leetcode-problemset/leetcode-cn/originData/minimum-cost-to-make-at-least-one-valid-path-in-a-grid.json

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            "questionId": "1485",
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            "title": "Minimum Cost to Make at Least One Valid Path in a Grid",
            "titleSlug": "minimum-cost-to-make-at-least-one-valid-path-in-a-grid",
            "content": "<p>Given an <code>m x n</code> grid. Each cell of the grid has a sign pointing to the next cell you should visit if you are currently in this cell. The sign of <code>grid[i][j]</code> can be:</p>\n\n<ul>\n\t<li><code>1</code> which means go to the cell to the right. (i.e go from <code>grid[i][j]</code> to <code>grid[i][j + 1]</code>)</li>\n\t<li><code>2</code> which means go to the cell to the left. (i.e go from <code>grid[i][j]</code> to <code>grid[i][j - 1]</code>)</li>\n\t<li><code>3</code> which means go to the lower cell. (i.e go from <code>grid[i][j]</code> to <code>grid[i + 1][j]</code>)</li>\n\t<li><code>4</code> which means go to the upper cell. (i.e go from <code>grid[i][j]</code> to <code>grid[i - 1][j]</code>)</li>\n</ul>\n\n<p>Notice that there could be some signs on the cells of the grid that point outside the grid.</p>\n\n<p>You will initially start at the upper left cell <code>(0, 0)</code>. A valid path in the grid is a path that starts from the upper left cell <code>(0, 0)</code> and ends at the bottom-right cell <code>(m - 1, n - 1)</code> following the signs on the grid. The valid path does not have to be the shortest.</p>\n\n<p>You can modify the sign on a cell with <code>cost = 1</code>. You can modify the sign on a cell <strong>one time only</strong>.</p>\n\n<p>Return <em>the minimum cost to make the grid have at least one valid path</em>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/13/grid1.png\" style=\"width: 400px; height: 390px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,1,1,1],[2,2,2,2],[1,1,1,1],[2,2,2,2]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> You will start at point (0, 0).\nThe path to (3, 3) is as follows. (0, 0) --&gt; (0, 1) --&gt; (0, 2) --&gt; (0, 3) change the arrow to down with cost = 1 --&gt; (1, 3) --&gt; (1, 2) --&gt; (1, 1) --&gt; (1, 0) change the arrow to down with cost = 1 --&gt; (2, 0) --&gt; (2, 1) --&gt; (2, 2) --&gt; (2, 3) change the arrow to down with cost = 1 --&gt; (3, 3)\nThe total cost = 3.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/13/grid2.png\" style=\"width: 350px; height: 341px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,1,3],[3,2,2],[1,1,4]]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> You can follow the path from (0, 0) to (2, 2).\n</pre>\n\n<p><strong>Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/13/grid3.png\" style=\"width: 200px; height: 192px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,2],[4,3]]\n<strong>Output:</strong> 1\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>1 &lt;= m, n &lt;= 100</code></li>\n\t<li><code>1 &lt;= grid[i][j] &lt;= 4</code></li>\n</ul>\n",
            "translatedTitle": "使网格图至少有一条有效路径的最小代价",
            "translatedContent": "<p>给你一个 m x n 的网格图&nbsp;<code>grid</code>&nbsp;。&nbsp;<code>grid</code>&nbsp;中每个格子都有一个数字，对应着从该格子出发下一步走的方向。&nbsp;<code>grid[i][j]</code>&nbsp;中的数字可能为以下几种情况：</p>\n\n<ul>\n\t<li><strong>1</strong>&nbsp;，下一步往右走，也就是你会从 <code>grid[i][j]</code>&nbsp;走到 <code>grid[i][j + 1]</code></li>\n\t<li><strong>2</strong>&nbsp;，下一步往左走，也就是你会从 <code>grid[i][j]</code>&nbsp;走到 <code>grid[i][j - 1]</code></li>\n\t<li><strong>3</strong>&nbsp;，下一步往下走，也就是你会从 <code>grid[i][j]</code>&nbsp;走到 <code>grid[i + 1][j]</code></li>\n\t<li><strong>4</strong>&nbsp;，下一步往上走，也就是你会从 <code>grid[i][j]</code>&nbsp;走到 <code>grid[i - 1][j]</code></li>\n</ul>\n\n<p>注意网格图中可能会有&nbsp;<strong>无效数字</strong>&nbsp;，因为它们可能指向&nbsp;<code>grid</code>&nbsp;以外的区域。</p>\n\n<p>一开始，你会从最左上角的格子&nbsp;<code>(0,0)</code>&nbsp;出发。我们定义一条&nbsp;<strong>有效路径</strong>&nbsp;为从格子&nbsp;<code>(0,0)</code>&nbsp;出发，每一步都顺着数字对应方向走，最终在最右下角的格子&nbsp;<code>(m - 1, n - 1)</code>&nbsp;结束的路径。有效路径&nbsp;<strong>不需要是最短路径</strong>&nbsp;。</p>\n\n<p>你可以花费&nbsp;<code>cost = 1</code>&nbsp;的代价修改一个格子中的数字，但每个格子中的数字&nbsp;<strong>只能修改一次</strong>&nbsp;。</p>\n\n<p>请你返回让网格图至少有一条有效路径的最小代价。</p>\n\n<p>&nbsp;</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/2020/02/29/grid1.png\" style=\"height: 528px; width: 542px;\"></p>\n\n<pre><strong>输入：</strong>grid = [[1,1,1,1],[2,2,2,2],[1,1,1,1],[2,2,2,2]]\n<strong>输出：</strong>3\n<strong>解释：</strong>你将从点 (0, 0) 出发。\n到达 (3, 3) 的路径为： (0, 0) --&gt; (0, 1) --&gt; (0, 2) --&gt; (0, 3) 花费代价 cost = 1 使方向向下 --&gt; (1, 3) --&gt; (1, 2) --&gt; (1, 1) --&gt; (1, 0) 花费代价 cost = 1 使方向向下 --&gt; (2, 0) --&gt; (2, 1) --&gt; (2, 2) --&gt; (2, 3) 花费代价 cost = 1 使方向向下 --&gt; (3, 3)\n总花费为 cost = 3.\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/02/29/grid2.png\" style=\"height: 408px; width: 419px;\"></p>\n\n<pre><strong>输入：</strong>grid = [[1,1,3],[3,2,2],[1,1,4]]\n<strong>输出：</strong>0\n<strong>解释：</strong>不修改任何数字你就可以从 (0, 0) 到达 (2, 2) 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/02/29/grid3.png\" style=\"height: 302px; width: 314px;\"></p>\n\n<pre><strong>输入：</strong>grid = [[1,2],[4,3]]\n<strong>输出：</strong>1\n</pre>\n\n<p><strong>示例 4：</strong></p>\n\n<pre><strong>输入：</strong>grid = [[2,2,2],[2,2,2]]\n<strong>输出：</strong>3\n</pre>\n\n<p><strong>示例 5：</strong></p>\n\n<pre><strong>输入：</strong>grid = [[4]]\n<strong>输出：</strong>0\n</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>1 &lt;= m, n &lt;= 100</code></li>\n</ul>\n",
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href=\\\"https:\\/\\/github.com\\/datastructures-js\\/queue\\\" target=\\\"_blank\\\"> datastructures-js\\/queue<\\/a>\\u3002<\\/p>\"],\"ruby\":[\"Ruby\",\"<p>\\u4f7f\\u7528<code>Ruby 3.1<\\/code>\\u6267\\u884c<\\/p>\\r\\n\\r\\n<p>\\u4e00\\u4e9b\\u5e38\\u7528\\u7684\\u6570\\u636e\\u7ed3\\u6784\\u5df2\\u5728 Algorithms \\u6a21\\u5757\\u4e2d\\u63d0\\u4f9b\\uff1ahttps:\\/\\/www.rubydoc.info\\/github\\/kanwei\\/algorithms\\/Algorithms<\\/p>\"],\"swift\":[\"Swift\",\"<p>\\u7248\\u672c\\uff1a<code>Swift 5.5.2<\\/code><\\/p>\\r\\n\\r\\n<p>\\u6211\\u4eec\\u901a\\u5e38\\u4fdd\\u8bc1\\u66f4\\u65b0\\u5230 <a href=\\\"https:\\/\\/swift.org\\/download\\/\\\" target=\\\"_blank\\\">Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\"<p>\\u7248\\u672c\\uff1a<code>Go 1.17<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 <a href=\\\"https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/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 2.13<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"<p>\\u7248\\u672c\\uff1a<code>Kotlin 1.3.10<\\/code><\\/p>\"],\"rust\":[\"Rust\",\"<p>\\u7248\\u672c\\uff1a<code>rust 1.58.1<\\/code><\\/p>\\r\\n\\r\\n<p>\\u652f\\u6301 crates.io \\u7684 <a href=\\\"https:\\/\\/crates.io\\/crates\\/rand\\\" target=\\\"_blank\\\">rand<\\/a><\\/p>\"],\"php\":[\"PHP\",\"<p><code>PHP 8.1<\\/code>.<\\/p>\\r\\n\\r\\n<p>With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"<p>TypeScript 4.5.4<\\/p>\\r\\n\\r\\n<p>Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2020<\\/p>\"],\"racket\":[\"Racket\",\"<p><a href=\\\"https:\\/\\/docs.racket-lang.org\\/guide\\/performance.html#%28tech._c%29\\\" target=\\\"_blank\\\">Racket CS<\\/a> v8.3<\\/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 24.2\"],\"elixir\":[\"Elixir\",\"Elixir 1.13.0 with Erlang\\/OTP 24.2\"]}",
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