The Minimum Number of Flips to Make Binary Grid Palindromic II coding problem is an advanced grid manipulation challenge. You are given a binary matrix and must flip the minimum number of 0s and 1s such that every row is a palindrome, every column is a palindrome, AND the total number of 1s in the final grid is divisible by 4. This adds a global constraint on top of the local palindromic symmetry.
Meta and Google often use this question to test a candidate's ability to handle multiple overlapping constraints. It evaluates symmetry-based reasoning and parity logic. The interviewer wants to see if you can correctly identify which cells are "linked" by the palindrome rules and how to satisfy the "divisible by 4" rule with the minimum possible flips.
This problem follows the Array, Matrix, Two Pointers interview pattern. The key is to group the cells that must be equal due to symmetry. Most cells come in groups of 4 (e.g., (r, c), (r, m-1-c), (n-1-r, c), and (n-1-r, m-1-c)). Within each group, you count 0s and 1s and flip to the majority. The tricky part is the middle row or middle column (if n or m is odd), which come in groups of 2. These groups of 2 must be handled carefully to satisfy the "divisible by 4" constraint for the total number of 1s.
Consider a 3x3 grid. The 4 corners must all be the same (Group 1). The middle of the top/bottom edges and left/right edges must match their counterparts (Group 2 and 3). The very center is its own group (Group 4). If the corners have three 1s and one 0, we flip the 0 to 1 (1 flip) to make them all 1s. This adds four 1s to the total, helping satisfy the "divisible by 4" rule. If we have two 1s and two 0s, we flip 2 cells—but which way we flip might depend on whether we need more 1s to reach a multiple of 4 later.
A common mistake is treating the "divisible by 4" rule separately from the palindromic flips. They are deeply interconnected. Another error is failing to handle the center cell correctly in odd-sized matrices (the center must be 0 to not affect the "divisible by 4" rule, as it's a single cell). Candidates also struggle with the logic for groups of size 2, where you might have "flexible" flips that can help satisfy the parity requirement.
Practice grouping elements by symmetry. Whenever you see "palindrome" in a 2D context, immediately think about which four cells (or two cells) must be identical. Master the logic of "parity" (divisibility), as it often appears as a secondary constraint in difficult grid problems.
| Title | Difficulty | Topics | LeetCode |
|---|---|---|---|
| Rotating the Box | Medium | Solve | |
| Candy Crush | Medium | Solve | |
| Image Overlap | Medium | Solve | |
| Product of Two Run-Length Encoded Arrays | Medium | Solve | |
| Number of Subarrays with Bounded Maximum | Medium | Solve |
