mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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205 lines
18 KiB
JSON
205 lines
18 KiB
JSON
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"questionId": "2697",
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"title": "Minimum Number of Visited Cells in a Grid",
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"content": "<p>You are given a <strong>0-indexed</strong> <code>m x n</code> integer matrix <code>grid</code>. Your initial position is at the <strong>top-left</strong> cell <code>(0, 0)</code>.</p>\n\n<p>Starting from the cell <code>(i, j)</code>, you can move to one of the following cells:</p>\n\n<ul>\n\t<li>Cells <code>(i, k)</code> with <code>j < k <= grid[i][j] + j</code> (rightward movement), or</li>\n\t<li>Cells <code>(k, j)</code> with <code>i < k <= grid[i][j] + i</code> (downward movement).</li>\n</ul>\n\n<p>Return <em>the minimum number of cells you need to visit to reach the <strong>bottom-right</strong> cell</em> <code>(m - 1, n - 1)</code>. If there is no valid path, return <code>-1</code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/01/25/ex1.png\" style=\"width: 271px; height: 171px;\" />\n<pre>\n<strong>Input:</strong> grid = [[3,4,2,1],[4,2,3,1],[2,1,0,0],[2,4,0,0]]\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The image above shows one of the paths that visits exactly 4 cells.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/01/25/ex2.png\" style=\"width: 271px; height: 171px;\" />\n<pre>\n<strong>Input:</strong> grid = [[3,4,2,1],[4,2,1,1],[2,1,1,0],[3,4,1,0]]\n<strong>Output:</strong> 3\n<strong>Explanation: </strong>The image above shows one of the paths that visits exactly 3 cells.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/01/26/ex3.png\" style=\"width: 181px; height: 81px;\" />\n<pre>\n<strong>Input:</strong> grid = [[2,1,0],[1,0,0]]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> It can be proven that no path exists.\n</pre>\n\n<p> </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 <= m, n <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= m * n <= 10<sup>5</sup></code></li>\n\t<li><code>0 <= grid[i][j] < m * n</code></li>\n\t<li><code>grid[m - 1][n - 1] == 0</code></li>\n</ul>\n",
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"For each cell (i,j), it is critical to find out the minimum number of steps to reach (i,j), denoted dis[i][j], quickly, given the tight constraint.",
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"Calculate dis[i][j] going left to right, top to bottom.",
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"Suppose we want to calculate dis[i][j], keep track of a priority queue that stores (dis[i][k], i, k) for all k ≤ j, and another priority queue that stores (dis[k][j], k, j) for all k ≤ i."
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