Introduction

In this blog post, we will explore how to solve the LeetCode problem "3148" 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 an m x n matrix grid consisting of positive integers. You can move from a cell in the matrix to any other cell that is either to the bottom or to the right (not necessarily adjacent). The score of a move from a cell with the value c1 to a cell with the value c2 is c2 - c1. You can start at any cell, and you have to make at least one move. Return the maximum total score you can achieve. Example 1: Input: grid = [[9,5,7,3],[8,9,6,1],[6,7,14,3],[2,5,3,1]] Output: 9 Explanation: We start at the cell (0, 1), and we perform the following moves: - Move from the cell (0, 1) to (2, 1) with a score of 7 - 5 = 2. - Move from the cell (2, 1) to (2, 2) with a score of 14 - 7 = 7. The total score is 2 + 7 = 9. Example 2: Input: grid = [[4,3,2],[3,2,1]] Output: -1 Explanation: We start at the cell (0, 0), and we perform one move: (0, 0) to (0, 1). The score is 3 - 4 = -1. Constraints: m == grid.length n == grid[i].length 2 <= m, n <= 1000 4 <= m * n <= 105 1 <= grid[i][j] <= 105

Explanation

Here's the solution:

• High-Level Approach:

  • Find the maximum and minimum values within the grid.
  • The maximum possible score is achieved by moving from the minimum value cell to the maximum value cell. Handle the edge case where min is equal to max by calculating the minimum difference between adjacent numbers.

• Complexity:

  • Runtime Complexity: O(m*n)
  • Storage Complexity: O(1)

Code

    def max_score(grid):
    """
    Calculates the maximum total score achievable by moving between cells in the grid.

    Args:
        grid: A list of lists representing the grid of positive integers.

    Returns:
        The maximum total score achievable.
    """
    m = len(grid)
    n = len(grid[0])

    min_val = float('inf')
    max_val = float('-inf')

    for i in range(m):
        for j in range(n):
            min_val = min(min_val, grid[i][j])
            max_val = max(max_val, grid[i][j])

    if min_val == max_val:
        min_diff = float('inf')
        for i in range(m):
            for j in range(n):
                if i + 1 < m:
                    min_diff = min(min_diff, grid[i + 1][j] - grid[i][j])
                if j + 1 < n:
                    min_diff = min(min_diff, grid[i][j + 1] - grid[i][j])
        return min_diff
    else:
        return max_val - min_val