leetcode-problemset/leetcode-cn/originData/maximum-non-negative-product-in-a-matrix.json

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            "title": "Maximum Non Negative Product in a Matrix",
            "titleSlug": "maximum-non-negative-product-in-a-matrix",
            "content": "<p>You are given a <code>m x n</code> matrix <code>grid</code>. Initially, you are located at the top-left corner <code>(0, 0)</code>, and in each step, you can only <strong>move right or down</strong> in the matrix.</p>\n\n<p>Among all possible paths starting from the top-left corner <code>(0, 0)</code> and ending in the bottom-right corner <code>(m - 1, n - 1)</code>, find the path with the <strong>maximum non-negative product</strong>. The product of a path is the product of all integers in the grid cells visited along the path.</p>\n\n<p>Return the <em>maximum non-negative product <strong>modulo</strong> </em><code>10<sup>9</sup> + 7</code>. <em>If the maximum product is <strong>negative</strong>, return </em><code>-1</code>.</p>\n\n<p>Notice that the modulo is performed after getting the maximum product.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/23/product1.jpg\" style=\"width: 244px; height: 245px;\" />\n<pre>\n<strong>Input:</strong> grid = [[-1,-2,-3],[-2,-3,-3],[-3,-3,-2]]\n<strong>Output:</strong> -1\n<strong>Explanation:</strong> It is not possible to get non-negative product in the path from (0, 0) to (2, 2), so return -1.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/23/product2.jpg\" style=\"width: 244px; height: 245px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,-2,1],[1,-2,1],[3,-4,1]]\n<strong>Output:</strong> 8\n<strong>Explanation:</strong> Maximum non-negative product is shown (1 * 1 * -2 * -4 * 1 = 8).\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/23/product3.jpg\" style=\"width: 164px; height: 165px;\" />\n<pre>\n<strong>Input:</strong> grid = [[1,3],[0,-4]]\n<strong>Output:</strong> 0\n<strong>Explanation:</strong> Maximum non-negative product is shown (1 * 0 * -4 = 0).\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>1 &lt;= m, n &lt;= 15</code></li>\n\t<li><code>-4 &lt;= grid[i][j] &lt;= 4</code></li>\n</ul>\n",
            "translatedTitle": "矩阵的最大非负积",
            "translatedContent": "<p>给你一个大小为 <code>m x n</code> 的矩阵 <code>grid</code> 。最初，你位于左上角 <code>(0, 0)</code> ，每一步，你可以在矩阵中 <strong>向右</strong> 或 <strong>向下</strong> 移动。</p>\n\n<p>在从左上角 <code>(0, 0)</code> 开始到右下角 <code>(m - 1, n - 1)</code> 结束的所有路径中，找出具有 <strong>最大非负积</strong> 的路径。路径的积是沿路径访问的单元格中所有整数的乘积。</p>\n\n<p>返回 <strong>最大非负积 </strong>对<strong><em> </em><code>10<sup>9</sup>&nbsp;+ 7</code></strong> <strong>取余</strong> 的结果。如果最大积为 <strong>负数</strong> ，则返回<em> </em><code>-1</code> 。</p>\n\n<p><strong>注意，</strong>取余是在得到最大积之后执行的。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/23/product1.jpg\" style=\"width: 244px; height: 245px;\" />\n<pre>\n<strong>输入：</strong>grid = [[-1,-2,-3],[-2,-3,-3],[-3,-3,-2]]\n<strong>输出：</strong>-1\n<strong>解释：</strong>从 (0, 0) 到 (2, 2) 的路径中无法得到非负积，所以返回 -1 。</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/23/product2.jpg\" style=\"width: 244px; height: 245px;\" />\n<pre>\n<strong>输入：</strong>grid = [[1,-2,1],[1,-2,1],[3,-4,1]]\n<strong>输出：</strong>8\n<strong>解释：</strong>最大非负积对应的路径如图所示 (1 * 1 * -2 * -4 * 1 = 8)\n</pre>\n\n<p><strong>示例 3：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/12/23/product3.jpg\" style=\"width: 164px; height: 165px;\" />\n<pre>\n<strong>输入：</strong>grid = [[1,3],[0,-4]]\n<strong>输出：</strong>0\n<strong>解释：</strong>最大非负积对应的路径如图所示 (1 * 0 * -4 = 0)\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</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 &lt;= m, n &lt;= 15</code></li>\n\t<li><code>-4 &lt;= grid[i][j] &lt;= 4</code></li>\n</ul>\n",
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