Introduction

In this blog post, we will explore how to solve the LeetCode problem "3276" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

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

Explanation

Here's a solution to the problem using dynamic programming and a greedy approach, along with explanations.

• High-Level Approach:

  • Sort each row in descending order to prioritize larger values.
  • Use dynamic programming to explore all possible combinations of cell selections, ensuring no two cells are in the same row and the selected values are unique. The DP state represents the rows considered and the set of used numbers.
  • Memoize the results to avoid redundant computations and improve efficiency.

• Complexity:

  • Runtime: O(m n 2ⁿ), where m is the number of rows and n is the number of columns. The sorting contributes O(m n log n), the dynamic programming part explores all combinations.
  • Space: O(m * 2ⁿ), due to the memoization table.

Code

    def max_score(grid):
    """
    Calculates the maximum score achievable by selecting cells from the grid
    such that no two cells are in the same row and the selected values are unique.

    Args:
        grid: A 2D matrix (list of lists) of positive integers.

    Returns:
        The maximum achievable score.
    """

    rows = len(grid)
    if rows == 0:
        return 0

    cols = len(grid[0])

    # Sort each row in descending order
    for i in range(rows):
        grid[i].sort(reverse=True)

    memo = {}  # Memoization table to store calculated results

    def solve(row_index, used_numbers):
        """
        Recursive helper function to calculate the maximum score.

        Args:
            row_index: The index of the current row being considered.
            used_numbers: A set of numbers that have already been selected.

        Returns:
            The maximum score achievable starting from the current row.
        """

        if row_index == rows:
            return 0  # Base case: All rows have been processed

        # Memoization check
        if (row_index, tuple(sorted(list(used_numbers)))) in memo:
            return memo[(row_index, tuple(sorted(list(used_numbers))))]

        max_score_from_here = 0

        # Option 1: Skip the current row
        max_score_from_here = max(max_score_from_here, solve(row_index + 1, used_numbers))

        # Option 2: Try selecting a cell from the current row
        for col_index in range(cols):
            current_number = grid[row_index][col_index]
            if current_number not in used_numbers:
                new_used_numbers = set(used_numbers)
                new_used_numbers.add(current_number)
                max_score_from_here = max(max_score_from_here, current_number + solve(row_index + 1, new_used_numbers))

        memo[(row_index, tuple(sorted(list(used_numbers))))] = max_score_from_here
        return max_score_from_here

    return solve(0, set())