Is Select Cells in Grid With Maximum Score easy or hard?

Select Cells in Grid With Maximum Score is classified as a Hard problem. The difficulty comes from recognizing that the row count is small enough for bitmask state compression and restructuring the problem from cell-level choices to value-based dynamic programming.

How to solve Select Cells in Grid With Maximum Score in O(V * 2^R)?

Compress row usage into a bitmask and iterate values sequentially. For each DP mask, attempt to place the current value into any row that contains that value and is not already used in the mask. Updating masks with bit operations avoids exploring redundant combinations and reduces the search space dramatically compared to naive recursion.

What is the best approach for Select Cells in Grid With Maximum Score?

The most efficient approach uses bitmask dynamic programming over rows. Group grid positions by value, then maintain a DP state where each bitmask represents which rows are already used. For each value, try assigning it to a row that contains it and is not set in the mask. This runs in O(V * 2^R * R) time and O(2^R) space, which works well because the number of rows is small.

Is Select Cells in Grid With Maximum Score asked at Google/Amazon/Meta?

Problems combining bitmask dynamic programming and grid selection patterns frequently appear in interviews at companies like Google, Amazon, and Meta. Variants that require selecting elements under row or column constraints with state compression are especially common in senior-level algorithm interviews.

What data structure is used in Select Cells in Grid With Maximum Score?

The solution relies on arrays or hash maps to group rows by value, along with a bitmask to represent which rows are already used. Dynamic programming over these bitmask states is the main technique, supported by bit manipulation operations to update row usage efficiently.

What is the time complexity of Select Cells in Grid With Maximum Score?

The optimal bitmask DP solution runs in O(V * 2^R * R) time, where V is the number of distinct values and R is the number of rows. Each DP state represents a subset of rows, and transitions attempt to place the current value in available rows. Space complexity is O(2^R) for storing DP states.

Select Cells in Grid With Maximum Score Python or Java solution approach?

Both Python and Java implementations typically build a map from value to list of rows, then run bitmask dynamic programming. A DP array of size 2^rows stores the best score for each row combination, and transitions update masks using bit operations. The logic is identical across languages with minor syntax differences.

Description Hints 2 Solution Video 13:41

3276. Select Cells in Grid With Maximum Score

Hard15.7% acceptance

You are given a 2D matrix grid consisting of positive integers.

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

No two selected cells are in the same row of the matrix.
The values in the set of selected cells are unique.

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

Return the maximum score you can achieve.

Example 1:

Input: grid = [[1,2,3],[4,3,2],[1,1,1]]

Output: 8

Explanation:

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

Example 2:

Input: grid = [[8,7,6],[8,3,2]]

Output: 15

Explanation:

We can select the cells with values 7 and 8 that are colored above.

Constraints:

1 <= grid.length, grid[i].length <= 10
1 <= grid[i][j] <= 100

Topics

Hints open one at a time

Hint 1

Sort all the cells in the grid by their values and keep track of their original positions.

Hint 2

Try dynamic programming with the following states: the current cell that we might select and a bitmask representing all the rows from which we have already selected a cell so far.

13:41

Still stuck?Read 3 approaches, or watch a walkthrough.

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1class Solution:
2    def maxScore(self, grid: List[List[int]]) -> int:
3        

Starter codePython 3Spaces: 4

Examples

Case 1Case 2

Input

[[1,2,3],[4,3,2],[1,1,1]]

Input

[[8,7,6],[8,3,2]]

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