mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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204 lines
17 KiB
JSON
204 lines
17 KiB
JSON
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"title": "Number of Increasing Paths in a Grid",
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"content": "<p>You are given an <code>m x n</code> integer matrix <code>grid</code>, where you can move from a cell to any adjacent cell in all <code>4</code> directions.</p>\n\n<p>Return <em>the number of <strong>strictly</strong> <strong>increasing</strong> paths in the grid such that you can start from <strong>any</strong> cell and end at <strong>any</strong> cell. </em>Since the answer may be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p>Two paths are considered different if they do not have exactly the same sequence of visited cells.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/05/10/griddrawio-4.png\" style=\"width: 181px; height: 121px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,1],[3,4]]\n<strong>Output:</strong> 8\n<strong>Explanation:</strong> The strictly increasing paths are:\n- Paths with length 1: [1], [1], [3], [4].\n- Paths with length 2: [1 -> 3], [1 -> 4], [3 -> 4].\n- Paths with length 3: [1 -> 3 -> 4].\nThe total number of paths is 4 + 3 + 1 = 8.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[1],[2]]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The strictly increasing paths are:\n- Paths with length 1: [1], [2].\n- Paths with length 2: [1 -> 2].\nThe total number of paths is 2 + 1 = 3.\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 <= 1000</code></li>\n\t<li><code>1 <= m * n <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= grid[i][j] <= 10<sup>5</sup></code></li>\n</ul>\n",
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"How can you calculate the number of increasing paths that start from a cell (i, j)? Think about dynamic programming.",
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"Define f(i, j) as the number of increasing paths starting from cell (i, j). Try to find how f(i, j) is related to each of f(i, j+1), f(i, j-1), f(i+1, j) and f(i-1, j)."
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