<p>Given a <code>matrix</code>&nbsp;and a <code>target</code>, return the number of non-empty submatrices that sum to <font face="monospace">target</font>.</p>

<p>A submatrix <code>x1, y1, x2, y2</code> is the set of all cells <code>matrix[x][y]</code> with <code>x1 &lt;= x &lt;= x2</code> and <code>y1 &lt;= y &lt;= y2</code>.</p>

<p>Two submatrices <code>(x1, y1, x2, y2)</code> and <code>(x1&#39;, y1&#39;, x2&#39;, y2&#39;)</code> are different if they have some coordinate&nbsp;that is different: for example, if <code>x1 != x1&#39;</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/09/02/mate1.jpg" style="width: 242px; height: 242px;" />
<pre>
<strong>Input:</strong> matrix = [[0,1,0],[1,1,1],[0,1,0]], target = 0
<strong>Output:</strong> 4
<strong>Explanation:</strong> The four 1x1 submatrices that only contain 0.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[1,-1],[-1,1]], target = 0
<strong>Output:</strong> 5
<strong>Explanation:</strong> The two 1x2 submatrices, plus the two 2x1 submatrices, plus the 2x2 submatrix.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> matrix = [[904]], target = 0
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>1 &lt;= matrix.length &lt;= 100</code></li>
	<li><code>1 &lt;= matrix[0].length &lt;= 100</code></li>
	<li><code>-1000 &lt;= matrix[i][j] &lt;= 1000</code></li>
	<li><code>-10^8 &lt;= target &lt;= 10^8</code></li>
</ul>


#include <vector>
#include <unordered_map>
using namespace std;

class Solution
{
public:
    unordered_map<int, int> map; // {prefixSum, count}
    int numSubmatrixSumTarget(vector<vector<int>> &matrix, int target)
    {
        int m = matrix.size(), n = matrix[0].size(), ans = 0, prefix = 0;
        if (m <= n)
        {
            for (int i = 0; i < m; ++i)
            {
                ans += rowSum(matrix[i], target);
                for (int j = i + 1; j < m; ++j)
                {
                    for (int k = 0; k < n; ++k)
                        matrix[i][k] += matrix[j][k];
                    ans += rowSum(matrix[i], target);
                }
            }
        }
        if (m > n)
        {
            for (int j = 0; j < n; ++j)
            {
                ans += colSum(matrix, j, target);
                for (int i = j + 1; i < n; ++i)
                {
                    for (int k = 0; k < m; ++k)
                        matrix[k][j] += matrix[k][i];
                    ans += colSum(matrix, j, target);
                }
            }
        }
        return ans;
    }
    int rowSum(vector<int> &row, int target)
    {
        int ans = 0, prefix = 0;
        map.clear();
        map[0] = 1;
        for (int i = 0; i < row.size(); ++i)
        {
            prefix += row[i];
            ans += map[prefix - target];
            map[prefix]++;
        }
        return ans;
    }

    int colSum(vector<vector<int>> &matrix, int col, int target)
    {
        int ans = 0, prefix = 0;
        map.clear();
        map[0] = 1;
        for (int i = 0; i < matrix.size(); ++i)
        {
            prefix += matrix[i][col];
            ans += map[prefix - target];
            map[prefix]++;
        }
        return ans;
    }
};
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