select-cells-in-grid-with-maximum-score

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Algorithms

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

You have to select one or more cells from the matrix such that the following conditions are satisfied:

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

Your score will be the sum of the values of the selected cells.

Return the maximum score you can achieve.

&nbsp;
Example 1:

<div class="example-block">
Input: grid = [[1,2,3],[4,3,2],[1,1,1]]

Output: 8

Explanation:

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

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

Example 2:

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

Output: 15

Explanation:

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

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

&nbsp;
Constraints:

<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>