mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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186 lines
17 KiB
JSON
186 lines
17 KiB
JSON
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"title": "Number of Submatrices That Sum to Target",
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"content": "<p>Given a <code>matrix</code> 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 <= x <= x2</code> and <code>y1 <= y <= y2</code>.</p>\n\n<p>Two submatrices <code>(x1, y1, x2, y2)</code> and <code>(x1', y1', x2', y2')</code> are different if they have some coordinate that is different: for example, if <code>x1 != x1'</code>.</p>\n\n<p> </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> </p>\n<p><strong>Constraints:</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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"categoryTitle": "Algorithms",
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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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