結果
| 問題 |
No.1197 モンスターショー
|
| コンテスト | |
| ユーザー |
 草苺奶昔
|
| 提出日時 | 2024-08-20 15:37:36 |
| 言語 | Go (1.23.4) |
| 結果 |
RE
|
| 実行時間 | - |
| コード長 | 24,067 bytes |
| コンパイル時間 | 11,943 ms |
| コンパイル使用メモリ | 226,548 KB |
| 実行使用メモリ | 43,080 KB |
| 最終ジャッジ日時 | 2024-08-20 15:37:56 |
| 合計ジャッジ時間 | 19,667 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | RE * 2 |
| other | RE * 41 |
ソースコード
// 路径修改
// 路径查询
// 子树查询
// MaxPath树上二分
package main
import (
"bufio"
"fmt"
"math/bits"
"os"
"strings"
)
func main() {
// demo()
// yosupoVertexAddPathSum()
yuki1197()
}
func demo() {
{
// 0
// / \
// 1 2
// / \
// 3 4
tree := NewTree32(5)
tree.AddEdge(0, 1, 0)
tree.AddEdge(0, 2, 0)
tree.AddEdge(2, 3, 0)
tree.AddEdge(2, 4, 0)
tree.Build(0)
S := NewTreeMonoid32Lazy(tree, false)
S.Build(func(vidOrEid int32) E { return int(vidOrEid) })
fmt.Println(S.QuerySubtree(0)) // 10
fmt.Println(S.QuerySubtree(1)) // 1
fmt.Println(S.QuerySubtree(2)) // 9
fmt.Println(S.QuerySubtree(3)) // 3
fmt.Println(S.QuerySubtree(4)) // 4
fmt.Println(S.QueryPath(1, 3)) // 6
S.Update(3, 10)
fmt.Println(S.QuerySubtree(0)) // 20
fmt.Println(S.MaxPath(1, 3, func(x E) bool { return x < 4 })) // 0
fmt.Println(S.MaxPath(1, 3, func(x E) bool { return x < -1 })) // 0
}
}
// https://judge.yosupo.jp/problem/vertex_add_path_sum
func yosupoVertexAddPathSum() {
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n, q int32
fmt.Fscan(in, &n, &q)
weights := make([]int, n)
for i := 0; i < int(n); i++ {
fmt.Fscan(in, &weights[i])
}
tree := NewTree32(n)
for i := 1; i < int(n); i++ {
var u, v int32
fmt.Fscan(in, &u, &v)
tree.AddEdge(u, v, 0)
}
tree.Build(0)
S := NewTreeMonoid32Lazy(tree, false)
S.Build(func(vidOrEid int32) E { return weights[vidOrEid] })
for i := 0; i < int(q); i++ {
var t int
fmt.Fscan(in, &t)
if t == 0 {
var v, x int32
fmt.Fscan(in, &v, &x)
S.Update(v, int(x))
} else {
var u, v int32
fmt.Fscan(in, &u, &v)
fmt.Fprintln(out, S.QueryPath(u, v))
}
}
}
// https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=GRL_5_E
// https://yukicoder.me/problems/no/1197
// No.1197 モンスターショー
// 树上移动距离之和(带修改版)
// 给定一个有 n 个节点的树，每个节点与一条边相连，边长为 1。
// 一开始，有 k 只史莱姆分别位于不同的节点上。现在，你需要支持以下操作：
// 1 i d: 将第 i 只史莱姆从其所在节点移到节点 d。
// !2 e :查询将所有史莱姆移到节点 e 时，史莱姆移动距离之和。
// 其中，史莱姆从一个节点到另一个节点的移动距离为其走过的边长之和。
// !固定0号根节点,统计每个史莱姆的深度之和,然后统计从根节点移动到各个点的距离之和.
func yuki1197() {
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n, k, q int32
fmt.Fscan(in, &n, &k, &q)
pos := make([]int32, k) // 史莱姆的初始位置
for i := range pos {
fmt.Fscan(in, &pos[i])
pos[i]--
}
tree := NewTree32(n)
for i := int32(0); i < n-1; i++ {
var u, v int32
fmt.Fscan(in, &u, &v)
u--
v--
tree.AddEdge(u, v, 1)
}
tree.Build(0)
LM := NewTreeMonoid32Lazy(tree, false)
for _, v := range pos {
LM.UpdatePath(0, v, 1)
}
depth := tree.Depth
depSum := 0
for _, v := range pos {
depSum += int(depth[v])
}
for i := int32(0); i < q; i++ {
var op int32
fmt.Fscan(in, &op)
if op == 1 { // 维护史莱姆的深度之和、根节点到各个结点的移动距离之和
var slime, moveTo int32
fmt.Fscan(in, &slime, &moveTo)
slime, moveTo = slime-1, moveTo-1
depSum -= int(depth[pos[slime]])
LM.UpdatePath(0, pos[slime], -1)
pos[slime] = moveTo
depSum += int(depth[pos[slime]])
LM.UpdatePath(0, pos[slime], 1)
} else {
var to int32
fmt.Fscan(in, &to)
to--
res := int(depth[to])*int(k) + depSum // 所有史莱姆先走到根节点,再走到to的距离之和
res -= 2 * LM.QueryPath(0, to) // 多算的距离
res += int(2 * k) // 线段树里把0-0的移动距离统计为1,所以要减去2k
fmt.Fprintln(out, res)
}
}
}
const commutative bool = true // !E是否可交换，即 op(a,b) == op(b,a)
type E = int
type Id = int
func e() E { return 0 }
func id() Id { return 0 }
func op(left, right E) E {
return left + right
}
func mapping(f Id, g E, size int) E {
return f*size + g
}
func composition(f, g Id) Id {
return f + g
}
type TreeMonoid32Lazy struct {
edge int32
n int32
tree *Tree32
seg, segR *LazySegTree32
}
func NewTreeMonoid32Lazy(tree *Tree32, edge bool) *TreeMonoid32Lazy {
var edgeValue int32
if edge {
edgeValue = 1
}
return &TreeMonoid32Lazy{edge: edgeValue, n: tree.n, tree: tree}
}
func (tag *TreeMonoid32Lazy) Build(f func(vidOrEid int32) E) {
idToNode := tag.tree.IdToNode
vToE := tag.tree.vToE
if tag.edge == 0 {
fv := func(i int32) E { return f(idToNode[i]) }
tag.seg = NewLazySegTree32(tag.n, fv, e, id, op, mapping, composition)
if !commutative {
tag.segR = NewLazySegTree32(tag.n, fv, e, id, func(a, b E) E { return op(b, a) }, mapping, composition)
}
} else {
fe := func(i int32) E {
if i == 0 {
return e()
}
return f(vToE[idToNode[i]])
}
tag.seg = NewLazySegTree32(tag.n, fe, e, id, op, mapping, composition)
if !commutative {
tag.segR = NewLazySegTree32(tag.n, fe, e, id, func(a, b E) E { return op(b, a) }, mapping, composition)
}
}
}
func (tag *TreeMonoid32Lazy) Set(i int32, x E) {
if tag.edge != 0 {
i = tag.tree.EToV(i)
}
i = tag.tree.Lid[i]
tag.seg.Set(i, x)
if !commutative {
tag.segR.Set(i, x)
}
}
func (tag *TreeMonoid32Lazy) Update(i int32, x E) {
if tag.edge != 0 {
i = tag.tree.EToV(i)
}
i = tag.tree.Lid[i]
tag.seg.Multiply(i, x)
if !commutative {
tag.segR.Multiply(i, x)
}
}
func (tag *TreeMonoid32Lazy) Get(i int32) E {
return tag.seg.Get(tag.tree.Lid[i])
}
func (tag *TreeMonoid32Lazy) QueryPath(from, to int32) E {
pd := tag.tree.GetPathDecomposition(from, to, tag.edge)
res := e()
for i := 0; i < len(pd); i++ {
res = op(res, tag.getProd(pd[i][0], pd[i][1]))
}
return res
}
func (tag *TreeMonoid32Lazy) QueryAll() E {
if !commutative {
panic("not implemented")
}
return tag.QueryAll()
}
func (tag *TreeMonoid32Lazy) QuerySubtree(u int32) E {
if !commutative {
panic("not implemented")
}
l, r := tag.tree.Lid[u], tag.tree.Rid[u]
return tag.seg.Query(l+tag.edge, r)
}
func (tag *TreeMonoid32Lazy) UpdateSubtree(u int32, f Id) {
l, r := tag.tree.Lid[u], tag.tree.Rid[u]
tag.seg.Update(l+tag.edge, r, f)
if !commutative {
tag.segR.Update(l+tag.edge, r, f)
}
}
// outtree: 除开u的子树外的其他节点
func (tag *TreeMonoid32Lazy) UpdateOuttree(u int32, f Id) {
l, r := tag.tree.Lid[u], tag.tree.Rid[u]
tag.seg.Update(tag.edge, l+tag.edge, f)
tag.seg.Update(r, tag.n, f)
if !commutative {
tag.segR.Update(tag.edge, l+tag.edge, f)
tag.segR.Update(r, tag.n, f)
}
}
func (tag *TreeMonoid32Lazy) UpdatePath(u, v int32, f Id) {
pd := tag.tree.GetPathDecomposition(u, v, tag.edge)
for i := 0; i < len(pd); i++ {
l, r := pd[i][0], pd[i][1]
if l > r {
l, r = r, l
}
tag.seg.Update(l, r+1, f)
if !commutative {
tag.segR.Update(l, r+1, f)
}
}
}
// 满足 check 为true的最远的节点.
// 如果不存在返回 -1.
func (tag *TreeMonoid32Lazy) MaxPath(from, to int32, check func(E) bool) int32 {
if tag.edge != 0 {
return tag.maxPathEdge(from, to, check)
}
if !check(tag.QueryPath(from, from)) {
return -1
}
pd := tag.tree.GetPathDecomposition(from, to, tag.edge)
val := e()
idToNode := tag.tree.IdToNode
for _, e := range pd {
x := tag.getProd(e[0], e[1])
if tmp := op(val, x); check(tmp) {
val = tmp
from = idToNode[e[1]]
continue
}
checkTmp := func(x E) bool { return check(op(val, x)) }
if e[0] <= e[1] {
i := tag.seg.MaxRight(e[0], checkTmp)
if i == e[0] {
return from
}
return idToNode[i-1]
} else {
i := int32(0)
if commutative {
i = tag.seg.MinLeft(e[0]+1, checkTmp)
} else {
i = tag.segR.MinLeft(e[0]+1, checkTmp)
}
if i == e[0]+1 {
return from
}
return idToNode[i]
}
}
return to
}
func (tag *TreeMonoid32Lazy) maxPathEdge(from, to int32, check func(E) bool) int32 {
if !check(e()) {
return -1
}
lca := tag.tree.Lca(from, to)
pd := tag.tree.GetPathDecomposition(from, lca, tag.edge)
val := e()
parent, idToNode := tag.tree.Parent, tag.tree.IdToNode
for _, e := range pd {
x := tag.getProd(e[0], e[1])
if tmp := op(val, x); check(tmp) {
val = tmp
from = parent[idToNode[e[1]]]
continue
}
checkTmp := func(x E) bool { return check(op(val, x)) }
i := int32(0)
if commutative {
i = tag.seg.MinLeft(e[0]+1, checkTmp)
} else {
i = tag.segR.MinLeft(e[0]+1, checkTmp)
}
if i == e[0]+1 {
return from
}
return parent[idToNode[i]]
}
pd = tag.tree.GetPathDecomposition(lca, to, tag.edge)
for _, e := range pd {
x := tag.getProd(e[0], e[1])
if tmp := op(val, x); check(tmp) {
val = tmp
from = idToNode[e[1]]
continue
}
checkTmp := func(x E) bool { return check(op(val, x)) }
i := tag.seg.MaxRight(e[0], checkTmp)
if i == e[0] {
return from
}
return idToNode[i-1]
}
return to
}
func (tag *TreeMonoid32Lazy) getProd(a, b int32) E {
if commutative {
if a <= b {
return tag.seg.Query(a, b+1)
}
return tag.seg.Query(b, a+1)
} else {
if a <= b {
return tag.seg.Query(a, b+1)
}
return tag.segR.Query(b, a+1)
}
}
// !template
type LazySegTree32 struct {
n int32
size int32
log int32
data []E
lazy []Id
e func() E
id func() Id
op func(E, E) E
mapping func(Id, E, int) E
composition func(Id, Id) Id
}
func NewLazySegTree32(
n int32, f func(int32) E,
e func() E, id func() Id,
op func(E, E) E, mapping func(Id, E, int) E, composition func(Id, Id) Id,
) *LazySegTree32 {
tree := &LazySegTree32{e: e, id: id, op: op, mapping: mapping, composition: composition}
tree.n = n
tree.log = int32(bits.Len32(uint32(n - 1)))
tree.size = 1 << tree.log
tree.data = make([]E, tree.size<<1)
tree.lazy = make([]Id, tree.size)
for i := range tree.data {
tree.data[i] = tree.e()
}
for i := range tree.lazy {
tree.lazy[i] = tree.id()
}
for i := int32(0); i < n; i++ {
tree.data[tree.size+i] = f(i)
}
for i := tree.size - 1; i >= 1; i-- {
tree.pushUp(i)
}
return tree
}
// 查询切片[left:right]的值
//
// 0<=left<=right<=len(tree.data)
func (tree *LazySegTree32) Query(left, right int32) E {
if left < 0 {
left = 0
}
if right > tree.n {
right = tree.n
}
if left >= right {
return tree.e()
}
left += tree.size
right += tree.size
for i := tree.log; i >= 1; i-- {
if ((left >> i) << i) != left {
tree.pushDown(left >> i)
}
if ((right >> i) << i) != right {
tree.pushDown((right - 1) >> i)
}
}
sml, smr := tree.e(), tree.e()
for left < right {
if left&1 != 0 {
sml = tree.op(sml, tree.data[left])
left++
}
if right&1 != 0 {
right--
smr = tree.op(tree.data[right], smr)
}
left >>= 1
right >>= 1
}
return tree.op(sml, smr)
}
func (tree *LazySegTree32) QueryAll() E {
return tree.data[1]
}
func (tree *LazySegTree32) GetAll() []E {
for i := int32(1); i < tree.size; i++ {
tree.pushDown(i)
}
res := make([]E, tree.n)
copy(res, tree.data[tree.size:tree.size+tree.n])
return res
}
// 更新切片[left:right]的值
//
// 0<=left<=right<=len(tree.data)
func (tree *LazySegTree32) Update(left, right int32, f Id) {
if left < 0 {
left = 0
}
if right > tree.n {
right = tree.n
}
if left >= right {
return
}
left += tree.size
right += tree.size
for i := tree.log; i >= 1; i-- {
if ((left >> i) << i) != left {
tree.pushDown(left >> i)
}
if ((right >> i) << i) != right {
tree.pushDown((right - 1) >> i)
}
}
l2, r2 := left, right
for left < right {
if left&1 != 0 {
tree.propagate(left, f)
left++
}
if right&1 != 0 {
right--
tree.propagate(right, f)
}
left >>= 1
right >>= 1
}
left = l2
right = r2
for i := int32(1); i <= tree.log; i++ {
if ((left >> i) << i) != left {
tree.pushUp(left >> i)
}
if ((right >> i) << i) != right {
tree.pushUp((right - 1) >> i)
}
}
}
// 二分查询最小的 left 使得切片 [left:right] 内的值满足 predicate
func (tree *LazySegTree32) MinLeft(right int32, predicate func(data E) bool) int32 {
if right == 0 {
return 0
}
right += tree.size
for i := tree.log; i >= 1; i-- {
tree.pushDown((right - 1) >> i)
}
res := tree.e()
for {
right--
for right > 1 && right&1 != 0 {
right >>= 1
}
if !predicate(tree.op(tree.data[right], res)) {
for right < tree.size {
tree.pushDown(right)
right = right<<1 | 1
if tmp := tree.op(tree.data[right], res); predicate(tmp) {
res = tmp
right--
}
}
return right + 1 - tree.size
}
res = tree.op(tree.data[right], res)
if (right & -right) == right {
break
}
}
return 0
}
// 二分查询最大的 right 使得切片 [left:right] 内的值满足 predicate
func (tree *LazySegTree32) MaxRight(left int32, predicate func(data E) bool) int32 {
if left == tree.n {
return tree.n
}
left += tree.size
for i := tree.log; i >= 1; i-- {
tree.pushDown(left >> i)
}
res := tree.e()
for {
for left&1 == 0 {
left >>= 1
}
if !predicate(tree.op(res, tree.data[left])) {
for left < tree.size {
tree.pushDown(left)
left <<= 1
if tmp := tree.op(res, tree.data[left]); predicate(tmp) {
res = tmp
left++
}
}
return left - tree.size
}
res = tree.op(res, tree.data[left])
left++
if (left & -left) == left {
break
}
}
return tree.n
}
// 单点查询(不需要 pushUp/op 操作时使用)
func (tree *LazySegTree32) Get(index int32) E {
index += tree.size
for i := tree.log; i >= 1; i-- {
tree.pushDown(index >> i)
}
return tree.data[index]
}
// 单点赋值
func (tree *LazySegTree32) Set(index int32, e E) {
index += tree.size
for i := tree.log; i >= 1; i-- {
tree.pushDown(index >> i)
}
tree.data[index] = e
for i := int32(1); i <= tree.log; i++ {
tree.pushUp(index >> i)
}
}
func (tree *LazySegTree32) Multiply(index int32, e E) {
index += tree.size
for i := tree.log; i >= 1; i-- {
tree.pushDown(index >> i)
}
tree.data[index] = tree.op(tree.data[index], e)
for i := int32(1); i <= tree.log; i++ {
tree.pushUp(index >> i)
}
}
func (tree *LazySegTree32) pushUp(root int32) {
tree.data[root] = tree.op(tree.data[root<<1], tree.data[root<<1|1])
}
func (tree *LazySegTree32) pushDown(root int32) {
if tree.lazy[root] != tree.id() {
tree.propagate(root<<1, tree.lazy[root])
tree.propagate(root<<1|1, tree.lazy[root])
tree.lazy[root] = tree.id()
}
}
func (tree *LazySegTree32) propagate(root int32, f Id) {
size := 1 << (tree.log - int32((bits.Len32(uint32(root)) - 1)) /**topbit**/)
tree.data[root] = tree.mapping(f, tree.data[root], size)
if root < tree.size {
tree.lazy[root] = tree.composition(f, tree.lazy[root])
}
}
func (tree *LazySegTree32) String() string {
var sb []string
sb = append(sb, "[")
for i := int32(0); i < tree.n; i++ {
if i != 0 {
sb = append(sb, ", ")
}
sb = append(sb, fmt.Sprintf("%v", tree.Get(i)))
}
sb = append(sb, "]")
return strings.Join(sb, "")
}
type neighbor = struct {
to int32
eid int32
cost int
}
type Tree32 struct {
Lid, Rid []int32
IdToNode []int32
Depth []int32
DepthWeighted []int
Parent []int32
Head []int32 // 重链头
Tree [][]neighbor
Edges [][2]int32
vToE []int32 // 节点v的父边的id
n int32
}
func NewTree32(n int32) *Tree32 {
res := &Tree32{Tree: make([][]neighbor, n), Edges: make([][2]int32, 0, n-1), n: n}
return res
}
func (t *Tree32) AddEdge(u, v int32, w int) {
eid := int32(len(t.Edges))
t.Tree[u] = append(t.Tree[u], neighbor{to: v, eid: eid, cost: w})
t.Tree[v] = append(t.Tree[v], neighbor{to: u, eid: eid, cost: w})
t.Edges = append(t.Edges, [2]int32{u, v})
}
func (t *Tree32) AddDirectedEdge(from, to int32, cost int) {
eid := int32(len(t.Edges))
t.Tree[from] = append(t.Tree[from], neighbor{to: to, eid: eid, cost: cost})
t.Edges = append(t.Edges, [2]int32{from, to})
}
func (t *Tree32) Build(root int32) {
if root != -1 && int32(len(t.Edges)) != t.n-1 {
panic("edges count != n-1")
}
n := t.n
t.Lid = make([]int32, n)
t.Rid = make([]int32, n)
t.IdToNode = make([]int32, n)
t.Depth = make([]int32, n)
t.DepthWeighted = make([]int, n)
t.Parent = make([]int32, n)
t.Head = make([]int32, n)
t.vToE = make([]int32, n)
for i := int32(0); i < n; i++ {
t.Depth[i] = -1
t.Head[i] = root
t.vToE[i] = -1
}
if root != -1 {
t._dfsSize(root, -1)
time := int32(0)
t._dfsHld(root, &time)
} else {
time := int32(0)
for i := int32(0); i < n; i++ {
if t.Depth[i] == -1 {
t._dfsSize(i, -1)
t._dfsHld(i, &time)
}
}
}
}
// 从v开始沿着重链向下收集节点.
func (t *Tree32) HeavyPathAt(v int32) []int32 {
path := []int32{v}
for {
a := path[len(path)-1]
for _, e := range t.Tree[a] {
if e.to != t.Parent[a] && t.Head[e.to] == v {
path = append(path, e.to)
break
}
}
if path[len(path)-1] == a {
break
}
}
return path
}
// 返回重儿子，如果没有返回 -1.
func (t *Tree32) HeavyChild(v int32) int32 {
k := t.Lid[v] + 1
if k == t.n {
return -1
}
w := t.IdToNode[k]
if t.Parent[w] == v {
return w
}
return -1
}
// 从v开始向上走k步.
func (t *Tree32) KthAncestor(v, k int32) int32 {
if k > t.Depth[v] {
return -1
}
for {
u := t.Head[v]
if t.Lid[v]-k >= t.Lid[u] {
return t.IdToNode[t.Lid[v]-k]
}
k -= t.Lid[v] - t.Lid[u] + 1
v = t.Parent[u]
}
}
func (t *Tree32) Lca(u, v int32) int32 {
for {
if t.Lid[u] > t.Lid[v] {
u, v = v, u
}
if t.Head[u] == t.Head[v] {
return u
}
v = t.Parent[t.Head[v]]
}
}
func (t *Tree32) LcaRooted(u, v, root int32) int32 {
return t.Lca(u, v) ^ t.Lca(u, root) ^ t.Lca(v, root)
}
func (t *Tree32) Dist(a, b int32) int32 {
c := t.Lca(a, b)
return t.Depth[a] + t.Depth[b] - 2*t.Depth[c]
}
func (t *Tree32) DistWeighted(a, b int32) int {
c := t.Lca(a, b)
return t.DepthWeighted[a] + t.DepthWeighted[b] - 2*t.DepthWeighted[c]
}
// c 是否在 p 的子树中.c和p不能相等.
func (t *Tree32) InSubtree(c, p int32) bool {
return t.Lid[p] <= t.Lid[c] && t.Lid[c] < t.Rid[p]
}
// 从 a 开始走 k 步到 b.
func (t *Tree32) Jump(a, b, k int32) int32 {
if k == 1 {
if a == b {
return -1
}
if t.InSubtree(b, a) {
return t.KthAncestor(b, t.Depth[b]-t.Depth[a]-1)
}
return t.Parent[a]
}
c := t.Lca(a, b)
dac := t.Depth[a] - t.Depth[c]
dbc := t.Depth[b] - t.Depth[c]
if k > dac+dbc {
return -1
}
if k <= dac {
return t.KthAncestor(a, k)
}
return t.KthAncestor(b, dac+dbc-k)
}
func (t *Tree32) SubtreeSize(v int32) int32 {
return t.Rid[v] - t.Lid[v]
}
func (t *Tree32) SubtreeSizeRooted(v, root int32) int32 {
if v == root {
return t.n
}
x := t.Jump(v, root, 1)
if t.InSubtree(v, x) {
return t.Rid[v] - t.Lid[v]
}
return t.n - t.Rid[x] + t.Lid[x]
}
func (t *Tree32) CollectChild(v int32) []int32 {
var res []int32
for _, e := range t.Tree[v] {
if e.to != t.Parent[v] {
res = append(res, e.to)
}
}
return res
}
// 收集与 v 相邻的轻边.
func (t *Tree32) CollectLight(v int32) []int32 {
var res []int32
skip := true
for _, e := range t.Tree[v] {
if e.to != t.Parent[v] {
if !skip {
res = append(res, e.to)
}
skip = false
}
}
return res
}
func (tree *Tree32) RestorePath(from, to int32) []int32 {
res := []int32{}
composition := tree.GetPathDecomposition(from, to, 0)
for _, e := range composition {
a, b := e[0], e[1]
if a <= b {
for i := a; i <= b; i++ {
res = append(res, tree.IdToNode[i])
}
} else {
for i := a; i >= b; i-- {
res = append(res, tree.IdToNode[i])
}
}
}
return res
}
// 返回沿着`路径顺序`的 [起点,终点] 的 欧拉序 `左闭右闭` 数组.
//
// !eg:[[2 0] [4 4]] 沿着路径顺序但不一定沿着欧拉序.
func (tree *Tree32) GetPathDecomposition(u, v int32, edge int32) [][2]int32 {
up, down := [][2]int32{}, [][2]int32{}
lid, head, parent := tree.Lid, tree.Head, tree.Parent
for {
if head[u] == head[v] {
break
}
if lid[u] < lid[v] {
down = append(down, [2]int32{lid[head[v]], lid[v]})
v = parent[head[v]]
} else {
up = append(up, [2]int32{lid[u], lid[head[u]]})
u = parent[head[u]]
}
}
if lid[u] < lid[v] {
down = append(down, [2]int32{lid[u] + edge, lid[v]})
} else if lid[v]+edge <= lid[u] {
up = append(up, [2]int32{lid[u], lid[v] + edge})
}
for i := 0; i < len(down)/2; i++ {
down[i], down[len(down)-1-i] = down[len(down)-1-i], down[i]
}
return append(up, down...)
}
// 遍历路径上的 `[起点,终点)` 欧拉序 `左闭右开` 区间.
func (tree *Tree32) EnumeratePathDecomposition(u, v int32, edge int32, f func(start, end int32)) {
head, lid, parent := tree.Head, tree.Lid, tree.Parent
for {
if head[u] == head[v] {
break
}
if lid[u] < lid[v] {
a, b := lid[head[v]], lid[v]
if a > b {
a, b = b, a
}
f(a, b+1)
v = parent[head[v]]
} else {
a, b := lid[u], lid[head[u]]
if a > b {
a, b = b, a
}
f(a, b+1)
u = parent[head[u]]
}
}
if lid[u] < lid[v] {
a, b := lid[u]+edge, lid[v]
if a > b {
a, b = b, a
}
f(a, b+1)
} else if lid[v]+edge <= lid[u] {
a, b := lid[u], lid[v]+edge
if a > b {
a, b = b, a
}
f(a, b+1)
}
}
// 返回 root 的欧拉序区间, 左闭右开, 0-indexed.
func (tree *Tree32) Id(root int32) (int32, int32) {
return tree.Lid[root], tree.Rid[root]
}
// 返回返回边 u-v 对应的 欧拉序起点编号, 1 <= eid <= n-1., 0-indexed.
func (tree *Tree32) Eid(u, v int32) int32 {
if tree.Lid[u] > tree.Lid[v] {
return tree.Lid[u]
}
return tree.Lid[v]
}
// 点v对应的父边的边id.如果v是根节点则返回-1.
func (tre *Tree32) VToE(v int32) int32 {
return tre.vToE[v]
}
// 第i条边对应的深度更深的那个节点.
func (tree *Tree32) EToV(i int32) int32 {
u, v := tree.Edges[i][0], tree.Edges[i][1]
if tree.Parent[u] == v {
return u
}
return v
}
func (tree *Tree32) ELid(u int32) int32 {
return 2*tree.Lid[u] - tree.Depth[u]
}
func (tree *Tree32) ERid(u int32) int32 {
return 2*tree.Rid[u] - tree.Depth[u] - 1
}
func (t *Tree32) _dfsSize(cur, pre int32) {
size := t.Rid
t.Parent[cur] = pre
if pre != -1 {
t.Depth[cur] = t.Depth[pre] + 1
} else {
t.Depth[cur] = 0
}
size[cur] = 1
nexts := t.Tree[cur]
for i := int32(len(nexts)) - 2; i >= 0; i-- {
e := nexts[i+1]
if t.Depth[e.to] == -1 {
nexts[i], nexts[i+1] = nexts[i+1], nexts[i]
}
}
hldSize := int32(0)
for i, e := range nexts {
to := e.to
if t.Depth[to] == -1 {
t.DepthWeighted[to] = t.DepthWeighted[cur] + e.cost
t.vToE[to] = e.eid
t._dfsSize(to, cur)
size[cur] += size[to]
if size[to] > hldSize {
hldSize = size[to]
if i != 0 {
nexts[0], nexts[i] = nexts[i], nexts[0]
}
}
}
}
}
func (t *Tree32) _dfsHld(cur int32, times *int32) {
t.Lid[cur] = *times
*times++
t.Rid[cur] += t.Lid[cur]
t.IdToNode[t.Lid[cur]] = cur
heavy := true
for _, e := range t.Tree[cur] {
to := e.to
if t.Depth[to] > t.Depth[cur] {
if heavy {
t.Head[to] = t.Head[cur]
} else {
t.Head[to] = to
}
heavy = false
t._dfsHld(to, times)
}
}
}
// 路径 [a,b] 与 [c,d] 的交集.
// 如果为空则返回 {-1,-1}，如果只有一个交点则返回 {x,x}，如果有两个交点则返回 {x,y}.
func (t *Tree32) PathIntersection(a, b, c, d int32) (int32, int32) {
ab := t.Lca(a, b)
ac := t.Lca(a, c)
ad := t.Lca(a, d)
bc := t.Lca(b, c)
bd := t.Lca(b, d)
cd := t.Lca(c, d)
x := ab ^ ac ^ bc // meet(a,b,c)
y := ab ^ ad ^ bd // meet(a,b,d)
if x != y {
return x, y
}
z := ac ^ ad ^ cd
if x != z {
x = -1
}
return x, x
}
func max(a, b int) int {
if a > b {
return a
}
return b
}
func min(a, b int) int {
if a < b {
return a
}
return b
}
func min32(a, b int32) int32 {
if a < b {
return a
}
return b
}
func max32(a, b int32) int32 {
if a > b {
return a
}
return b
}
func abs(a int) int {
if a < 0 {
return -a
}
return a
}