# 矩形区域不超过 K 的最大数值和

<p>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。</p>

<p>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。</p>

<p> </p>

<p><strong>示例 1：</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/03/18/sum-grid.jpg" style="width: 255px; height: 176px;" />
<pre>
<strong>输入：</strong>matrix = [[1,0,1],[0,-2,3]], k = 2
<strong>输出：</strong>2
<strong>解释：</strong>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>

<p><strong>示例 2：</strong></p>

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

<p> </p>

<p><strong>提示：</strong></p>

<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>-10<sup>5</sup> <= k <= 10<sup>5</sup></code></li>
</ul>

<p> </p>

<p><strong>进阶：</strong>如果行数远大于列数，该如何设计解决方案？</p>


## template

```cpp
#include <bits/stdc++.h>
using namespace std;

class Solution
{
public:
    int maxSumSubmatrix(vector<vector<int>> &mat, int k)
    {
        int m = mat.size(), n = mat[0].size();
        vector<vector<int>> sum(m + 1, vector<int>(n + 1, 0));
        for (int i = 1; i <= m; i++)
        {
            for (int j = 1; j <= n; j++)
            {
                sum[i][j] = sum[i - 1][j] + sum[i][j - 1] - sum[i - 1][j - 1] + mat[i - 1][j - 1];
            }
        }
        int ans = INT_MIN;
        for (int top = 1; top <= m; top++)
        {
            for (int bot = top; bot <= m; bot++)
            {
                set<int> st;
                st.insert(0);
                for (int r = 1; r <= n; r++)
                {
                    int right = sum[bot][r] - sum[top - 1][r];
                    auto left = st.lower_bound(right - k);
                    if (left != st.end())
                    {
                        int cur = right - *left;
                        ans = max(ans, cur);
                    }
                    st.insert(right);
                }
            }
        }
        return ans;
    }
};


```

## 答案

```cpp

```

## 选项

### A

```cpp

```

### B

```cpp

```

### C

```cpp

```