max-sum-of-rectangle-no-larger-than-k

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Algorithms

Given an <code>m x n</code> matrix <code>matrix</code> and an integer <code>k</code>, return the max sum of a rectangle in the matrix such that its sum is no larger than <code>k</code>.

It is guaranteed that there will be a rectangle with a sum no larger than <code>k</code>.

&nbsp;
Example 1:
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/18/sum-grid.jpg" style="width: 255px; height: 176px;" />
<pre>
Input: matrix = [[1,0,1],[0,-2,3]], k = 2
Output: 2
Explanation: Because the sum of the blue rectangle [[0, 1], [-2, 3]] is 2, and 2 is the max number no larger than k (k = 2).
</pre>

Example 2:

<pre>
Input: matrix = [[2,2,-1]], k = 3
Output: 3
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
	<li><code>-100 &lt;= matrix[i][j] &lt;= 100</code></li>
	<li><code>-105 &lt;= k &lt;= 105</code></li>
</ul>

&nbsp;
Follow up: What if the number of rows is much larger than the number of columns?

maxSumSubmatrix

Max Sum of Rectangle No Larger Than K

Array

Binary Search

Matrix

Ordered Set

Prefix Sum

给你一个 <code>m x n</code> 的矩阵 <code>matrix</code> 和一个整数 <code>k</code> ，找出并返回矩阵内部矩形区域的不超过 <code>k</code> 的最大数值和。

题目数据保证总会存在一个数值和不超过 <code>k</code> 的矩形区域。

 

示例 1：
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/18/sum-grid.jpg" style="width: 255px; height: 176px;" />
<pre>
输入：matrix = [[1,0,1],[0,-2,3]], k = 2
输出：2
解释：蓝色边框圈出来的矩形区域 <code>[[0, 1], [-2, 3]]</code> 的数值和是 2，且 2 是不超过 k 的最大数字（k = 2）。
</pre>

示例 2：

<pre>
输入：matrix = [[2,2,-1]], k = 3
输出：3
</pre>

 

提示：

<ul>
	<li><code>m == matrix.length</code></li>
	<li><code>n == matrix[i].length</code></li>
	<li><code>1 <= m, n <= 100</code></li>
	<li><code>-100 <= matrix[i][j] <= 100</code></li>
	<li><code>-105 <= k <= 105</code></li>
</ul>

 

进阶：如果行数远大于列数，该如何设计解决方案？