mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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181 lines
18 KiB
JSON
181 lines
18 KiB
JSON
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"questionId": "2625",
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"title": "Increment Submatrices by One",
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"content": "<p>You are given a positive integer <code>n</code>, indicating that we initially have an <code>n x n</code> <strong>0-indexed</strong> integer matrix <code>mat</code> filled with zeroes.</p>\n\n<p>You are also given a 2D integer array <code>query</code>. For each <code>query[i] = [row1<sub>i</sub>, col1<sub>i</sub>, row2<sub>i</sub>, col2<sub>i</sub>]</code>, you should do the following operation:</p>\n\n<ul>\n\t<li>Add <code>1</code> to <strong>every element</strong> in the submatrix with the <strong>top left</strong> corner <code>(row1<sub>i</sub>, col1<sub>i</sub>)</code> and the <strong>bottom right</strong> corner <code>(row2<sub>i</sub>, col2<sub>i</sub>)</code>. That is, add <code>1</code> to <code>mat[x][y]</code> for all <code>row1<sub>i</sub> <= x <= row2<sub>i</sub></code> and <code>col1<sub>i</sub> <= y <= col2<sub>i</sub></code>.</li>\n</ul>\n\n<p>Return<em> the matrix</em> <code>mat</code><em> after performing every query.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/11/24/p2example11.png\" style=\"width: 531px; height: 121px;\" />\n<pre>\n<strong>Input:</strong> n = 3, queries = [[1,1,2,2],[0,0,1,1]]\n<strong>Output:</strong> [[1,1,0],[1,2,1],[0,1,1]]\n<strong>Explanation:</strong> The diagram above shows the initial matrix, the matrix after the first query, and the matrix after the second query.\n- In the first query, we add 1 to every element in the submatrix with the top left corner (1, 1) and bottom right corner (2, 2).\n- In the second query, we add 1 to every element in the submatrix with the top left corner (0, 0) and bottom right corner (1, 1).\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2022/11/24/p2example22.png\" style=\"width: 261px; height: 82px;\" />\n<pre>\n<strong>Input:</strong> n = 2, queries = [[0,0,1,1]]\n<strong>Output:</strong> [[1,1],[1,1]]\n<strong>Explanation:</strong> The diagram above shows the initial matrix and the matrix after the first query.\n- In the first query we add 1 to every element in the matrix.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 500</code></li>\n\t<li><code>1 <= queries.length <= 10<sup>4</sup></code></li>\n\t<li><code>0 <= row1<sub>i</sub> <= row2<sub>i</sub> < n</code></li>\n\t<li><code>0 <= col1<sub>i</sub> <= col2<sub>i</sub> < n</code></li>\n</ul>\n",
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"code": "# @param {Integer} n\n# @param {Integer[][]} queries\n# @return {Integer[][]}\ndef range_add_queries(n, queries)\n \nend",
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"Imagine each row as a separate array. Instead of updating the whole submatrix together, we can use prefix sum to update each row separately.",
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"For each query, iterate over the rows i in the range [row1, row2] and add 1 to prefix sum S[i][col1], and subtract 1 from S[i][col2 + 1].",
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"After doing this operation for all the queries, update each row separately with S[i][j] = S[i][j] + S[i][j - 1]."
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