<p>You are given an <code>m x n</code> integer matrix <code>mat</code> and an integer <code>target</code>.</p>

<p>Choose one integer from <strong>each row</strong> in the matrix such that the <strong>absolute difference</strong> between <code>target</code> and the <strong>sum</strong> of the chosen elements is <strong>minimized</strong>.</p>

<p>Return <em>the <strong>minimum absolute difference</strong></em>.</p>

<p>The <strong>absolute difference</strong> between two numbers <code>a</code> and <code>b</code> is the absolute value of <code>a - b</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1.png" style="width: 181px; height: 181px;" />
<pre>
<strong>Input:</strong> mat = [[1,2,3],[4,5,6],[7,8,9]], target = 13
<strong>Output:</strong> 0
<strong>Explanation:</strong> One possible choice is to:
- Choose 1 from the first row.
- Choose 5 from the second row.
- Choose 7 from the third row.
The sum of the chosen elements is 13, which equals the target, so the absolute difference is 0.
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1-1.png" style="width: 61px; height: 181px;" />
<pre>
<strong>Input:</strong> mat = [[1],[2],[3]], target = 100
<strong>Output:</strong> 94
<strong>Explanation:</strong> The best possible choice is to:
- Choose 1 from the first row.
- Choose 2 from the second row.
- Choose 3 from the third row.
The sum of the chosen elements is 6, and the absolute difference is 94.
</pre>

<p><strong class="example">Example 3:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/08/03/matrix1-3.png" style="width: 301px; height: 61px;" />
<pre>
<strong>Input:</strong> mat = [[1,2,9,8,7]], target = 6
<strong>Output:</strong> 1
<strong>Explanation:</strong> The best choice is to choose 7 from the first row.
The absolute difference is 1.
</pre>

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

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 70</code></li>
	<li><code>1 &lt;= mat[i][j] &lt;= 70</code></li>
	<li><code>1 &lt;= target &lt;= 800</code></li>
</ul>

class Solution:
    def minimizeTheDifference(self, mat: List[List[int]], target: int) -> int:
        dp = {}
        r = len(mat)
        c = len(mat[0])

        newMat = []
        for row in mat:
            sortedRow = sorted(row)
            newRow = [sortedRow[0]]
            for i in range(1, len(sortedRow)):
                if sortedRow[i] != sortedRow[i - 1]:
                    newRow.append(sortedRow[i])
            newMat.append(newRow)

        def recurse(subtarget, curRow):
            if (subtarget, curRow) in dp:
                return dp[(subtarget, curRow)]
            elif curRow < 0:
                return subtarget
            nextRow = []
            for i in range(len(newMat[curRow])):
                dif = subtarget - newMat[curRow][i]
                nextRow.append(recurse(dif, curRow - 1))
                if dif < 0:
                    break
            
            dp[(subtarget, curRow)] = min([abs(i) for i in nextRow])

            return dp[(subtarget, curRow)]

        return recurse(target, r - 1)
        
62600