How do you solve Select Cells in Grid With Maximum Score on LeetCode?

Select Cells in Grid With Maximum Score (LeetCode #3276) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n * m * 2^n) time complexity and O(2^n) space complexity. Key insight: Sorting cells by value helps prioritize higher scores.

What is the brute force solution for Select Cells in Grid With Maximum Score?

The brute force approach for Select Cells in Grid With Maximum Score is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute force approach involves checking all possible combinations of cells that can be selected while adhering to the constraints. This means we will explore every possible selection of cells to find the maximum score. The optimal Optimal Solution approach improves this to O(n * m * 2^n).

What are the interview tips for Select Cells in Grid With Maximum Score?

Clearly explain your thought process while coding. Discuss edge cases, such as minimum grid sizes. Practice explaining your code to ensure clarity.

What are common mistakes when solving Select Cells in Grid With Maximum Score?

Not considering unique values when selecting cells. Failing to account for the constraints of row selection.

#3276

Select Cells in Grid With Maximum Score

Hard

ArrayDynamic ProgrammingBit ManipulationMatrixBitmaskDynamic ProgrammingBit Manipulation

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n * m * 2^n)
Space	O(1)	O(2^n)

💡

Intuition

Time O(n * m * 2^n)Space O(2^n)

The optimal solution uses dynamic programming with bit manipulation to efficiently track selected cells across rows. By sorting the cells and using a bitmask to represent selected rows, we can maximize the score while ensuring uniqueness.

⚙️

Algorithm

4 steps

1Step 1: Flatten the grid into a list of tuples containing (value, row, col).
2Step 2: Sort this list by value in descending order.
3Step 3: Use a dynamic programming array where dp[mask] represents the maximum score achievable with the selected rows represented by 'mask'.
4Step 4: Iterate through the sorted list and update the dp array based on the current cell's row and value.

solution.py10 lines

1def maxScore(grid):
2    from itertools import product
3    n, m = len(grid), len(grid[0])
4    cells = sorted([(grid[i][j], i, j) for i in range(n) for j in range(m)], reverse=True)
5    dp = [0] * (1 << n)
6    for value, row, col in cells:
7        for mask in range((1 << n) - 1, -1, -1):
8            if (mask & (1 << row)) == 0:
9                dp[mask | (1 << row)] = max(dp[mask | (1 << row)], dp[mask] + value)
10    return max(dp)

ℹ

Complexity note: The time complexity is O(n * m * 2^n) because we iterate through all cells and update the dp array for each possible selection of rows represented by the bitmask.

1Sorting cells by value helps prioritize higher scores.
2Using bit manipulation allows efficient tracking of selected rows.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.