Introduction

In this blog post, we will explore how to solve the LeetCode problem "782" using AI. LeetCode is a popular platform for preparing for coding interviews, and with the help of AI tools like Chatmagic, we can generate solutions quickly and efficiently - helping you pass the interviews and get the job offer without having to study for months.

Problem Statement

You are given an n x n binary grid board. In each move, you can swap any two rows with each other, or any two columns with each other. Return the minimum number of moves to transform the board into a chessboard board. If the task is impossible, return -1. A chessboard board is a board where no 0's and no 1's are 4-directionally adjacent. Example 1: Input: board = [[0,1,1,0],[0,1,1,0],[1,0,0,1],[1,0,0,1]] Output: 2 Explanation: 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 Explanation: 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 Explanation: 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.

Explanation

Here's the solution approach, complexity analysis, and Python code:

• High-Level Approach:

  • Validation: Check if a chessboard arrangement is even possible given the input board. This involves ensuring the number of rows/columns with the same pattern is balanced (either equal or differing by 1 if n is odd).
  • Row/Column Transformation: Calculate the minimum swaps needed to arrange rows and columns into a valid chessboard pattern independently. This is done by counting discrepancies from the ideal pattern and dividing by two (since each swap corrects two discrepancies).
  • Choose Best Start: Since a chessboard can start with either 0 or 1 in the top-left corner, calculate the swaps needed for both configurations and take the minimum.

• Complexity:

  • Runtime: O(n²)
  • Storage: O(n)

Code

    def movesToChessboard(board):
    n = len(board)

    # Check if valid chessboard is possible
    row_sum = 0
    col_sum = 0
    row_diff = 0
    col_diff = 0
    for i in range(n):
        row_sum += board[0][i]
        col_sum += board[i][0]
        if board[0][i] != board[i][0]:
            return -1  # Check if row and col patterns are same
        row_diff += board[i][0] ^ (i % 2)
        col_diff += board[0][i] ^ (i % 2)

    if n // 2 > row_sum or row_sum > (n + 1) // 2:
        return -1
    if n // 2 > col_sum or col_sum > (n + 1) // 2:
        return -1

    # Calculate minimum swaps for rows and columns
    row_swaps = min(row_diff, n - row_diff) // 2
    col_swaps = min(col_diff, n - col_diff) // 2

    if n % 2 == 1:
        if row_diff % 2 == 1:
            row_swaps = (n - row_diff) // 2
        if col_diff % 2 == 1:
            col_swaps = (n - col_diff) // 2

    return row_swaps + col_swaps