leetcode-problemset/leetcode-cn/problem (English)/子矩阵元素加 1(English) [increment-submatrices-by-one].html

<p>You are given a positive integer <code>n</code>, indicating that we initially have an <code>n x n</code>&nbsp;<strong>0-indexed</strong> integer matrix <code>mat</code> filled with zeroes.</p>

<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>

<ul>
	<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> &lt;= x &lt;= row2<sub>i</sub></code> and <code>col1<sub>i</sub> &lt;= y &lt;= col2<sub>i</sub></code>.</li>
</ul>

<p>Return<em> the matrix</em> <code>mat</code><em> after performing every query.</em></p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/11/24/p2example11.png" style="width: 531px; height: 121px;" />
<pre>
<strong>Input:</strong> n = 3, queries = [[1,1,2,2],[0,0,1,1]]
<strong>Output:</strong> [[1,1,0],[1,2,1],[0,1,1]]
<strong>Explanation:</strong> The diagram above shows the initial matrix, the matrix after the first query, and the matrix after the second query.
- 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).
- 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).
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2022/11/24/p2example22.png" style="width: 261px; height: 82px;" />
<pre>
<strong>Input:</strong> n = 2, queries = [[0,0,1,1]]
<strong>Output:</strong> [[1,1],[1,1]]
<strong>Explanation:</strong> The diagram above shows the initial matrix and the matrix after the first query.
- In the first query we add 1 to every element in the matrix.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 500</code></li>
	<li><code>1 &lt;= queries.length &lt;= 10<sup>4</sup></code></li>
	<li><code>0 &lt;= row1<sub>i</sub> &lt;= row2<sub>i</sub> &lt; n</code></li>
	<li><code>0 &lt;= col1<sub>i</sub> &lt;= col2<sub>i</sub> &lt; n</code></li>
</ul>