Maximum Difference Score in a Grid
<p>You are given an <code>m x n</code> matrix <code>grid</code> consisting of <strong>positive</strong> integers. You can move from a cell in the matrix to <strong>any</strong> other cell that is either to the bottom or to the right (not necessarily adjacent). The score of a move from a cell with the value <code>c1</code> to a cell with the value <code>c2</code> is <code>c2 - c1</code>.<!-- notionvc: 8819ca04-8606-4ecf-815b-fb77bc63b851 --></p>

<p>You can start at <strong>any</strong> cell, and you have to make <strong>at least</strong> one move.</p>

<p>Return the <strong>maximum</strong> total score you can achieve.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3100-3199/3148.Maximum%20Difference%20Score%20in%20a%20Grid/images/grid1.png" style="width: 240px; height: 240px;" />
<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[9,5,7,3],[8,9,6,1],[6,7,14,3],[2,5,3,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">9</span></p>

<p><strong>Explanation:</strong> We start at the cell <code>(0, 1)</code>, and we perform the following moves:<br />
- Move from the cell <code>(0, 1)</code> to <code>(2, 1)</code> with a score of <code>7 - 5 = 2</code>.<br />
- Move from the cell <code>(2, 1)</code> to <code>(2, 2)</code> with a score of <code>14 - 7 = 7</code>.<br />
The total score is <code>2 + 7 = 9</code>.</p>
</div>

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

<p><img alt="" src="https://fastly.jsdelivr.net/gh/doocs/leetcode@main/solution/3100-3199/3148.Maximum%20Difference%20Score%20in%20a%20Grid/images/moregridsdrawio-1.png" style="width: 180px; height: 116px;" /></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[4,3,2],[3,2,1]]</span></p>

<p><strong>Output:</strong> <span class="example-io">-1</span></p>

<p><strong>Explanation:</strong> We start at the cell <code>(0, 0)</code>, and we perform one move: <code>(0, 0)</code> to <code>(0, 1)</code>. The score is <code>3 - 4 = -1</code>.</p>
</div>

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

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>2 &lt;= m, n &lt;= 1000</code></li>
	<li><code>4 &lt;= m * n &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 10<sup>5</sup></code></li>
</ul>
Array; Dynamic Programming; Matrix
function maxScore(grid: number[][]): number {
    const [m, n] = [grid.length, grid[0].length];
    const f: number[][] = Array.from({ length: m }, () => Array.from({ length: n }, () => 0));
    let ans = -Infinity;
    for (let i = 0; i < m; ++i) {
        for (let j = 0; j < n; ++j) {
            let mi = Infinity;
            if (i) {
                mi = Math.min(mi, f[i - 1][j]);
            }
            if (j) {
                mi = Math.min(mi, f[i][j - 1]);
            }
            ans = Math.max(ans, grid[i][j] - mi);
            f[i][j] = Math.min(mi, grid[i][j]);
        }
    }
    return ans;
}
