[LeetCode] Surrounded Regions（DFS、BFS）

Given a 2D board containing 'X' and 'O', capture all regions surrounded by 'X'.

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

For example,

X X X X
X O O X
X X O X
X O X X

After running your function, the board should be:

X X X X
X X X X
X X X X
X O X X

方法1：DFS的Recursive实现，由于递归实现占用额外内存，当递归深度大时出现RunTime Error
      思想是从board的外层四周开始，找到需要替换的‘O’先标记为‘V’，看此‘O’上下左右有没有需要替换的‘O’，不断深入。

  class Solution {
    public:
        typedef vector<vector<char> > BOARDTYPE;

        void solve(BOARDTYPE &board) {
            if (board.empty() || board[0].empty()) return;
            int N = board.size(), M = board[0].size();
            for (int i = 0; i < N; ++i)
                for (int j = 0; j < M; ++j)
                    if (i == 0 || j == 0 || i == N-1 || j == M-1)
                        dfs(board, i, j); // you may call dfs or bfs here!
            for (int i = 0; i < N; ++i)
                for (int j = 0; j < M; ++j)
                    board[i][j] = (board[i][j] == 'V') ? 'O' : 'X';
        }

         void dfs(BOARDTYPE &board, int row, int col) {
            int N = board.size(), M = board[0].size();
            if (row < 0 || row >= N || col < 0 || col >= M) return;
            if (board[row][col] != 'O') return;
            board[row][col] = 'V';//把不需要更改的‘O’设为‘V’.
            dfs(board, row+1, col);
            dfs(board, row-1, col);
            dfs(board, row, col+1);
            dfs(board, row, col-1);
        }
    };

方法2：DFS的stack实现

It pushes all neighbors into stack, and pick the top one, which is one of the neighbors just pushed in, and further gets its neighbors.

仔细考虑一下，这个乍一看很容易被认为是BFS的实现。

  class Solution {
    public:
        typedef vector<vector<char> > BOARDTYPE;

        void solve(BOARDTYPE &board) {
            if (board.empty() || board[0].empty()) return;
            int N = board.size(), M = board[0].size();
            for (int i = 0; i < N; ++i)
                for (int j = 0; j < M; ++j)
                    if (i == 0 || j == 0 || i == N-1 || j == M-1)
                        dfs(board, i, j); // you may call dfs or bfs here!
            for (int i = 0; i < N; ++i)
                for (int j = 0; j < M; ++j)
                    board[i][j] = (board[i][j] == 'V') ? 'O' : 'X';
        }

         void dfs(BOARDTYPE &board, int row, int col) {
            int N = board.size(), M = board[0].size();
            if (row < 0 || row >= N || col < 0 || col >= M) return;
            if (board[row][col] != 'O') return;
            stack<pair<int,int>> s;
            s.push(make_pair(row,col));
            board[row][col] = 'V';//把不需要更改的‘O’设为‘V’.
            while(!s.empty()){
                row = s.top().first;
                col = s.top().second;
                s.pop();
                if(row+1<N && board[row+1][col]=='O'){
                    s.push(make_pair(row+1,col));
                    board[row+1][col]='V';
                }
                if(row-1>=0 && board[row-1][col]=='O'){
                    s.push(make_pair(row-1,col));
                    board[row-1][col]='V';
                }
                if(col+1<M && board[row][col+1]=='O'){
                    s.push(make_pair(row,col+1));
                    board[row][col+1]='V';
                }
                if(col-1<N && board[row][col-1]=='O'){
                    s.push(make_pair(row,col-1));
                    board[row][col-1]='V';
                }
            }//end while
        }
    };

方法3：BFS的queue实现

 class Solution {
    public:
        typedef vector<vector<char> > BOARDTYPE;

        void solve(BOARDTYPE &board) {
            if (board.empty() || board[0].empty()) return;
            int N = board.size(), M = board[0].size();
            queue<pair<int,int>> q;
            
            for (int i = 0; i < N; ++i){
                if(board[i][M-1]=='O' ){
                    q.push(make_pair(i,M-1));
                    board[i][M-1]='V';     
                }    
                if(board[i][0]=='O'){
                    q.push(make_pair(i,0));
                    board[i][0]='V';
                }
            }
            for (int j = 0; j < M; ++j){
                if(board[0][j]=='O'){
                    q.push(make_pair(0,j));    
                    board[0][j]='V';
                }     
                if( board[N-1][j]=='O'){
                    q.push(make_pair(N-1,j));
                    board[N-1][j]='V';
                }
                      
            }
            bfs(board,q);
            for (int i = 0; i < N; ++i)
                for (int j = 0; j < M; ++j)
                    board[i][j] = (board[i][j] == 'V') ? 'O' : 'X';
        }

         void bfs(BOARDTYPE &board, queue<pair<int,int>> &q) {
            int N = board.size(), M = board[0].size();
            
            while(!q.empty()){
                int row = q.front().first;
                int col = q.front().second;
                q.pop();
            
                
                if(row+1<N && board[row+1][col]=='O'){
                    q.push(make_pair(row+1,col));
                    board[row+1][col]='V';
                }
                if(row-1>=0 && board[row-1][col]=='O'){
                    q.push(make_pair(row-1,col));
                    board[row-1][col]='V';
                }
                if(col+1<M && board[row][col+1]=='O'){
                    q.push(make_pair(row,col+1));
                    board[row][col+1]='V';
                }
                if(col-1<N && board[row][col-1]=='O'){
                    q.push(make_pair(row,col-1));
                    board[row][col-1]='V';
                }
            }//end while
        }
    };