LeetCode 959. 有斜杠划分区域-526互联

题目： https://leetcode.cn/problems/regions-cut-by-slashes/description/

题解（参考了讨论区）：将初始N*N的网格看做4 * N* N的三角形集合，根据输入合并对应的三角形。

C# 实现

public class Solution {
    public int RegionsBySlashes(string[] grid) {
        UnionFind uf = new UnionFind(4 * grid.Length * grid.Length);
        for (int i = 0; i < grid.Length; i++)
        {
            for (int j = 0; j < grid.Length; j++)
            {
                int start = 4 * (i * grid.Length + j);
                switch (grid[i][j])
                {
                    case ' ':
                        uf.Union(start, start + 1);
                        uf.Union(start + 2, start + 3);
                        uf.Union(start, start + 2);
                        break;
                    case '/':
                        uf.Union(start, start + 3);
                        uf.Union(start + 1, start + 2);
                        break;
                    case '\\':
                        uf.Union(start, start + 1);
                        uf.Union(start + 2, start + 3);
                        break;
                }

                if (i > 0)
                {
                    uf.Union(start, start - 4 * grid.Length + 2);
                }

                if (j > 0)
                {
                    uf.Union(start + 3, start - 3);
                }
            }
        }

        return uf.GetGroups();
    }

　　//该实现采用了路径压缩算法，以保证最坏情况下合并操作的成本小于logN
    public class UnionFind
    {
        private int[] uf;
        private int[] ufSize;

        public UnionFind(int N)
        {
            uf = new int[N];
            ufSize = new int[N];
            for (int i = 0; i < N; i++)
            {
                uf[i] = i;
                ufSize[i] = 1;
            }
        }

        public int Find(int p)
        {
            int root = p;
            while (root != uf[root])
            {
                root = uf[root];
            }

            while (p != root)
            {
                int newP = uf[p];
                uf[p] = root;
                p = newP;
            }

            return root;
        }

        public void Union(int p, int q)
        {
            int pRoot = Find(p);
            int qRoot = Find(q);
            if (pRoot != qRoot)
            {
                if (ufSize[pRoot] > ufSize[qRoot])
                {
                    uf[qRoot] = pRoot;
                    ufSize[pRoot] += ufSize[qRoot];
                }
                else
                {
                    uf[pRoot] = qRoot;
                    ufSize[qRoot] += ufSize[pRoot];
                }
            }
        }

        public int GetGroups()
        {
            int count = 0;
            for (int i = 0; i < uf.Length; i++)
            {
                if (uf[i] == i)
                    count++;
            }
            return count;
        }
    }
}