<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:
        N, M = len(mat), len(mat[0])
        dp = [[-1 for j in range(5000)] for i in range(N)]
        # dp[x][y] stores min difference b/w sum from row x to N-1 and y
        def calc(x: int, y: int, s: int):
            if x == N:
                return abs(y-s)
            if dp[x][y]==-1:
                dp[x][y] = 1e7
                mat[x].sort()
                for i in range(M):
                    dp[x][y] = min(dp[x][y], calc(x+1, y + mat[x][i], s))
                    if dp[x][y] == 0 or y + mat[x][i] > s:
                        break

            return dp[x][y]
        
        return calc(0, 0, target)
32299