leetcode-problemset/leetcode-cn/originData/construct-product-matrix.json

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            "questionId": "3031",
            "questionFrontendId": "2906",
            "categoryTitle": "Algorithms",
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            "title": "Construct Product Matrix",
            "titleSlug": "construct-product-matrix",
            "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>&nbsp;</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>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n == grid.length&nbsp;&lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= m == grid[i].length&nbsp;&lt;= 10<sup>5</sup></code></li>\n\t<li><code>2 &lt;= n * m &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
            "translatedTitle": "构造乘积矩阵",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始、大小为 <code>n * m</code> 的二维整数矩阵 <code><font face=\"monospace\">grid</font></code><font face=\"monospace\"> ，定义一个下标从 <strong>0</strong> 开始、大小为 <code>n * m</code> 的的二维矩阵</font> <code>p</code>。如果满足以下条件，则称 <code>p</code> 为 <code>grid</code> 的 <strong>乘积矩阵</strong> ：</p>\n\n<ul>\n\t<li>对于每个元素 <code>p[i][j]</code> ，它的值等于除了 <code>grid[i][j]</code> 外所有元素的乘积。乘积对 <code>12345</code> 取余数。</li>\n</ul>\n\n<p>返回 <code>grid</code> 的乘积矩阵。</p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>grid = [[1,2],[3,4]]\n<strong>输出：</strong>[[24,12],[8,6]]\n<strong>解释：</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\n所以答案是 [[24,12],[8,6]] 。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>grid = [[12345],[2],[1]]\n<strong>输出：</strong>[[2],[0],[0]]\n<strong>解释：</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 ，所以 p[0][1] = 0\np[0][2] = grid[0][0] * grid[0][1] = 12345 * 2 = 24690. 24690 % 12345 = 0 ，所以 p[0][2] = 0\n所以答案是 [[2],[0],[0]] 。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= n == grid.length&nbsp;&lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= m == grid[i].length&nbsp;&lt;= 10<sup>5</sup></code></li>\n\t<li><code>2 &lt;= n * m &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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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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