結果

問題 No.1254 補強への架け橋
ユーザー 草苺奶昔
提出日時 2023-03-27 02:13:20
言語 Go
(1.23.4)
結果
AC  
実行時間 234 ms / 2,000 ms
コード長 12,443 bytes
コンパイル時間 13,452 ms
コンパイル使用メモリ 227,288 KB
実行使用メモリ 45,252 KB
最終ジャッジ日時 2024-09-19 10:06:18
合計ジャッジ時間 27,394 ms
ジャッジサーバーID
(参考情報)
judge3 / 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 * 3
other AC * 123
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"
"sort"
"strings"
)
func main() {
// a, b, c := BuildNamoriForest(5, []Edge{{0, 1, 1, 0}, {1, 2, 1, 1}, {2, 3, 1, 2}, {3, 4, 1, 3}, {4, 0, 1, 4}}, false)
// fmt.Println(a[0].CycleEdges, b, c)
yuki1254()
}
func yuki1254() {
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n int
fmt.Fscan(in, &n)
g := make([][]Edge, n)
for i := 0; i < n; i++ {
var a, b int
fmt.Fscan(in, &a, &b)
a--
b--
g[a] = append(g[a], Edge{a, b, 1, i})
g[b] = append(g[b], Edge{b, a, 1, i})
}
G := NewNamoriGraph(g)
G.Build(false)
res := []int{}
for _, e := range G.CycleEdges {
res = append(res, e.id+1)
}
sort.Ints(res)
fmt.Fprintln(out, len(res))
for _, v := range res {
fmt.Fprint(out, v, " ")
}
}
func abc266_f() {
// https://atcoder.jp/contests/abc266/tasks/abc266_f
// ,xy
// =>
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n int
fmt.Fscan(in, &n)
graph := make([][]Edge, n)
for i := 0; i < n; i++ {
var a, b int
fmt.Fscan(in, &a, &b)
a--
b--
graph[a] = append(graph[a], Edge{a, b, 1, i})
graph[b] = append(graph[b], Edge{b, a, 1, i})
}
G := NewNamoriGraph(graph)
G.Build(false) // !without HLD
var q int
fmt.Fscan(in, &q)
for i := 0; i < q; i++ {
var x, y int
fmt.Fscan(in, &x, &y)
x--
y--
root1, _ := G.GetId(x)
root2, _ := G.GetId(y)
if root1 == root2 {
fmt.Fprintln(out, "Yes")
} else {
fmt.Fprintln(out, "No")
}
}
}
func namoriCut() {
// https://judge.u-aizu.ac.jp/onlinejudge/description.jsp?id=2891
// q(x,y)
// 使xy
// ,2
// 1()
in := bufio.NewReader(os.Stdin)
out := bufio.NewWriter(os.Stdout)
defer out.Flush()
var n int
fmt.Fscan(in, &n)
graph := make([][]Edge, n)
for i := 0; i < n; i++ {
var a, b int
fmt.Fscan(in, &a, &b)
a, b = a-1, b-1
graph[a] = append(graph[a], Edge{a, b, 1, i})
graph[b] = append(graph[b], Edge{b, a, 1, i})
}
G := NewNamoriGraph(graph)
G.Build(false)
var q int
fmt.Fscan(in, &q)
for i := 0; i < q; i++ {
var x, y int
fmt.Fscan(in, &x, &y)
x, y = x-1, y-1
_, treeId1 := G.GetId(x)
_, treeId2 := G.GetId(y)
if treeId1 != 0 || treeId2 != 0 {
fmt.Fprintln(out, 1)
} else {
fmt.Fprintln(out, 2)
}
}
}
func BuildNamoriForest(n int, edges []Edge, needHLD bool) (forest []*NamoriGraph, groupId, idInGroup []int) {
uf := NewUnionFindArray(n)
for _, e := range edges {
uf.Union(e.from, e.to)
}
groups := uf.GetGroups()
idInGroup = make([]int, n) //
groupId = make([]int, n) //
gs := make([]Graph, 0, len(groups)) // !
gid := 0
for _, g := range groups {
id := 0
for _, v := range g {
groupId[v] = gid
idInGroup[v] = id
id++
}
gs = append(gs, make(Graph, len(g)))
gid++
}
for _, e := range edges {
u, v := e.from, e.to
gid := groupId[u]
id1, id2 := idInGroup[u], idInGroup[v]
gs[gid][id1] = append(gs[gid][id1], Edge{from: id1, to: id2, cost: e.cost, id: e.id})
}
forest = make([]*NamoriGraph, len(gs))
for i, g := range gs {
forest[i] = NewNamoriGraph(g)
forest[i].Build(needHLD)
}
return
}
type NamoriGraph struct {
// !i
Trees []Graph
// !,i root ii+1 (i>=0)
CycleEdges []Edge
// (Build(needHLD=true)使)
HLDs []*_HLD
g Graph
iv [][]int
markId, id []int
}
type Edge = struct{ from, to, cost, id int }
type Graph = [][]Edge
func NewNamoriGraph(g Graph) *NamoriGraph {
return &NamoriGraph{g: g}
}
// needHLD :.
func (ng *NamoriGraph) Build(needHLD bool) {
n := len(ng.g)
deg := make([]int, n)
used := make([]bool, n)
que := []int{}
for i := 0; i < n; i++ {
deg[i] = len(ng.g[i])
if deg[i] == 1 {
que = append(que, i)
used[i] = true
}
}
for len(que) > 0 {
idx := que[0]
que = que[1:]
for _, e := range ng.g[idx] {
if used[e.to] {
continue
}
deg[e.to]--
if deg[e.to] == 1 {
que = append(que, e.to)
used[e.to] = true
}
}
}
mx := 0
for _, edges := range ng.g {
for _, e := range edges {
mx = max(mx, e.id)
}
}
edgeUsed := make([]bool, mx+1)
loop := []int{}
for i := 0; i < n; i++ {
if used[i] {
continue
}
for update := true; update; {
update = false
loop = append(loop, i)
for _, e := range ng.g[i] {
if used[e.to] || edgeUsed[e.id] {
continue
}
edgeUsed[e.id] = true
ng.CycleEdges = append(ng.CycleEdges, Edge{i, e.to, e.cost, e.id})
i = e.to
update = true
break
}
}
break
}
if len(loop) > 0 {
loop = loop[:len(loop)-1]
}
ng.markId = make([]int, n)
ng.id = make([]int, n)
for i := 0; i < len(loop); i++ {
pre := loop[(i+len(loop)-1)%len(loop)]
nxt := loop[(i+1)%len(loop)]
sz := 0
ng.markId[loop[i]] = i
ng.iv = append(ng.iv, []int{})
ng.id[loop[i]] = sz
sz++
ng.iv[len(ng.iv)-1] = append(ng.iv[len(ng.iv)-1], loop[i])
for _, e := range ng.g[loop[i]] {
if e.to != pre && e.to != nxt {
ng.markDfs(e.to, loop[i], i, &sz)
}
}
tree := make(Graph, sz)
for _, e := range ng.g[loop[i]] {
if e.to != pre && e.to != nxt {
tree[ng.id[loop[i]]] = append(tree[ng.id[loop[i]]], Edge{ng.id[loop[i]], ng.id[e.to], e.cost, e.id})
tree[ng.id[e.to]] = append(tree[ng.id[e.to]], Edge{ng.id[e.to], ng.id[loop[i]], e.cost, e.id})
ng.buildDfs(e.to, loop[i], tree)
}
}
ng.Trees = append(ng.Trees, tree)
}
// HLD
if !needHLD {
return
}
t := len(ng.Trees)
ng.HLDs = make([]*_HLD, 0, t)
for _, tree := range ng.Trees {
hld := _NewHLD(tree)
hld.Build(0)
ng.HLDs = append(ng.HLDs, hld)
}
}
// rawV,rawVrawV.
func (ng *NamoriGraph) GetId(rawV int) (rootId, idInTree int) {
return ng.markId[rawV], ng.id[rawV]
}
// rootidInTree,.
// GetInvId(root,0) root.
func (ng *NamoriGraph) GetInvId(rootId, idInTree int) (rawV int) {
return ng.iv[rootId][idInTree]
}
func (ng *NamoriGraph) markDfs(idx, par, k int, l *int) {
ng.markId[idx] = k
ng.id[idx] = *l
*l++
ng.iv[len(ng.iv)-1] = append(ng.iv[len(ng.iv)-1], idx)
for _, e := range ng.g[idx] {
if e.to != par {
ng.markDfs(e.to, idx, k, l)
}
}
}
func (ng *NamoriGraph) buildDfs(idx, par int, tree Graph) {
for _, e := range ng.g[idx] {
if e.to != par {
tree[ng.id[idx]] = append(tree[ng.id[idx]], Edge{ng.id[idx], ng.id[e.to], e.cost, e.id})
tree[ng.id[e.to]] = append(tree[ng.id[e.to]], Edge{ng.id[e.to], ng.id[idx], e.cost, e.id})
ng.buildDfs(e.to, idx, tree)
}
}
}
func max(a, b int) int {
if a > b {
return a
}
return b
}
type _HLD struct {
Tree Graph
SubSize, Depth, Parent []int
dfn, dfnToNode, top, heavySon []int
dfnId int
}
func (hld *_HLD) Build(root int) {
hld.build(root, -1, 0)
hld.markTop(root, root)
}
func _NewHLD(tree Graph) *_HLD {
n := len(tree)
dfn := make([]int, n) // vertex => dfn
dfnToNode := make([]int, n) // dfn => vertex
top := make([]int, n) // /
subSize := make([]int, n) //
depth := make([]int, n) //
parent := make([]int, n) //
heavySon := make([]int, n) //
return &_HLD{
Tree: tree,
dfn: dfn,
dfnToNode: dfnToNode,
top: top,
SubSize: subSize,
Depth: depth,
Parent: parent,
heavySon: heavySon,
}
}
// u [down, up).
// 0 <= down < up <= n.
func (hld *_HLD) Id(u int) (down, up int) {
down, up = hld.dfn[u], hld.dfn[u]+hld.SubSize[u]
return
}
// u-v .
func (hld *_HLD) Eid(u, v int) int {
id1, _ := hld.Id(u)
id2, _ := hld.Id(v)
if id1 < id2 {
return id2
}
return id1
}
// .
// 0 <= start <= end <= n, [start,end).
func (hld *_HLD) QueryPath(u, v int, vertex bool, f func(start, end int)) {
if vertex {
hld.forEach(u, v, f)
} else {
hld.forEachEdge(u, v, f)
}
}
// root .
// 0 <= start <= end <= n, [start,end).
func (hld *_HLD) QuerySubTree(u int, vertex bool, f func(start, end int)) {
if vertex {
f(hld.dfn[u], hld.dfn[u]+hld.SubSize[u])
} else {
f(hld.dfn[u]+1, hld.dfn[u]+hld.SubSize[u])
}
}
func (hld *_HLD) forEach(u, v int, cb func(start, end int)) {
for {
if hld.dfn[u] > hld.dfn[v] {
u, v = v, u
}
cb(max(hld.dfn[hld.top[v]], hld.dfn[u]), hld.dfn[v]+1)
if hld.top[u] != hld.top[v] {
v = hld.Parent[hld.top[v]]
} else {
break
}
}
}
func (hld *_HLD) LCA(u, v int) int {
for {
if hld.dfn[u] > hld.dfn[v] {
u, v = v, u
}
if hld.top[u] == hld.top[v] {
return u
}
v = hld.Parent[hld.top[v]]
}
}
func (hld *_HLD) Dist(u, v int) int {
return hld.Depth[u] + hld.Depth[v] - 2*hld.Depth[hld.LCA(u, v)]
}
// start top ,heavyPath[-1] .
func (hld *_HLD) GetHeavyPath(start int) []int {
heavyPath := []int{start}
cur := start
for hld.heavySon[cur] != -1 {
cur = hld.heavySon[cur]
heavyPath = append(heavyPath, cur)
}
return heavyPath
}
func (hld *_HLD) forEachEdge(u, v int, cb func(start, end int)) {
for {
if hld.dfn[u] > hld.dfn[v] {
u, v = v, u
}
if hld.top[u] != hld.top[v] {
cb(hld.dfn[hld.top[v]], hld.dfn[v]+1)
v = hld.Parent[hld.top[v]]
} else {
if u != v {
cb(hld.dfn[u]+1, hld.dfn[v]+1)
}
break
}
}
}
func (hld *_HLD) build(cur, pre, dep int) int {
subSize, heavySize, heavySon := 1, 0, -1
for _, e := range hld.Tree[cur] {
next := e.to
if next != pre {
nextSize := hld.build(next, cur, dep+1)
subSize += nextSize
if nextSize > heavySize {
heavySize, heavySon = nextSize, next
}
}
}
hld.Depth[cur] = dep
hld.SubSize[cur] = subSize
hld.heavySon[cur] = heavySon
hld.Parent[cur] = pre
return subSize
}
func (hld *_HLD) markTop(cur, top int) {
hld.top[cur] = top
hld.dfn[cur] = hld.dfnId
hld.dfnId++
hld.dfnToNode[hld.dfn[cur]] = cur
if hld.heavySon[cur] != -1 {
hld.markTop(hld.heavySon[cur], top)
for _, e := range hld.Tree[cur] {
next := e.to
if next != hld.heavySon[cur] && next != hld.Parent[cur] {
hld.markTop(next, next)
}
}
}
}
// NewUnionFindWithCallback ...
func NewUnionFindArray(n int) *UnionFindArray {
parent, rank := make([]int, n), make([]int, n)
for i := 0; i < n; i++ {
parent[i] = i
rank[i] = 1
}
return &UnionFindArray{
Part: n,
rank: rank,
n: n,
parent: parent,
}
}
type UnionFindArray struct {
//
Part int
rank []int
n int
parent []int
}
func (ufa *UnionFindArray) Union(key1, key2 int) bool {
root1, root2 := ufa.Find(key1), ufa.Find(key2)
if root1 == root2 {
return false
}
if ufa.rank[root1] > ufa.rank[root2] {
root1, root2 = root2, root1
}
ufa.parent[root1] = root2
ufa.rank[root2] += ufa.rank[root1]
ufa.Part--
return true
}
func (ufa *UnionFindArray) Find(key int) int {
for ufa.parent[key] != key {
ufa.parent[key] = ufa.parent[ufa.parent[key]]
key = ufa.parent[key]
}
return key
}
func (ufa *UnionFindArray) IsConnected(key1, key2 int) bool {
return ufa.Find(key1) == ufa.Find(key2)
}
func (ufa *UnionFindArray) GetGroups() map[int][]int {
groups := make(map[int][]int)
for i := 0; i < ufa.n; i++ {
root := ufa.Find(i)
groups[root] = append(groups[root], i)
}
return groups
}
func (ufa *UnionFindArray) Size(key int) int {
return ufa.rank[ufa.Find(key)]
}
func (ufa *UnionFindArray) String() string {
sb := []string{"UnionFindArray:"}
for root, member := range ufa.GetGroups() {
cur := fmt.Sprintf("%d: %v", root, member)
sb = append(sb, cur)
}
sb = append(sb, fmt.Sprintf("Part: %d", ufa.Part))
return strings.Join(sb, "\n")
}
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