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// @Title: 飞地的数量 (Number of Enclaves)
// @Author: 15816537946@163.com
// @Date: 2022-02-12 16:23:40
// @Runtime: 64 ms
// @Memory: 7.2 MB
type unionFind struct {
    parent []int
    rank []int
    onEdge []bool
}

func newUnionFind(grid [][]int) unionFind {
    m,n := len(grid), len(grid[0])
    parent := make([]int, m*n)
    rank := make([]int, m*n)
    onEdge := make([]bool, m*n)

    for i, row := range grid {
        for j, v := range row {
            if v == 1 {
                idx := i*n+j
                parent[idx] = idx
                if i ==0 || i == m-1 || j ==0 || j == n-1 {
                    onEdge[idx] = true
                }
            }
        }
    }

    return unionFind{parent,rank, onEdge}
}

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) merge(x,y int) {
    x,y = uf.find(x), uf.find(y)
    if x == y {
        return
    }
    if uf.rank[x] > uf.rank[y] {
        uf.parent[y] = x
        uf.onEdge[x] = uf.onEdge[x] || uf.onEdge[y]
    } else if uf.rank[x] < uf.rank[y] {
        uf.parent[x] = y
        uf.onEdge[y] = uf.onEdge[y] || uf.onEdge[x]
    } else {
        uf.parent[y] = x
        uf.onEdge[x] = uf.onEdge[x] || uf.onEdge[y]
        uf.rank[x]++
    }
}

func numEnclaves(grid [][]int) (ans int) {
    uf := newUnionFind(grid)
    m,n := len(grid), len(grid[0])
    for i, row := range grid {
        for j,v := range row {
            if v == 1 {
                idx := i *n +j
                if j+1<n &&  grid[i][j+1] == 1 {
                    uf.merge(idx, idx+1)
                }
                if i+1 <m && grid[i+1][j] == 1 {
                    uf.merge(idx, idx+n)
                }
            }
        }
    }
    for i :=1;i<m-1;i++ {
        for j :=1;j<n-1;j++ {
            if grid[i][j] == 1 && !uf.onEdge[uf.find(i*n+j)] {
                ans++
            }
        }
    }

    return
}