<p>You are given a 2D matrix <code>grid</code> consisting of positive integers.</p>

<p>You have to select <em>one or more</em> cells from the matrix such that the following conditions are satisfied:</p>

<ul>
	<li>No two selected cells are in the <strong>same</strong> row of the matrix.</li>
	<li>The values in the set of selected cells are <strong>unique</strong>.</li>
</ul>

<p>Your score will be the <strong>sum</strong> of the values of the selected cells.</p>

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

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

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

<p><strong>Output:</strong> <span class="example-io">8</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/07/29/grid1drawio.png" /></p>

<p>We can select the cells with values 1, 3, and 4 that are colored above.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">grid = [[8,7,6],[8,3,2]]</span></p>

<p><strong>Output:</strong> <span class="example-io">15</span></p>

<p><strong>Explanation:</strong></p>

<p><img alt="" src="https://assets.leetcode.com/uploads/2024/07/29/grid8_8drawio.png" style="width: 170px; height: 114px;" /></p>

<p>We can select the cells with values 7 and 8 that are colored above.</p>
</div>

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

<ul>
	<li><code>1 &lt;= grid.length, grid[i].length &lt;= 10</code></li>
	<li><code>1 &lt;= grid[i][j] &lt;= 100</code></li>
</ul>

class Solution:
    def maxScore(self, grid: List[List[int]]) -> int:
        n_all = sorted(set(v for row in grid for v in row), reverse=1)
        row_set = [set(row) for row in grid]
        d = defaultdict(set)   # 字典: {数字: 包含该数字的行号集合}
        for x in n_all:
            for i, rs in enumerate(row_set):
                if x in rs:
                    d[x].add(i)
        ans = 0
        res = [set()]
        for x in n_all:
            if all(r >= d[x] for r in res): continue # 贪心时发现, 当前数字实在无法添加了, 直接跳过
            nres = []
            for r in res:
                for dv in d[x]:
                    if dv not in r:
                        nres += r | {dv},
            ans += x
            res = nres
            # if len(res[0]) >= len(grid): break  # 没用的剪枝
        return ans
31840