How do you solve Maximum Matrix Sum on LeetCode?

Maximum Matrix Sum (LeetCode #1975) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(n²) time complexity and O(1) space complexity. Key insight: Flipping adjacent elements can help convert negatives to positives, maximizing the sum.

What is the brute force solution for Maximum Matrix Sum?

The brute force approach for Maximum Matrix Sum is Brute Force, with O(n²) time complexity and O(1) space complexity. The brute-force approach involves trying every possible combination of adjacent elements to maximize the sum. This means flipping the signs of pairs of adjacent elements until no further improvement can be made. The optimal Optimal Solution approach improves this to O(n²).

What algorithm or data structure is used to solve Maximum Matrix Sum?

Maximum Matrix Sum uses the following concepts: Array, Greedy, Matrix. The recommended patterns to study are: Greedy, Array.

What are the interview tips for Maximum Matrix Sum?

Always think about edge cases, such as all elements being negative or only one negative. Clarify the operation rules with the interviewer to ensure you understand the problem correctly. Discuss your thought process aloud to demonstrate your problem-solving approach.

What are common mistakes when solving Maximum Matrix Sum?

Not considering the case when there's an odd number of negatives. Failing to calculate the minimum absolute value correctly.

#1975

Maximum Matrix Sum

Medium

ArrayGreedyMatrixGreedyArray

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n²)
Space	O(1)	O(1)

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Intuition

Time O(n²)Space O(1)

The optimal solution leverages the fact that we can maximize the sum by ensuring that we can flip pairs of negative numbers to positive. The key is to count the number of negative numbers and the smallest absolute value to determine if we can achieve the maximum sum.

⚙️

Algorithm

3 steps

1Step 1: Calculate the total sum of absolute values of all elements in the matrix.
2Step 2: Count the number of negative elements in the matrix.
3Step 3: If the count of negative numbers is odd, subtract twice the smallest absolute value from the total sum to account for the unflipped negative number.

solution.py13 lines

1def maxMatrixSum(matrix):
2    total_sum = 0
3    min_abs = float('inf')
4    negative_count = 0
5    for row in matrix:
6        for val in row:
7            total_sum += abs(val)
8            if val < 0:
9                negative_count += 1
10            min_abs = min(min_abs, abs(val))
11    if negative_count % 2 == 1:
12        total_sum -= 2 * min_abs
13    return total_sum

ℹ

Complexity note: The time complexity remains O(n²) as we still iterate through the matrix. The space complexity is O(1) since we only use a few variables to keep track of counts and sums.

1Flipping adjacent elements can help convert negatives to positives, maximizing the sum.
2The parity of negative numbers (odd/even) determines whether the smallest absolute value affects the total sum.

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