結果

問題 No.1976 Cut then Connect
ユーザー 草苺奶昔草苺奶昔
提出日時 2023-03-16 00:17:53
言語 Go
(1.23.4)
結果
AC  
実行時間 158 ms / 2,000 ms
コード長 7,837 bytes
コンパイル時間 15,031 ms
コンパイル使用メモリ 221,512 KB
実行使用メモリ 31,744 KB
最終ジャッジ日時 2024-11-24 12:19:48
合計ジャッジ時間 12,819 ms
ジャッジサーバーID
(参考情報)
judge2 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 2
other AC * 31
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

package main
import (
"bufio"
"fmt"
"os"
)
func main() {
// https://yukicoder.me/problems/no/1976
// No.1976 Cut then Connect-
// , :
// , 使2
// , ,
// !: ?
// :
// 1. ,
// ! max(x,y,ceil(x/2)+ceil(y/2)+1) x,y
// 2. ,dp
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n int
fmt.Fscan(in, &n)
R := NewRerootingEdge(n)
edges := make([][2]int, n-1)
for i := 0; i < n-1; i++ {
var a, b int
fmt.Fscan(in, &a, &b)
a, b = a-1, b-1
edges[i] = [2]int{a, b}
R.AddEdge(a, b, 1)
}
// !E: (,)
R.ReRooting(
func() E { return E{0, 0} },
func(dp1, dp2 E) E {
return E{max(max(dp1.dia, dp2.dia), dp1.dist+dp2.dist), max(dp1.dist, dp2.dist)}
},
func(dp E, from int) E { return dp },
func(dp E, edge Edge) E {
return E{dp.dia, dp.dist + 1}
},
)
res := n
for _, e := range edges {
u, v := e[0], e[1]
dia1, dia2 := R.Get(u, v).dia, R.Get(v, u).dia
res = min(res, max(max(dia1, dia2), (dia1+1)/2+(dia2+1)/2+1))
}
fmt.Fprintln(out, res)
}
type E = struct{ dia, dist int }
type ReRootingEdge struct {
tree *_T
dp1 []E // parent-root root dp
dp2 []E // parent-root parent dp
dp []E // v dp
}
type Edge = struct{ from, to, weight, eid int }
func NewRerootingEdge(n int) *ReRootingEdge {
return &ReRootingEdge{tree: _NT(n)}
}
func (rr *ReRootingEdge) AddEdge(from, to, weight int) {
rr.tree.AddEdge(from, to, weight)
}
// !root , v dp
func (rr *ReRootingEdge) Get(root, v int) E {
if root == v {
return rr.dp[v]
}
if !rr.tree.IsInSubtree(root, v) {
return rr.dp1[v]
}
w := rr.tree.Jump(v, root, 1)
return rr.dp2[w]
}
func (rr *ReRootingEdge) ReRooting(
e func() E,
op func(dp1, dp2 E) E,
composition func(dp E, from int) E,
compositionEdge func(dp E, edge Edge) E,
) []E {
rr.tree.Build(-1)
unit := e()
N := len(rr.tree.Tree)
dp1, dp2, dp := make([]E, N), make([]E, N), make([]E, N)
for i := 0; i < N; i++ {
dp1[i] = unit
dp2[i] = unit
dp[i] = unit
}
V := rr.tree.idToNode
par := rr.tree.Parent
for i := N - 1; i >= 0; i-- {
v := V[i]
ch := rr.tree.CollectChild(v)
n := len(ch)
x1, x2 := make([]E, n+1), make([]E, n+1)
for i := range x1 {
x1[i] = unit
x2[i] = unit
}
for i := 0; i < n; i++ {
x1[i+1] = op(x1[i], dp2[ch[i]])
}
for i := n - 1; i >= 0; i-- {
x2[i] = op(dp2[ch[i]], x2[i+1])
}
for i := 0; i < n; i++ {
dp2[ch[i]] = op(x1[i], x2[i+1])
}
dp[v] = x2[0]
dp1[v] = composition(dp[v], v)
for _, e := range rr.tree.Tree[v] {
to := e.to
if to == par[v] {
dp2[v] = compositionEdge(dp1[v], e)
}
}
}
v := V[0]
dp[v] = composition(dp[v], v)
for _, e := range rr.tree.Tree[v] {
to := e.to
dp2[to] = composition(dp2[to], v)
}
for i := 0; i < N; i++ {
v := V[i]
for _, e := range rr.tree.Tree[v] {
if e.to == par[v] {
continue
}
x := compositionEdge(dp2[e.to], e)
for _, f := range rr.tree.Tree[e.to] {
if f.to == par[e.to] {
continue
}
dp2[f.to] = op(dp2[f.to], x)
dp2[f.to] = composition(dp2[f.to], e.to)
}
x = op(dp[e.to], x)
dp[e.to] = composition(x, e.to)
}
}
rr.dp1, rr.dp2, rr.dp = dp1, dp2, dp
return dp
}
type _T struct {
Tree [][]Edge
Depth []int
Parent []int
LID, RID []int // [in,out)
idToNode []int
top, heavySon []int
timer int
eid int
}
func _NT(n int) *_T {
tree := make([][]Edge, n)
lid := make([]int, n)
rid := make([]int, n)
idToNode := make([]int, n)
top := make([]int, n) // /
depth := make([]int, n) //
parent := make([]int, n) //
heavySon := make([]int, n) //
for i := range parent {
parent[i] = -1
}
return &_T{
Tree: tree,
Depth: depth,
Parent: parent,
LID: lid,
RID: rid,
idToNode: idToNode,
top: top,
heavySon: heavySon,
}
}
// u-v, w.
func (tree *_T) AddEdge(u, v, w int) {
tree.Tree[u] = append(tree.Tree[u], Edge{from: u, to: v, weight: w, eid: tree.eid})
tree.Tree[v] = append(tree.Tree[v], Edge{from: v, to: u, weight: w, eid: tree.eid})
tree.eid++
}
// u->v, w.
func (tree *_T) AddDirectedEdge(u, v, w int) {
tree.Tree[u] = append(tree.Tree[u], Edge{from: u, to: v, weight: w, eid: tree.eid})
tree.eid++
}
// root:0-based
// root-10访
func (tree *_T) Build(root int) {
if root != -1 {
tree.build(root, -1, 0)
tree.markTop(root, root)
} else {
for i := 0; i < len(tree.Tree); i++ {
if tree.Parent[i] == -1 {
tree.build(i, -1, 0)
tree.markTop(i, i)
}
}
}
}
func (tree *_T) LCA(u, v int) int {
for {
if tree.LID[u] > tree.LID[v] {
u, v = v, u
}
if tree.top[u] == tree.top[v] {
return u
}
v = tree.Parent[tree.top[v]]
}
}
// k: 0-based
// k-1
func (tree *_T) KthAncestor(root, k int) int {
if k > tree.Depth[root] {
return -1
}
for {
u := tree.top[root]
if tree.LID[root]-k >= tree.LID[u] {
return tree.idToNode[tree.LID[root]-k]
}
k -= tree.LID[root] - tree.LID[u] + 1
root = tree.Parent[u]
}
}
// from to , step (0-indexed)
// ,,-1
func (tree *_T) Jump(from, to, step int) int {
if step == 1 {
if from == to {
return -1
}
if tree.IsInSubtree(to, from) {
return tree.KthAncestor(to, tree.Depth[to]-tree.Depth[from]-1)
}
return tree.Parent[from]
}
c := tree.LCA(from, to)
dac := tree.Depth[from] - tree.Depth[c]
dbc := tree.Depth[to] - tree.Depth[c]
if step > dac+dbc {
return -1
}
if step <= dac {
return tree.KthAncestor(from, step)
}
return tree.KthAncestor(to, dac+dbc-step)
}
func (tree *_T) CollectChild(root int) []int {
res := []int{}
for _, e := range tree.Tree[root] {
next := e.to
if next != tree.Parent[root] {
res = append(res, next)
}
}
return res
}
func (tree *_T) SubtreeSize(u int) int {
return tree.RID[u] - tree.LID[u]
}
// child root (childroot)
func (tree *_T) IsInSubtree(child, root int) bool {
return tree.LID[root] <= tree.LID[child] && tree.LID[child] < tree.RID[root]
}
func (tree *_T) build(cur, pre, dep int) int {
subSize, heavySize, heavySon := 1, 0, -1
for _, e := range tree.Tree[cur] {
next := e.to
if next != pre {
nextSize := tree.build(next, cur, dep+1)
subSize += nextSize
if nextSize > heavySize {
heavySize, heavySon = nextSize, next
}
}
}
tree.Depth[cur] = dep
tree.heavySon[cur] = heavySon
tree.Parent[cur] = pre
return subSize
}
func (tree *_T) markTop(cur, top int) {
tree.top[cur] = top
tree.LID[cur] = tree.timer
tree.idToNode[tree.timer] = cur
tree.timer++
if tree.heavySon[cur] != -1 {
tree.markTop(tree.heavySon[cur], top)
for _, e := range tree.Tree[cur] {
next := e.to
if next != tree.heavySon[cur] && next != tree.Parent[cur] {
tree.markTop(next, next)
}
}
}
tree.RID[cur] = tree.timer
}
func min(a, b int) int {
if a < b {
return a
}
return b
}
func max(a, b int) int {
if a > b {
return a
}
return b
}
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