <code>0</code> to <code>m * n - 1</code>. You can move in this matrix from a cell to any other cell in the <strong>next</strong> row. That is, if you are in cell <code>(x, y)</code> such that <code>x &lt; m - 1</code>, you can move to any of the cells <code>(x + 1, 0)</code>, <code>(x + 1, 1)</code>, ..., <code>(x + 1, n - 1)</code>. <strong>Note</strong> that it is not possible to move from cells in the last row.</p>\n\n<p>Each possible move has a cost given by a <strong>0-indexed</strong> 2D array <code>moveCost</code> of size <code>(m * n) x n</code>, where <code>moveCost[i][j]</code> is the cost of moving from a cell with value <code>i</code> to a cell in column <code>j</code> of the next row. The cost of moving from cells in the last row of <code>grid</code> can be ignored.</p>\n\n<p>The cost of a path in <code>grid</code> is the <strong>sum</strong> of all values of cells visited plus the <strong>sum</strong> of costs of all the moves made. Return <em>the <strong>minimum</strong> cost of a path that starts from any cell in the <strong>first</strong> row and ends at any cell in the <strong>last</strong> row.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/28/griddrawio-2.png\" style=\"width: 301px; height: 281px;\" />\n<pre>\n<strong>Input:</strong> grid = [[5,3],[4,0],[2,1]], moveCost = [[9,8],[1,5],[10,12],[18,6],[2,4],[14,3]]\n<strong>Output:</strong> 17\n<strong>Explanation: </strong>The path with the minimum possible cost is the path 5 -&gt; 0 -&gt; 1.\n- The sum of the values of cells visited is 5 + 0 + 1 = 6.\n- The cost of moving from 5 to 0 is 3.\n- The cost of moving from 0 to 1 is 8.\nSo the total cost of the path is 6 + 3 + 8 = 17.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[5,1,2],[4,0,3]], moveCost = [[12,10,15],[20,23,8],[21,7,1],[8,1,13],[9,10,25],[5,3,2]]\n<strong>Output:</strong> 6\n<strong>Explanation:</strong> The path with the minimum possible cost is the path 2 -&gt; 3.\n- The sum of the values of cells visited is 2 + 3 = 5.\n- The cost of moving from 2 to 3 is 1.\nSo the total cost of this path is 5 + 1 = 6.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>2 &lt;= m, n &lt;= 50</code></li>\n\t<li><code>grid</code> consists of distinct integers from <code>0</code> to <code>m * n - 1</code>.</li>\n\t<li><code>moveCost.length == m * n</code></li>\n\t<li><code>moveCost[i].length == n</code></li>\n\t<li><code>1 &lt;= moveCost[i][j] &lt;= 100</code></li>\n</ul>\n",
            "translatedTitle": "网格中的最小路径代价",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的整数矩阵&nbsp;<code>grid</code> ，矩阵大小为 <code>m x n</code> ，由从 <code>0</code> 到 <code>m * n - 1</code> 的不同整数组成。你可以在此矩阵中，从一个单元格移动到 <strong>下一行</strong> 的任何其他单元格。如果你位于单元格 <code>(x, y)</code> ，且满足 <code>x &lt; m - 1</code> ，你可以移动到 <code>(x + 1, 0)</code>, <code>(x + 1, 1)</code>, ..., <code>(x + 1, n - 1)</code><strong> </strong>中的任何一个单元格。<strong>注意：</strong>&nbsp;在最后一行中的单元格不能触发移动。</p>\n\n<p>每次可能的移动都需要付出对应的代价，代价用一个下标从 <strong>0</strong> 开始的二维数组 <code>moveCost</code> 表示，该数组大小为 <code>(m * n) x n</code> ，其中 <code>moveCost[i][j]</code> 是从值为 <code>i</code> 的单元格移动到下一行第 <code>j</code> 列单元格的代价。从&nbsp;<code>grid</code> 最后一行的单元格移动的代价可以忽略。</p>\n\n<p><code>grid</code> 一条路径的代价是：所有路径经过的单元格的 <strong>值之和</strong> 加上 所有移动的 <strong>代价之和 </strong>。从 <strong>第一行</strong> 任意单元格出发，返回到达 <strong>最后一行</strong> 任意单元格的最小路径代价<em>。</em></p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/04/28/griddrawio-2.png\" style=\"width: 301px; height: 281px;\" /></p>\n\n<pre>\n<strong>输入：</strong>grid = [[5,3],[4,0],[2,1]], moveCost = [[9,8],[1,5],[10,12],[18,6],[2,4],[14,3]]\n<strong>输出：</strong>17\n<strong>解释：</strong>最小代价的路径是 5 -&gt; 0 -&gt; 1 。\n- 路径途经单元格值之和 5 + 0 + 1 = 6 。\n- 从 5 移动到 0 的代价为 3 。\n- 从 0 移动到 1 的代价为 8 。\n路径总代价为 6 + 3 + 8 = 17 。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>grid = [[5,1,2],[4,0,3]], moveCost = [[12,10,15],[20,23,8],[21,7,1],[8,1,13],[9,10,25],[5,3,2]]\n<strong>输出：</strong>6\n<strong>解释：</strong>\n最小代价的路径是 2 -&gt; 3 。 \n- 路径途经单元格值之和 2 + 3 = 5 。 \n- 从 2 移动到 3 的代价为 1 。 \n路径总代价为 5 + 1 = 6 。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>2 &lt;= m, n &lt;= 50</code></li>\n\t<li><code>grid</code> 由从 <code>0</code> 到 <code>m * n - 1</code> 的不同整数组成</li>\n\t<li><code>moveCost.length == m * n</code></li>\n\t<li><code>moveCost[i].length == n</code></li>\n\t<li><code>1 &lt;= moveCost[i][j] &lt;= 100</code></li>\n</ul>\n",
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\\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.11<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap \\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 <a href=\\\"http:\\/\\/www.grantjenks.com\\/docs\\/sortedcontainers\\/\\\" target=\\\"_blank\\\">sortedcontainers<\\/a> \\u5e93\\u3002<\\/p>\"],\"scala\":[\"Scala\",\"<p>\\u7248\\u672c\\uff1a<code>Scala 3.3.1<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"<p>\\u7248\\u672c\\uff1a<code>Kotlin 1.9.0<\\/code><\\/p>\\r\\n\\r\\n<p>\\u6211\\u4eec\\u4f7f\\u7528\\u7684\\u662f JetBrains \\u63d0\\u4f9b\\u7684 experimental compiler\\u3002\\u5982\\u679c\\u60a8\\u8ba4\\u4e3a\\u60a8\\u9047\\u5230\\u4e86\\u7f16\\u8bd1\\u5668\\u76f8\\u5173\\u7684\\u95ee\\u9898\\uff0c\\u8bf7\\u5411\\u6211\\u4eec\\u53cd\\u9988<\\/p>\"],\"rust\":[\"Rust\",\"<p>\\u7248\\u672c\\uff1a<code>rust 1.79.0<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 crates.io \\u7684 <a href=\\\"https:\\/\\/crates.io\\/crates\\/rand\\\" target=\\\"_blank\\\">rand<\\/a> \\u548c <a href=\\\"https:\\/\\/crates.io\\/crates\\/regex\\\" target=\\\"_blank\\\">regex<\\/a><\\/p>\"],\"php\":[\"PHP\",\"<p><code>PHP 8.2<\\/code>.<\\/p>\\r\\n\\r\\n<p>With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"<p>TypeScript 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href=\\\"https:\\/\\/docs.racket-lang.org\\/guide\\/performance.html#%28tech._c%29\\\" target=\\\"_blank\\\">Racket CS<\\/a> v8.15<\\/p>\\r\\n\\r\\n<p>\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n<p>\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 26\"],\"elixir\":[\"Elixir\",\"Elixir 1.17 with Erlang\\/OTP 26\"],\"dart\":[\"Dart\",\"<p>Dart 3.2\\u3002\\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 <a href=\\\"https:\\/\\/pub.dev\\/packages\\/collection\\/versions\\/1.18.0\\\" target=\\\"_blank\\\">collection<\\/a> \\u5305<\\/p>\\r\\n\\r\\n<p>\\u60a8\\u7684\\u4ee3\\u7801\\u5c06\\u4f1a\\u88ab\\u4e0d\\u7f16\\u8bd1\\u76f4\\u63a5\\u8fd0\\u884c<\\/p>\"],\"cangjie\":[\"Cangjie\",\"<p>\\u7248\\u672c\\uff1a0.53.11 (cjnative)<\\/p>\\r\\n\\r\\n<p>\\u7f16\\u8bd1\\u53c2\\u6570\\uff1a<code>-O2 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