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// @Title: 由斜杠划分区域 (Regions Cut By Slashes)
// @Author: 15816537946@163.com
// @Date: 2021-01-25 23:02:02
// @Runtime: 0 ms
// @Memory: 4.6 MB
type unionFind struct {
	parent, size []int
	setCount     int // 当前连通分量
}

func newUnionFind(n int) *unionFind {
	parent := make([]int, n)
	size := make([]int, n)
	for i := range parent {
		parent[i] = i
		size[i] = 1
	}
	return &unionFind{parent, size, n}
}

// 路径压缩
func (uf *unionFind) find(x int) int {
	if uf.parent[x] != x {
		uf.parent[x] = uf.find(uf.parent[x])
	}
	return uf.parent[x]
}

func (uf *unionFind) union(x, y int) {
	fx, fy := uf.find(x), uf.find(y)
	if fx == fy {
		return
	}
	if uf.size[fx] < uf.size[fy] {
		fx, fy = fy, fx
	}
	uf.parent[fy] = fx
	uf.size[fx] += uf.size[fy]
	uf.setCount--

}

func regionsBySlashes(grid []string) int {
	n := len(grid)
	uf := newUnionFind(4 * n * n)

	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			idx := i*n + j
			if i < n-1 {
				bottom := idx + n
				uf.union(idx*4+2, bottom*4)
			}
			if j < n-1 {
				right := idx + 1
				uf.union(idx*4+1, right*4+3)
			}
			if grid[i][j] == '/' {
				uf.union(idx*4, idx*4+3)
				uf.union(idx*4+1, idx*4+2)
			} else if grid[i][j] == '\\' {
				uf.union(idx*4, idx*4+1)
				uf.union(idx*4+2, idx*4+3)
			} else {
				uf.union(idx*4, idx*4+1)
				uf.union(idx*4+1, idx*4+2)
				uf.union(idx*4+2, idx*4+3)
			}
		}
	}

	return uf.setCount

}