Maximum Matrix Sum · Interview Problem

Leetcode

Medium

Arrays

Matrices

Math

Greedy

Maximum Matrix Sum

Maximize the total sum of a matrix after repeatedly flipping the signs of entries subject to the problem’s operation rules.

Acceptance 100%

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Problem Statement

You are given an $m \times n$ matrix of integers. By applying the allowed operation any number of times, you may change the signs of values in the matrix according to the problem’s rules. Your goal is to make the final sum of all matrix entries as large as possible.

Think about what information actually matters after all operations are considered: the magnitudes of the values, how many negatives there are, and whether a zero can neutralize an unavoidable sign issue.

Input Format

A matrix of integers with $m$ rows and $n$ columns.
The exact operation details are determined by the problem statement.
Values may be positive, negative, or zero.

Output Format

Return the maximum possible sum of the matrix after performing the allowed operations.

Constraints

Matrix dimensions are finite and reasonably sized for an interview problem.
Entries are integers that may be negative, zero, or positive.
A greedy or parity-based observation is typically sufficient.

Examples

Sample cases returned by the problem API.

Example 1

Input

matrix = [[1,-1],[-1,1]]

Output

Explanation

All values can be made positive in the optimal configuration, so the maximum sum is 1 + 1 + 1 + 1 = 4.

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