This problem requires counting and rearranging rows and columns to meet chessboard constraints. A valid solution involves verifying parity and pattern consistency, then calculating minimum swaps. If the board's configuration cannot satisfy the alternating 0-1 pattern in both rows and columns, the answer is -1.
Problem Statement
Given an n x n binary grid where each element is 0 or 1, you may swap any two rows or any two columns in one move. Your goal is to rearrange the board so that it forms a chessboard pattern, where no two identical numbers are adjacent horizontally or vertically.
Return the minimum number of moves needed to transform the grid into a valid chessboard. If it is impossible to achieve a chessboard through any sequence of row or column swaps, return -1.
Examples
Example 1
Input: board = [[0,1,1,0],[0,1,1,0],[1,0,0,1],[1,0,0,1]]
Output: 2
One potential sequence of moves is shown. The first move swaps the first and second column. The second move swaps the second and third row.
Example 2
Input: board = [[0,1],[1,0]]
Output: 0
Also note that the board with 0 in the top left corner, is also a valid chessboard.
Example 3
Input: board = [[1,0],[1,0]]
Output: -1
No matter what sequence of moves you make, you cannot end with a valid chessboard.
Constraints
- n == board.length
- n == board[i].length
- 2 <= n <= 30
- board[i][j] is either 0 or 1.
Solution Approach
Validate Row and Column Patterns
Check that all rows and all columns occur in exactly two patterns differing only in inversion. Count occurrences to ensure the board can be rearranged into a chessboard without violating adjacency rules.
Calculate Minimum Swaps for Rows and Columns
Determine the number of swaps needed to align rows and columns to the chessboard pattern using bitwise operations. Count mismatches against an ideal alternating sequence and compute swaps using integer division and parity checks.
Return Result or Detect Impossibility
Sum the calculated row and column swaps. If any validation step fails due to uneven counts or impossible pattern combinations, immediately return -1; otherwise, return the total number of swaps required.
Complexity Analysis
| Metric | Value |
|---|---|
| Time | Depends on the final approach |
| Space | Depends on the final approach |
Time complexity depends on iterating through the n x n board for pattern counting and swap calculations, yielding O(n^2). Space complexity is O(n) for storing row and column pattern counts and intermediate computations.
What Interviewers Usually Probe
- Check for equal counts of rows and columns with each pattern before attempting swaps.
- Use bit manipulation to efficiently compare row and column patterns for mismatches.
- Watch for parity issues: a chessboard requires even distribution or one-off differences depending on n being even or odd.
Common Pitfalls or Variants
Common pitfalls
- Failing to validate that only two unique row and column patterns exist can lead to incorrect swap counts.
- Ignoring parity constraints may suggest an achievable solution when it is impossible.
- Counting swaps incorrectly without considering alternating sequence alignment often results in overestimating moves.
Follow-up variants
- Compute swaps when only row swaps are allowed, ignoring column swaps.
- Transform a non-square m x n binary board into a partial chessboard pattern under swap constraints.
- Determine minimum swaps when initial board has more than two repeating row patterns and some cannot align.
How GhostInterview Helps
- Automatically verifies row and column pattern constraints to detect impossible boards quickly.
- Calculates minimum swaps efficiently using bitwise alignment strategies for the chessboard pattern.
- Highlights mismatch positions and provides step-by-step guidance to transform any valid configuration.
Topic Pages
Related GhostInterview Pages
- LeetCode Interview Copilot - Use GhostInterview as a live solver when you want direct help with LeetCode-style coding questions.
- Coding Interview Assistant - See how GhostInterview supports array, string, linked list, graph, and tree interview workflows.
- How GhostInterview Works - Review the screenshot, reasoning, and answer flow before using the solver in a live interview.
FAQ
What is the main pattern recognition in Transform to Chessboard?
The core pattern involves ensuring exactly two unique row and column patterns exist, differing only by inversion, which aligns with the chessboard requirement.
Can I only swap rows or only swap columns to solve this problem?
Yes, but the minimum swaps must be calculated separately for rows and columns; some configurations may become impossible if restricted.
How do I detect if a board cannot become a chessboard?
Validate that each row and column occurs in exactly two patterns and satisfies parity constraints; any violation indicates impossibility.
What role does bit manipulation play in this solution?
Bit manipulation efficiently counts mismatches and aligns rows or columns with the ideal alternating sequence for calculating swaps.
Does board size affect the solution approach?
Yes, odd or even n changes parity checks and swap calculations, impacting whether a board configuration can reach a chessboard.
Need direct help with Transform to Chessboard instead of spending more time grinding it?
Download GhostInterview when you want a LeetCode solver, not another long practice loop. Capture Transform to Chessboard from a screenshot, get the answer path and complexity, and use supported stealth workflows that stay outside captured layers.
Capture the prompt fast instead of rewriting the problem by hand.
Get the solution path, trade-offs, and complexity summary in one pass.
Stay outside captured layers on supported screen-share workflows.
Stay in the same pattern family
Determine whether an integer array can be partitioned into two non-empty subarrays with the same average using dynamic programming.
Open problem page#810 Chalkboard XOR GameThe Chalkboard XOR Game is a game theory problem involving array manipulation and bitwise XOR, where players alternate erasing elements from a chalkboard.
Open problem page#832 Flipping an ImageFlip each row of a binary matrix horizontally and invert its values efficiently using a two-pointer scanning approach.
Open problem page