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// @Title: 最小体力消耗路径 (Path With Minimum Effort)
// @Author: 15816537946@163.com
// @Date: 2021-01-29 21:14:07
// @Runtime: 160 ms
// @Memory: 8.1 MB
type unionFind struct {
	parent, size []int
}

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}
}

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.size[fx] += uf.size[fy]
	uf.parent[fy] = fx
}

func (uf *unionFind) inSameSet(x, y int) bool {
	return uf.find(x) == uf.find(y)
}

type edge struct {
	v, w, diff int
}

func minimumEffortPath(heights [][]int) int {
	n, m := len(heights), len(heights[0])
	edges := []edge{}

	for i, row := range heights {
		for j, h := range row {
			id := i*m + j
			if i > 0 {
				edges = append(edges, edge{id - m, id, abs(h - heights[i-1][j])})
			}
			if j > 0 {
				edges = append(edges, edge{id - 1, id, abs(h - heights[i][j-1])})
			}
		}
	}

	sort.Slice(edges, func(i, j int) bool { return edges[i].diff < edges[j].diff })

	uf := newUnionFind(n * m)
	for _, e := range edges {
		uf.union(e.v, e.w)
		if uf.inSameSet(0, n*m-1) {
			return e.diff
		}
	}
	return 0
}

func abs(x int) int {
	if x < 0 {
		return -x
	}
	return x
}