leetcode-problemset/leetcode-cn/originData/check-if-matrix-is-x-matrix.json

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            "questionId": "2398",
            "questionFrontendId": "2319",
            "categoryTitle": "Algorithms",
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            "title": "Check if Matrix Is X-Matrix",
            "titleSlug": "check-if-matrix-is-x-matrix",
            "content": "<p>A square matrix is said to be an <strong>X-Matrix</strong> if <strong>both</strong> of the following conditions hold:</p>\n\n<ol>\n\t<li>All the elements in the diagonals of the matrix are <strong>non-zero</strong>.</li>\n\t<li>All other elements are 0.</li>\n</ol>\n\n<p>Given a 2D integer array <code>grid</code> of size <code>n x n</code> representing a square matrix, return <code>true</code><em> if </em><code>grid</code><em> is an X-Matrix</em>. Otherwise, return <code>false</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/05/03/ex1.jpg\" style=\"width: 311px; height: 320px;\" />\n<pre>\n<strong>Input:</strong> grid = [[2,0,0,1],[0,3,1,0],[0,5,2,0],[4,0,0,2]]\n<strong>Output:</strong> true\n<strong>Explanation:</strong> Refer to the diagram above. \nAn X-Matrix should have the green elements (diagonals) be non-zero and the red elements be 0.\nThus, grid is an X-Matrix.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/05/03/ex2.jpg\" style=\"width: 238px; height: 246px;\" />\n<pre>\n<strong>Input:</strong> grid = [[5,7,0],[0,3,1],[0,5,0]]\n<strong>Output:</strong> false\n<strong>Explanation:</strong> Refer to the diagram above.\nAn X-Matrix should have the green elements (diagonals) be non-zero and the red elements be 0.\nThus, grid is not an X-Matrix.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == grid.length == grid[i].length</code></li>\n\t<li><code>3 &lt;= n &lt;= 100</code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
            "translatedTitle": "判断矩阵是否是一个 X 矩阵",
            "translatedContent": "<p>如果一个正方形矩阵满足下述 <strong>全部</strong> 条件，则称之为一个 <strong>X 矩阵</strong> ：</p>\n\n<ol>\n\t<li>矩阵对角线上的所有元素都 <strong>不是 0</strong></li>\n\t<li>矩阵中所有其他元素都是 <strong>0</strong></li>\n</ol>\n\n<p>给你一个大小为 <code>n x n</code> 的二维整数数组 <code>grid</code> ，表示一个正方形矩阵。如果<em> </em><code>grid</code><em> </em>是一个 <strong>X 矩阵 </strong>，返回 <code>true</code> ；否则，返回 <code>false</code> 。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/05/03/ex1.jpg\" style=\"width: 311px; height: 320px;\">\n<pre><strong>输入：</strong>grid = [[2,0,0,1],[0,3,1,0],[0,5,2,0],[4,0,0,2]]\n<strong>输出：</strong>true\n<strong>解释：</strong>矩阵如上图所示。\nX 矩阵应该满足：绿色元素（对角线上）都不是 0 ，红色元素都是 0 。\n因此，grid 是一个 X 矩阵。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/05/03/ex2.jpg\" style=\"width: 238px; height: 246px;\">\n<pre><strong>输入：</strong>grid = [[5,7,0],[0,3,1],[0,5,0]]\n<strong>输出：</strong>false\n<strong>解释：</strong>矩阵如上图所示。\nX 矩阵应该满足：绿色元素（对角线上）都不是 0 ，红色元素都是 0 。\n因此，grid 不是一个 X 矩阵。\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == grid.length == grid[i].length</code></li>\n\t<li><code>3 &lt;= n &lt;= 100</code></li>\n\t<li><code>0 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>\n</ul>\n",
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                "Assuming a 0-indexed matrix, for a given cell on row i and column j, it is in a diagonal if and only if i == j or i == n - 1 - j.",
                "We can then iterate through the elements in the matrix to check if all the elements in the diagonals are non-zero and all other elements are zero."
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