mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-11 02:58:13 +08:00
166 lines
22 KiB
JSON
166 lines
22 KiB
JSON
{
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"questionId": "576",
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"questionFrontendId": "576",
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"categoryTitle": "Algorithms",
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"boundTopicId": 1515,
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"title": "Out of Boundary Paths",
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"titleSlug": "out-of-boundary-paths",
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"content": "<p>There is an <code>m x n</code> grid with a ball. The ball is initially at the position <code>[startRow, startColumn]</code>. You are allowed to move the ball to one of the four adjacent cells in the grid (possibly out of the grid crossing the grid boundary). You can apply <strong>at most</strong> <code>maxMove</code> moves to the ball.</p>\n\n<p>Given the five integers <code>m</code>, <code>n</code>, <code>maxMove</code>, <code>startRow</code>, <code>startColumn</code>, return the number of paths to move the ball out of the grid boundary. Since the answer can be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_1.png\" style=\"width: 500px; height: 296px;\" />\n<pre>\n<strong>Input:</strong> m = 2, n = 2, maxMove = 2, startRow = 0, startColumn = 0\n<strong>Output:</strong> 6\n</pre>\n\n<p><strong>Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_2.png\" style=\"width: 500px; height: 293px;\" />\n<pre>\n<strong>Input:</strong> m = 1, n = 3, maxMove = 3, startRow = 0, startColumn = 1\n<strong>Output:</strong> 12\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= m, n <= 50</code></li>\n\t<li><code>0 <= maxMove <= 50</code></li>\n\t<li><code>0 <= startRow < m</code></li>\n\t<li><code>0 <= startColumn < n</code></li>\n</ul>\n",
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"translatedTitle": "出界的路径数",
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"translatedContent": "<p>给你一个大小为 <code>m x n</code> 的网格和一个球。球的起始坐标为 <code>[startRow, startColumn]</code> 。你可以将球移到在四个方向上相邻的单元格内(可以穿过网格边界到达网格之外)。你 <strong>最多</strong> 可以移动 <code>maxMove</code> 次球。</p>\n\n<p>给你五个整数 <code>m</code>、<code>n</code>、<code>maxMove</code>、<code>startRow</code> 以及 <code>startColumn</code> ,找出并返回可以将球移出边界的路径数量。因为答案可能非常大,返回对 <code>10<sup>9</sup> + 7</code> <strong>取余</strong> 后的结果。</p>\n\n<p> </p>\n\n<p><strong>示例 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_1.png\" style=\"width: 500px; height: 296px;\" />\n<pre>\n<strong>输入:</strong>m = 2, n = 2, maxMove = 2, startRow = 0, startColumn = 0\n<strong>输出:</strong>6\n</pre>\n\n<p><strong>示例 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/04/28/out_of_boundary_paths_2.png\" style=\"width: 500px; height: 293px;\" />\n<pre>\n<strong>输入:</strong>m = 1, n = 3, maxMove = 3, startRow = 0, startColumn = 1\n<strong>输出:</strong>12\n</pre>\n\n<p> </p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 <= m, n <= 50</code></li>\n\t<li><code>0 <= maxMove <= 50</code></li>\n\t<li><code>0 <= startRow < m</code></li>\n\t<li><code>0 <= startColumn < n</code></li>\n</ul>\n",
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"code": "# @param {Integer} m\n# @param {Integer} n\n# @param {Integer} max_move\n# @param {Integer} start_row\n# @param {Integer} start_column\n# @return {Integer}\ndef find_paths(m, n, max_move, start_row, start_column)\n\nend",
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"Is traversing every path feasible? There are many possible paths for a small matrix. Try to optimize it.",
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"Can we use some space to store the number of paths and update them after every move?",
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"One obvious thing: the ball will go out of the boundary only by crossing it. Also, there is only one possible way the ball can go out of the boundary from the boundary cell except for corner cells. From the corner cell, the ball can go out in two different ways.\r\n\r\nCan you use this thing to solve the problem?"
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