Surrounded Regions

To solve this coding challenge involving surrounded regions in an m x n board containing 'X' and 'O', we'll use a Depth-First Search (DFS) approach. Through DFS, we'll identify and mark the 'O's that are connected to the border and hence should not be flipped. The rest of the 'O's will be converted to 'X's.

Explanation

The challenge requires that any 'O' not on the border and not connected to an 'O' on the border be flipped to 'X'. Here's a detailed approach to achieve this:
  1. Initialization :
    • If the board is empty, simply return.
    • Determine the number of rows and columns in the board.
  2. DFS Marking :
    • We will define a DFS function that marks 'O's connected to the border with a temporary character, say 'S'.
    • Traverse through the border of the board and apply the DFS function to mark all 'O's connected to the border.
  3. Region Conversion :
    • Iterate through the entire board. If a cell contains 'O', it means it's surrounded and will be converted to 'X'.
    • If a cell contains 'S', change it back to 'O' since it was originally connected to the border.
    This solution ensures that all surrounded regions are accurately captured. Let's break this down into pseudocode with detailed comments to illustrate each step.

    Pseudocode

    Step 1: Initialization
                                                
    # Check if the board is empty, if so, return immediately
    if board is empty:
    return
    
    # Determine the number of rows and columns
    number_of_rows = length of board
    number_of_columns = length of the first row in board
    
                                            
    Step 2: Define the DFS Function
                                                
    # Define the DFS function to mark connected 'O's with 'S'
    function dfs(row, col):
    # Check for base cases: if index is out of bounds or the cell is not 'O'
    if row is out of bounds or col is out of bounds or board[row][col] is not 'O':
    return
    
    # Mark the cell as 'S' to identify it as connected to the border
    board[row][col] = 'S'
    
    # Explore all 4-directionally connected neighbors
    dfs(row + 1, col)  # down
    dfs(row - 1, col)  # up
    dfs(row, col + 1)  # right
    dfs(row, col - 1)  # left
    
                                            
    Step 3: Mark Border-Connected 'O's
                                                
    # Traverse and apply DFS to all 'O's on the border rows and columns
    for each row from 0 to number_of_rows - 1:
    dfs(row, 0)                   # First column
    dfs(row, number_of_columns-1) # Last column
    
    for each column from 0 to number_of_columns - 1:
    dfs(0, column)                # First row
    dfs(number_of_rows-1, column) # Last row
    
                                            
    Step 4: Convert Regions
                                                
    # Iterate through the entire board to convert the regions
    for each row from 0 to number_of_rows - 1:
    for each column from 0 to number_of_columns - 1:
    if cell contains 'O':
    # This 'O' is surrounded and should be flipped to 'X'
    board[row][col] = 'X'
    else if cell contains 'S':
    # This 'O' was connected to the border, revert it back to 'O'
    board[row][col] = 'O'
    
                                            

    Step-by-Step Explanation of Detailed Steps in Pseudocode

  4. Initialization :
    • Check if the board is empty and return if so to avoid any further errors.
    • Calculate the number of rows and columns in the board to facilitate navigation.
  5. DFS Function :
    • This function helps mark all connected 'O's starting from any given cell (row, col).
    • If the cell is out of bounds or is not an 'O', the function returns.
    • Otherwise, mark the cell as 'S' (a placeholder to indicate it's connected to the border) and recursively apply DFS in all four directions.
  6. Mark Border-Connected 'O's :
    • Apply the DFS function to all border cells (both on rows and columns).
    • This step ensures all border-connected 'O's are marked with 'S'.
  7. Convert the Regions :
    • Iterate through every cell in the board.
    • Convert 'O's (that are not marked) to 'X' since they are surrounded.
    • Revert the 'S' cells back to 'O' as they represent the border-connected regions.
This method ensures an optimal approach to solving the problem within the constraints provided.