leetcode-problemset/leetcode-cn/originData/number-of-submatrices-that-sum-to-target.json

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            "title": "Number of Submatrices That Sum to Target",
            "titleSlug": "number-of-submatrices-that-sum-to-target",
            "content": "<p>Given a <code>matrix</code>&nbsp;and a <code>target</code>, return the number of non-empty submatrices that sum to <font face=\"monospace\">target</font>.</p>\n\n<p>A submatrix <code>x1, y1, x2, y2</code> is the set of all cells <code>matrix[x][y]</code> with <code>x1 &lt;= x &lt;= x2</code> and <code>y1 &lt;= y &lt;= y2</code>.</p>\n\n<p>Two submatrices <code>(x1, y1, x2, y2)</code> and <code>(x1&#39;, y1&#39;, x2&#39;, y2&#39;)</code> are different if they have some coordinate&nbsp;that is different: for example, if <code>x1 != x1&#39;</code>.</p>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/09/02/mate1.jpg\" style=\"width: 242px; height: 242px;\" />\n<pre>\n<strong>Input:</strong> matrix = [[0,1,0],[1,1,1],[0,1,0]], target = 0\n<strong>Output:</strong> 4\n<strong>Explanation:</strong> The four 1x1 submatrices that only contain 0.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> matrix = [[1,-1],[-1,1]], target = 0\n<strong>Output:</strong> 5\n<strong>Explanation:</strong> The two 1x2 submatrices, plus the two 2x1 submatrices, plus the 2x2 submatrix.\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> matrix = [[904]], target = 0\n<strong>Output:</strong> 0\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= matrix.length &lt;= 100</code></li>\n\t<li><code>1 &lt;= matrix[0].length &lt;= 100</code></li>\n\t<li><code>-1000 &lt;= matrix[i] &lt;= 1000</code></li>\n\t<li><code>-10^8 &lt;= target &lt;= 10^8</code></li>\n</ul>\n",
            "translatedTitle": "元素和为目标值的子矩阵数量",
            "translatedContent": "<p>给出矩阵 <code>matrix</code> 和目标值 <code>target</code>，返回元素总和等于目标值的非空子矩阵的数量。</p>\n\n<p>子矩阵 <code>x1, y1, x2, y2</code> 是满足 <code>x1 <= x <= x2</code> 且 <code>y1 <= y <= y2</code> 的所有单元 <code>matrix[x][y]</code> 的集合。</p>\n\n<p>如果 <code>(x1, y1, x2, y2)</code> 和 <code>(x1', y1', x2', y2')</code> 两个子矩阵中部分坐标不同（如：<code>x1 != x1'</code>），那么这两个子矩阵也不同。</p>\n\n<p> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/09/02/mate1.jpg\" style=\"width: 242px; height: 242px;\" /></p>\n\n<pre>\n<strong>输入：</strong>matrix = [[0,1,0],[1,1,1],[0,1,0]], target = 0\n<strong>输出：</strong>4\n<strong>解释：</strong>四个只含 0 的 1x1 子矩阵。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>matrix = [[1,-1],[-1,1]], target = 0\n<strong>输出：</strong>5\n<strong>解释：</strong>两个 1x2 子矩阵，加上两个 2x1 子矩阵，再加上一个 2x2 子矩阵。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>matrix = [[904]], target = 0\n<strong>输出：</strong>0\n</pre>\n\n<p> </p>\n\n<p><strong><strong>提示：</strong></strong></p>\n\n<ul>\n\t<li><code>1 <= matrix.length <= 100</code></li>\n\t<li><code>1 <= matrix[0].length <= 100</code></li>\n\t<li><code>-1000 <= matrix[i] <= 1000</code></li>\n\t<li><code>-10^8 <= target <= 10^8</code></li>\n</ul>\n",
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                "Using a 2D prefix sum, we can query the sum of any submatrix in O(1) time.\r\nNow for each (r1, r2), we can find the largest sum of a submatrix that uses every row in [r1, r2] in linear time using a sliding window."
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