<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 findSumTarget(vector<int> vec, int target){
        unordered_map<int, int> ump;
        int cnt = 0;
        
        for(int i = 1; i < vec.size(); i++){
            vec[i] += vec[i - 1];
        }

        for(int c: vec){
            if(ump.count(c - target)){
                cnt += ump[c - target];
            }
            if(c == target){
                cnt++;
            }
            ump[c]++;
        }
        return cnt;
    }

    int numSubmatrixSumTarget(vector<vector<int>>& matrix, int target) {
        // idea is to iterate over left and irght boundary of matrices

        int n = matrix.size(), m = matrix[0].size();

        vector<vector<int>> preSumCols = matrix;

        for(int i = 0; i < n; i++){
            for(int j = 1; j < m; j++){
                preSumCols[i][j]+=preSumCols[i][j-1];
            }
        }

        int countSumTarget = 0;
        for(int j1 = 0; j1 < m; j1++){
            for(int j2 = j1; j2 < m; j2++){
                //i .. j for the array
                vector<int> vec;
                for(int i = 0; i < n; i++){
                    vec.push_back(preSumCols[i][j2] - preSumCols[i][j1] + matrix[i][j1]);
                }
                countSumTarget += findSumTarget(vec, target);
            }
        }

        return countSumTarget;
    }
};
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