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leetcode-problemset/leetcode/originData/maximum-number-of-moves-in-a-grid.json

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"title": "Maximum Number of Moves in a Grid",
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"content": "<p>You are given a <strong>0-indexed</strong> <code>m x n</code> matrix <code>grid</code> consisting of <strong>positive</strong> integers.</p>\n\n<p>You can start at <strong>any</strong> cell in the first column of the matrix, and traverse the grid in the following way:</p>\n\n<ul>\n\t<li>From a cell <code>(row, col)</code>, you can move to any of the cells: <code>(row - 1, col + 1)</code>, <code>(row, col + 1)</code> and <code>(row + 1, col + 1)</code> such that the value of the cell you move to, should be <strong>strictly</strong> bigger than the value of the current cell.</li>\n</ul>\n\n<p>Return <em>the <strong>maximum</strong> number of <strong>moves</strong> that you can perform.</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/2023/04/11/yetgriddrawio-10.png\" style=\"width: 201px; height: 201px;\" />\n<pre>\n<strong>Input:</strong> grid = [[2,4,3,5],[5,4,9,3],[3,4,2,11],[10,9,13,15]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> We can start at the cell (0, 0) and make the following moves:\n- (0, 0) -&gt; (0, 1).\n- (0, 1) -&gt; (1, 2).\n- (1, 2) -&gt; (2, 3).\nIt can be shown that it is the maximum number of moves that can be made.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2023/04/12/yetgrid4drawio.png\" />\n<strong>Input:</strong> grid = [[3,2,4],[2,1,9],[1,1,7]]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> Starting from any cell in the first column we cannot perform any moves.\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;= 1000</code></li>\n\t<li><code>4 &lt;= m * n &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>6</sup></code></li>\n</ul>\n",
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"Consider using dynamic programming to find the maximum number of moves that can be made from each cell.",
"The final answer will be the maximum value in cells of the first column."
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