Minimum Number of Flips to Make Binary Grid Palindromic I

Problem Description

You are given an m x n binary matrix grid. A row or column is considered palindromic if its values read the same forward and backward. You can flip any number of cells in grid from 0 to 1, or from 1 to 0. Return the minimum number of cells that need to be flipped to make either all rows palindromic or all columns palindromic.

Key Insights

• A row is palindromic if the first half mirrors the second half.
• Each cell can be flipped, so we need to consider how many flips are necessary to achieve palindromic rows or columns.
• We can analyze pairs of symmetric cells in rows and columns to determine the minimum flips required.

Space and Time Complexity

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

Solution

To solve the problem, we will iterate through each row and column and check pairs of symmetric positions (i.e., positions that need to match to form a palindrome). We will calculate the number of flips required for both rows and columns. Finally, we will return the minimum of the two results.

1. For each row, compare the first half with the mirrored second half.
2. Count how many flips are needed to make that row palindromic.
3. Repeat the process for columns.
4. The result will be the minimum number of flips required for either all rows or all columns to become palindromic.

Code Solutions