130. Surrounded Regions

Given an m x n matrix board containing ‘X’ and ‘O’, capture all regions that are 4-directionally surrounded by ‘X’.

A region is captured by flipping all ‘O’ s into ‘X’ s in that surrounded region.
 

Example 1:

Input: board = [[“X”,“X”,“X”,“X”],[“X”,“O”,“O”,“X”],[“X”,“X”,“O”,“X”],[“X”,“O”,“X”,“X”]]
Output: [[“X”,“X”,“X”,“X”],[“X”,“X”,“X”,“X”],[“X”,“X”,“X”,“X”],[“X”,“O”,“X”,“X”]]
Explanation: Notice that an ‘O’ should not be flipped if:

• It is on the border, or
• It is adjacent to an ‘O’ that should not be flipped.

The bottom ‘O’ is on the border, so it is not flipped.
The other three ‘O’ form a surrounded region, so they are flipped.

Example 2:

Input: board = [[“X”]]
Output: [[“X”]]

Constraints:

• m == board.length
• n == board[i].length
• 1 <= m, n <= 200
• board[i][j] is ‘X’ or ‘O’.

From: LeetCode
Link: 130. Surrounded Regions

Solution:

Ideas：

1. Iterate over the boundary (four sides) of the board.
2. For every ‘O’ on the boundary, perform a Depth First Search (DFS) to mark all 'O’s connected to it with a temporary marker, such as ‘B’, to denote that these 'O’s are on the boundary or connected to the boundary and should not be flipped.
3. After marking all 'O’s on the boundary and the ones connected to it, iterate over the entire board. Perform the following operations:
   • Change all ‘B’ to ‘O’ as these are not surrounded by ‘X’.
   • Change all remaining ‘O’ to ‘X’ as these are surrounded by ‘X’.

Code:

void dfs(char** board, int i, int j, int m, int n) {
    
    
    if(i < 0 || i >= m || j < 0 || j >= n || board[i][j] != 'O') return;
    
    // mark the current cell as 'B'
    board[i][j] = 'B';
    
    // perform DFS in all four directions
    dfs(board, i+1, j, m, n);
    dfs(board, i-1, j, m, n);
    dfs(board, i, j+1, m, n);
    dfs(board, i, j-1, m, n);
}

void solve(char** board, int boardSize, int* boardColSize) {
    
    
    if(boardSize == 0 || boardColSize[0] == 0) return;
    
    int m = boardSize, n = boardColSize[0];
    
    // Step 1: mark the boundary 'O's and the ones connected to them with 'B'
    for(int i = 0; i < m; i++) {
    
    
        dfs(board, i, 0, m, n); // left boundary
        dfs(board, i, n-1, m, n); // right boundary
    }
    
    for(int j = 0; j < n; j++) {
    
    
        dfs(board, 0, j, m, n); // top boundary
        dfs(board, m-1, j, m, n); // bottom boundary
    }
    
    // Step 2: flip the remaining 'O's to 'X' and 'B's back to 'O'
    for(int i = 0; i < m; i++) {
    
    
        for(int j = 0; j < n; j++) {
    
    
            if(board[i][j] == 'O') board[i][j] = 'X';
            if(board[i][j] == 'B') board[i][j] = 'O';
        }
    }
}