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c.go
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c.go
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package main
import (
"math"
"sort"
)
// github.com/EndlessCheng/codeforces-go
func minCostConnectPoints_N2(points [][]int) (ans int) {
abs := func(x int) int {
if x < 0 {
return -x
}
return x
}
dis := func(p, q []int) int { return abs(p[0]-q[0]) + abs(p[1]-q[1]) }
n := len(points)
dist := make([][]int, n)
for i := range dist {
dist[i] = make([]int, n)
for j := range dist[i] {
dist[i][j] = dis(points[i], points[j])
}
}
min := func(a, b int) int {
if a < b {
return a
}
return b
}
const inf int = 1e7
minWeights := make([]int, n)
for i := range minWeights {
minWeights[i] = inf
}
minWeights[0] = 0
used := make([]bool, n)
for {
v := -1
for i, u := range used {
if !u && (v == -1 || minWeights[i] < minWeights[v]) {
v = i
}
}
if v == -1 {
break
}
used[v] = true
ans += minWeights[v]
for w := range minWeights {
minWeights[w] = min(minWeights[w], dist[v][w])
}
}
return
}
//
type unionFind struct {
parent, rank []int
}
func newUnionFind(n int) *unionFind {
parent := make([]int, n)
rank := make([]int, n)
for i := range parent {
parent[i] = i
rank[i] = 1
}
return &unionFind{parent, rank}
}
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) bool {
fx, fy := uf.find(x), uf.find(y)
if fx == fy {
return false
}
if uf.rank[fx] < uf.rank[fy] {
fx, fy = fy, fx
}
uf.rank[fx] += uf.rank[fy]
uf.parent[fy] = fx
return true
}
type fenwickTree struct {
tree, idRec []int
}
func newFenwickTree(n int) *fenwickTree {
tree := make([]int, n)
idRec := make([]int, n)
for i := range tree {
tree[i], idRec[i] = math.MaxInt64, -1
}
return &fenwickTree{tree, idRec}
}
func (f *fenwickTree) update(pos, val, id int) {
for ; pos > 0; pos &= pos - 1 {
if val < f.tree[pos] {
f.tree[pos], f.idRec[pos] = val, id
}
}
}
func (f *fenwickTree) query(pos int) int {
minVal, minID := math.MaxInt64, -1
for ; pos < len(f.tree); pos += pos & -pos {
if f.tree[pos] < minVal {
minVal, minID = f.tree[pos], f.idRec[pos]
}
}
return minID
}
func dist(p, q []int) int {
return abs(p[0]-q[0]) + abs(p[1]-q[1])
}
func minCostConnectPoints(points [][]int) (ans int) {
n := len(points)
for i, p := range points {
points[i] = append(p, i)
}
type edge struct{ v, w, dis int }
edges := []edge{}
build := func() {
sort.Slice(points, func(i, j int) bool { a, b := points[i], points[j]; return a[0] < b[0] || a[0] == b[0] && a[1] < b[1] })
// 离散化 y-x
type pair struct{ v, i int }
ps := make([]pair, n)
for i, p := range points {
ps[i] = pair{p[1] - p[0], i}
}
sort.Slice(ps, func(i, j int) bool { return ps[i].v < ps[j].v })
kth := make([]int, n)
k := 1
kth[ps[0].i] = k
for i := 1; i < n; i++ {
if ps[i].v != ps[i-1].v {
k++
}
kth[ps[i].i] = k
}
t := newFenwickTree(k + 1)
for i := n - 1; i >= 0; i-- {
p := points[i]
pos := kth[i]
if j := t.query(pos); j != -1 {
q := points[j]
edges = append(edges, edge{p[2], q[2], dist(p, q)})
}
t.update(pos, p[0]+p[1], i)
}
}
build()
for _, p := range points {
p[0], p[1] = p[1], p[0]
}
build()
for _, p := range points {
p[0] = -p[0]
}
build()
for _, p := range points {
p[0], p[1] = p[1], p[0]
}
build()
sort.Slice(edges, func(i, j int) bool { return edges[i].dis < edges[j].dis })
uf := newUnionFind(n)
left := n - 1
for _, e := range edges {
if uf.union(e.v, e.w) {
ans += e.dis
left--
if left == 0 {
break
}
}
}
return
}
func abs(x int) int {
if x < 0 {
return -x
}
return x
}