【LC总结】Union Find系列(Num of Islands I&II/Graph Valid Tree/etc)

Surrounded Regions

Problem

Given a 2D board containing 'X' and 'O' (the letter 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

Note

不得不说，对于这道题而言，Union Find是一种很木讷的模板。

主函数：按矩阵大小建立：

1. 一个UnionFind类进行后续操作；

2. 一个dummy结点用来连接边角不可能被X围绕的O；

3. 一个node()函数对矩阵元素进行结点线性化。

操作：

1. 遍历所有结点，矩阵边角的O与dummy相连，矩阵内部的O与相邻的O相连；

2. 遍历所有结点，与dummy相连的结点设置为O，其它所有结点设置为X。

UnionFind函数：建立：

1. 全局变量parents；

2. 初始化函数UnionFind(int size)；

3. 查找parents函数find(int node)；

4. 归并函数union(int node1, int node2)；

5. 测试两结点是否相连函数isConnected(int node1, int node2)；

操作：

1. find(int node): 用while循环向上查找node的parent，注意先向上迭代parents[node]，再迭代node，否则会超时；

2. union(int node1, int node2): 找到两个结点的parents，r1和r2，令parents[r1] = r2；

3. isConnected(int n1, int n2): 查看两个结点的parents是否相等。

Solution

public class Solution {
    int row, col;
    public void solve(char[][] board) {
        if (board == null || board.length == 0) return;
        row = board.length;
        col = board[0].length;
        UnionFind uf = new UnionFind(row*col+1);
        int dummy = row*col;
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                if (board[i][j] == 'O') {
                    if (i == 0 || i == row-1 || j == 0 || j == col-1) uf.union(node(i, j), dummy);
                    else {
                        if (i > 0 && board[i-1][j] == 'O') uf.union(node(i, j), node(i-1, j));
                        if (i > 0 && board[i+1][j] == 'O') uf.union(node(i, j), node(i+1, j));
                        if (j > 0 && board[i][j-1] == 'O') uf.union(node(i, j), node(i, j-1));
                        if (j > 0 && board[i][j+1] == 'O') uf.union(node(i, j), node(i, j+1));
                    }
                }
            }
        }
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < col; j++) {
                if (uf.isConnected(node(i, j), dummy)) board[i][j] = 'O';
                else board[i][j] = 'X';
            }
        }
    }
    public int node(int i, int j) {
        return i*col+j;
    }
}

class UnionFind {
    int[] parents;
    public UnionFind(int n) {
        parents = new int[n];
        for (int i = 0; i < n; i++) parents[i] = i;
    }
    public void union(int n1, int n2) {
        int r1 = find(n1);
        int r2 = find(n2);
        if (r1 != r2) parents[r1] = r2;
    }
    public int find(int node) {
        if (parents[node] == node) return node;
        parents[node] = find(parents[node]);
        return parents[node];
    }    
    public boolean isConnected(int n1, int n2) {
        return find(n1) == find(n2);
    }
}

Graph Valid Tree

Problem

Given n nodes labeled from 0 to n - 1 and a list of undirected edges (each edge is a pair of nodes), write a function to check whether these edges make up a valid tree.

For example:

Given n = 5 and edges = [[0, 1], [0, 2], [0, 3], [1, 4]], return true.

Given n = 5 and edges = [[0, 1], [1, 2], [2, 3], [1, 3], [1, 4]], return false.

Note

同理，find，union，在主函数中初始化后调用。

Solution

public class Solution {
    int[] parents;
    public boolean validTree(int n, int[][] edges) {
        if (edges.length != n-1) return false;
        parents = new int[n];
        for (int i = 0; i < n; i++) parents[i] = i;
        for (int i = 0; i < n-1; i++) {
            if (find(edges[i][0]) == find(edges[i][1])) return false;
            union(edges[i][0], edges[i][1]);
        }
        return true;
    }
    public int find(int n) {
        if (parents[n] == n) return n;
        parents[n] = find(parents[n]);
        return parents[n];
    }
    public void union(int n1, int n2) {
        int r1 = find(n1);
        int r2 = find(n2);
        if (r1 != r2) parents[r1] = r2;
    }
}

Number of Islands

Problem

Given a 2d grid map of '1's (land) and '0's (water), count the number of islands. An island is surrounded by water and is formed by connecting adjacent lands horizontally or vertically. You may assume all four edges of the grid are all surrounded by water.

Example 1:

11110
11010
11000
00000

Answer: 1

Example 2:

11000
11000
00100
00011

Answer: 3

Note

Solution

public class Solution {

    class UnionFind {
        public int count;
        public int[] parents;
        public UnionFind(int m, int n, char[][] grid) {
            for (int i = 0; i < m; i++) {
                for (int j = 0; j < n; j++) {
                    if (grid[i][j] == '1') count++;
                }
            }
            parents = new int[m*n];
            for (int i = 0; i < m*n; i++) parents[i] = i;
        }
        public int find(int i) {
            if (i == parents[i]) return i;
            parents[i] = find(parents[i]);
            return parents[i];
        }
        public void union(int i, int j) {
            int pi = find(i);
            int pj = find(j);
            if (pi == pj) return;
            else parents[pi] = pj;
            count--;
        }
        public boolean isConnected(int i, int j) {
            return find(i) == find(j);
        }
    }
    public int numIslands(char[][] grid) {
        if (grid == null || grid.length == 0 || grid[0].length == 0) return 0;
        int m = grid.length, n = grid[0].length;
        UnionFind uf = new UnionFind(m, n, grid);
        for (int i = 0; i < m; i++) {
            for (int j = 0; j < n; j++) {
                if (grid[i][j] == '0') continue;
                int x = i*n+j;
                int y;
                if (i < m-1 && grid[i+1][j] == '1') {
                    y = x+n;
                    uf.union(x, y);
                }
                if (j < n-1 && grid[i][j+1] == '1') {
                    y = x+1;
                    uf.union(x, y);
                }
            }
        }
        return uf.count;
    }
}