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"categoryTitle": "Algorithms",
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"title": "Count Square Submatrices with All Ones",
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"content": "<p>Given a <code>m * n</code> matrix of ones and zeros, return how many <strong>square</strong> submatrices have all ones.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> matrix =\n[\n&nbsp; [0,1,1,1],\n&nbsp; [1,1,1,1],\n&nbsp; [0,1,1,1]\n]\n<strong>Output:</strong> 15\n<strong>Explanation:</strong> \nThere are <strong>10</strong> squares of side 1.\nThere are <strong>4</strong> squares of side 2.\nThere is <strong>1</strong> square of side 3.\nTotal number of squares = 10 + 4 + 1 = <strong>15</strong>.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> matrix = \n[\n [1,0,1],\n [1,1,0],\n [1,1,0]\n]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> \nThere are <b>6</b> squares of side 1. \nThere is <strong>1</strong> square of side 2. \nTotal number of squares = 6 + 1 = <b>7</b>.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= arr.length&nbsp;&lt;= 300</code></li>\n\t<li><code>1 &lt;= arr[0].length&nbsp;&lt;= 300</code></li>\n\t<li><code>0 &lt;= arr[i][j] &lt;= 1</code></li>\n</ul>\n",
"translatedTitle": "统计全为 1 的正方形子矩阵",
"translatedContent": "<p>给你一个&nbsp;<code>m * n</code>&nbsp;的矩阵,矩阵中的元素不是 <code>0</code> 就是 <code>1</code>,请你统计并返回其中完全由 <code>1</code> 组成的 <strong>正方形</strong> 子矩阵的个数。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1</strong></p>\n\n<pre><strong>输入:</strong>matrix =\n[\n&nbsp; [0,1,1,1],\n&nbsp; [1,1,1,1],\n&nbsp; [0,1,1,1]\n]\n<strong>输出:</strong>15\n<strong>解释:</strong> \n边长为 1 的正方形有 <strong>10</strong> 个。\n边长为 2 的正方形有 <strong>4</strong> 个。\n边长为 3 的正方形有 <strong>1</strong> 个。\n正方形的总数 = 10 + 4 + 1 = <strong>15</strong>.\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre><strong>输入:</strong>matrix = \n[\n [1,0,1],\n [1,1,0],\n [1,1,0]\n]\n<strong>输出:</strong>7\n<strong>解释:</strong>\n边长为 1 的正方形有 <strong>6</strong> 个。 \n边长为 2 的正方形有 <strong>1</strong> 个。\n正方形的总数 = 6 + 1 = <strong>7</strong>.\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= arr.length&nbsp;&lt;= 300</code></li>\n\t<li><code>1 &lt;= arr[0].length&nbsp;&lt;= 300</code></li>\n\t<li><code>0 &lt;= arr[i][j] &lt;= 1</code></li>\n</ul>\n",
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"Create an additive table that counts the sum of elements of submatrix with the superior corner at (0,0).",
"Loop over all subsquares in O(n^3) and check if the sum make the whole array to be ones, if it checks then add 1 to the answer."
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