mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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180 lines
18 KiB
JSON
180 lines
18 KiB
JSON
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"questionId": "3031",
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"title": "Construct Product Matrix",
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"content": "<p>Given a <strong>0-indexed</strong> 2D integer matrix <code><font face=\"monospace\">grid</font></code><font face=\"monospace\"> </font>of size <code>n * m</code>, we define a <strong>0-indexed</strong> 2D matrix <code>p</code> of size <code>n * m</code> as the <strong>product</strong> matrix of <code>grid</code> if the following condition is met:</p>\n\n<ul>\n\t<li>Each element <code>p[i][j]</code> is calculated as the product of all elements in <code>grid</code> except for the element <code>grid[i][j]</code>. This product is then taken modulo <code><font face=\"monospace\">12345</font></code>.</li>\n</ul>\n\n<p>Return <em>the product matrix of</em> <code><font face=\"monospace\">grid</font></code>.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[1,2],[3,4]]\n<strong>Output:</strong> [[24,12],[8,6]]\n<strong>Explanation:</strong> p[0][0] = grid[0][1] * grid[1][0] * grid[1][1] = 2 * 3 * 4 = 24\np[0][1] = grid[0][0] * grid[1][0] * grid[1][1] = 1 * 3 * 4 = 12\np[1][0] = grid[0][0] * grid[0][1] * grid[1][1] = 1 * 2 * 4 = 8\np[1][1] = grid[0][0] * grid[0][1] * grid[1][0] = 1 * 2 * 3 = 6\nSo the answer is [[24,12],[8,6]].</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[12345],[2],[1]]\n<strong>Output:</strong> [[2],[0],[0]]\n<strong>Explanation:</strong> p[0][0] = grid[0][1] * grid[0][2] = 2 * 1 = 2.\np[0][1] = grid[0][0] * grid[0][2] = 12345 * 1 = 12345. 12345 % 12345 = 0. So p[0][1] = 0.\np[0][2] = grid[0][0] * grid[0][1] = 12345 * 2 = 24690. 24690 % 12345 = 0. So p[0][2] = 0.\nSo the answer is [[2],[0],[0]].</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n == grid.length <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= m == grid[i].length <= 10<sup>5</sup></code></li>\n\t<li><code>2 <= n * m <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= grid[i][j] <= 10<sup>9</sup></code></li>\n</ul>\n",
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"difficulty": "Medium",
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"categoryTitle": "Algorithms",
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"name": "Prefix Sum",
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"code": "(define/contract (construct-product-matrix grid)\n (-> (listof (listof exact-integer?)) (listof (listof exact-integer?)))\n )",
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"code": "-spec construct_product_matrix(Grid :: [[integer()]]) -> [[integer()]].\nconstruct_product_matrix(Grid) ->\n .",
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"Try to solve this without using the <code>'/'</code> (division operation).",
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"Create two 2D arrays for <b>suffix</b> and <b>prefix</b> product, and use them to find the product for each position."
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