<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>

class Solution {
public:
    int numSubmatrixSumTarget(vector<vector<int>>& matrix, int target) {
        int m=matrix.size();
        int n=matrix[0].size();
        vector<vector<int>> pref(m+1,vector<int>(n+1,0));
        
        for(int i=1;i<=m;i++){
            for(int j=1;j<=n;j++){
                pref[i][j]=pref[i][j-1]+matrix[i-1][j-1];
            }
        }
        // for(int i=0;i<=m;i++){
        //     for(int j=0;j<=n;j++){
        //         cout<<pref[i][j]<<" ";
        //     }
        //     cout<<endl;
        // }
        int ans=0;
        for(int j=0;j<n;j++){
            for(int k=j+1;k<=n;k++){
                unordered_map<int,int> mp;
                mp[0]++;
                int cursum=0;
                for(int i=1;i<=m;i++){
                   int presum=pref[i][k]-pref[i][j];
                   cursum+=presum;
                   if(mp.count(cursum-target)){
                      ans+=mp[cursum-target];
                   }
                   mp[cursum]++;
                }
            }
        }
        return ans;
    }
};
131035