130. Surrounded Regions

最新推荐文章于 2024-01-21 17:09:59 发布

原创最新推荐文章于 2024-01-21 17:09:59 发布 · 412 阅读

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#need another try #union-find

本文介绍了一种解决二维棋盘中'O'被'X'包围问题的方法，使用并查集(Union-Find)算法来标记边界上的'O'并与内部'O'区分，最后将非边界的'O'转换为'X'。

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

用 DFS , UNION-FIND 都行。关键是要想到图形学中的 flood fill, 从边缘boarder开始

class UnionFind {
    vector<int> id;
    vector<int> rank;
    int count;
    
public:
    UnionFind( int n ): count(n) {
        id.resize(n, 0);
        rank.resize(n,0);
        for( int i = 0; i < n; i++ ) {
            id[i] = i;
        }
    }
    
    int find( int i ) {
        while( i != id[i]) {
            id[i] = id[id[i]];
            i = id[i];
        }
        return i;
    }
    
    bool is_connected(int p, int q) {
        int i = find(p);
        int j = find(q);
        if( i != j) return false;
        return true;
    }
    void union_by_rank( int p , int q) {
        int i = find(p);
        int j = find(q);
        if (i == j) return;
        if (rank[i] < rank[j]) id[i] = j;
        else if (rank[i] > rank[j]) id[j] = i;
        else {
            id[i] = j;
            rank[j]++;
        }
        count--;
    }
    
};

class Solution {
public:
    void solve(vector<vector<char>>& board) {
        if(board.empty() || board[0].empty()) return;
        
        const int M = board.size(), N = board[0].size();
        
        UnionFind uf(M*N + 1);
        for( int i = 0; i < M ; i++) {
            for( int j = 0; j < N; j++) {
                if( i == 0 || i == M - 1 || j == 0 || j == N - 1 ) {
                    if(board[i][j] == 'O')
                        uf.union_by_rank( i*N + j , M*N);
                }
                else if( board[i][j] == 'O' ) {
                    if( board[i-1][j] == 'O') {
                        uf.union_by_rank( i*N + j, (i-1)*N+j);
                    }
                    if( board[i+1][j] == 'O') {
                        uf.union_by_rank( i*N + j, (i+1)*N+j);
                    }
                    if( board[i][j-1] == 'O') {
                        uf.union_by_rank( i*N + j, i*N+j-1 );
                    }
                    if( board[i][j+1] == 'O') {
                        uf.union_by_rank( i*N + j, i*N+j+1);
                    }
                }
                
            }
        }
        
        for( int i = 0; i < M ; i++ ) {
            for( int j = 0; j < N; j++ ) {
                if(!uf.is_connected( i*N + j, M*N)) {
                    board[i][j] = 'X';
                }
            }
        }
        return;
    }
};