How do you solve Maximum Difference Score in a Grid on LeetCode?

Maximum Difference Score in a Grid (LeetCode #3148) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(m * n) time complexity and O(1) space complexity. Key insight: The maximum score can be derived from the difference between the current cell and the minimum value seen so far.

What is the brute force solution for Maximum Difference Score in a Grid?

The brute force approach for Maximum Difference Score in a Grid is Brute Force, with O(m * n * m * n) time complexity and O(1) space complexity. We can check every possible starting cell and calculate the maximum score by comparing it with every other cell that can be reached by moving down or right. This approach is straightforward but inefficient. The optimal Optimal Solution approach improves this to O(m * n).

What algorithm or data structure is used to solve Maximum Difference Score in a Grid?

Maximum Difference Score in a Grid uses the following concepts: Array, Dynamic Programming, Matrix. The recommended patterns to study are: Dynamic Programming, Greedy Algorithms.

What are the interview tips for Maximum Difference Score in a Grid?

Always clarify the problem constraints and requirements before jumping into coding. Think about how you can optimize your solution after implementing a brute-force version. Practice explaining your thought process clearly, as communication is key in interviews.

What are common mistakes when solving Maximum Difference Score in a Grid?

Not considering that you must make at least one move, leading to incorrect initial conditions. Overlooking the need to track the minimum value efficiently.

#3148

Maximum Difference Score in a Grid

Medium

ArrayDynamic ProgrammingMatrixDynamic ProgrammingGreedy Algorithms

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

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

💡

Intuition

Time O(m * n)Space O(1)

Instead of checking every possible cell, we can keep track of the minimum value seen so far as we traverse the grid. This allows us to calculate the maximum score in a single pass.

⚙️

Algorithm

5 steps

1Step 1: Initialize a variable to keep track of the minimum value seen so far.
2Step 2: Iterate through each cell in the grid.
3Step 3: For each cell, calculate the score based on the current cell value and the minimum value seen so far.
4Step 4: Update the maximum score if the current score is higher.
5Step 5: Update the minimum value if the current cell value is lower.

solution.py11 lines

1def maxDifferenceScore(grid):
2    max_score = float('-inf')
3    min_value = float('inf')
4    m, n = len(grid), len(grid[0])
5    for i in range(m):
6        for j in range(n):
7            min_value = min(min_value, grid[i][j])
8            if i > 0 or j > 0:
9                score = grid[i][j] - min_value
10                max_score = max(max_score, score)
11    return max_score

ℹ

Complexity note: This complexity is efficient because we only traverse the grid once, keeping track of the minimum value and maximum score simultaneously.

1The maximum score can be derived from the difference between the current cell and the minimum value seen so far.
2Tracking the minimum value as we traverse helps avoid unnecessary comparisons.

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