結果
問題 | No.1254 補強への架け橋 |
ユーザー |
|
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 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 123 |
ソースコード
package mainimport ("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 intfmt.Fscan(in, &n)g := make([][]Edge, n)for i := 0; i < n; i++ {var a, b intfmt.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// 给定一个基环树,问从x到y的路径是否唯一// 等价于不能走环上=>在同一个子树中in := bufio.NewReader(os.Stdin)out := bufio.NewWriter(os.Stdout)defer out.Flush()var n intfmt.Fscan(in, &n)graph := make([][]Edge, n)for i := 0; i < n; i++ {var a, b intfmt.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 HLDvar q intfmt.Fscan(in, &q)for i := 0; i < q; i++ {var x, y intfmt.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// 给定一个基环树 q个询问(x,y)// 求使得x和y不连通最少需要切掉多少条边// 如果两个点都在环上,则答案为2// 否则答案为1(两点之间只有唯一的一条路径)in := bufio.NewReader(os.Stdin)out := bufio.NewWriter(os.Stdout)defer out.Flush()var n intfmt.Fscan(in, &n)graph := make([][]Edge, n)for i := 0; i < n; i++ {var a, b intfmt.Fscan(in, &a, &b)a, b = a-1, b-1graph[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 intfmt.Fscan(in, &q)for i := 0; i < q; i++ {var x, y intfmt.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) // 每个点在连通块中的编号groupId = make([]int, n) // 每个点所在的连通块编号gs := make([]Graph, 0, len(groups)) // !每个连通块的图gid := 0for _, g := range groups {id := 0for _, v := range g {groupId[v] = gididInGroup[v] = idid++}gs = append(gs, make(Graph, len(g)))gid++}for _, e := range edges {u, v := e.from, e.togid := 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 {// !以环上各个顶点i为根的无向树Trees []Graph// !基环树中在环上的边,边i连接着树的 root i和i+1 (i>=0)CycleEdges []Edge// 每个树的重链剖分(需要在Build(needHLD=true)后才能使用)HLDs []*_HLDg Graphiv [][]intmarkId, id []int}type Edge = struct{ from, to, cost, id int }type Graph = [][]Edgefunc NewNamoriGraph(g Graph) *NamoriGraph {return &NamoriGraph{g: g}}// needHLD :是否需要对各个子树进行重链剖分.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 := 0for _, 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 = falseloop = append(loop, i)for _, e := range ng.g[i] {if used[e.to] || edgeUsed[e.id] {continue}edgeUsed[e.id] = trueng.CycleEdges = append(ng.CycleEdges, Edge{i, e.to, e.cost, e.id})i = e.toupdate = truebreak}}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 := 0ng.markId[loop[i]] = ing.iv = append(ng.iv, []int{})ng.id[loop[i]] = szsz++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)}// HLDif !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)}}// 给定原图的顶点rawV,返回rawV所在的树的根节点和rawV在树中的编号.func (ng *NamoriGraph) GetId(rawV int) (rootId, idInTree int) {return ng.markId[rawV], ng.id[rawV]}// 给定树的顶点编号root和某个点在树中的顶点编号idInTree,返回这个点在原图中的顶点编号.// GetInvId(root,0) 表示在环上的顶点root在原图中对应的顶点.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] = kng.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 GraphSubSize, Depth, Parent []intdfn, dfnToNode, top, heavySon []intdfnId 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 => dfndfnToNode := make([]int, n) // dfn => vertextop := make([]int, n) // 所处轻/重链的顶点(深度最小),轻链的顶点为自身subSize := make([]int, n) // 子树大小depth := make([]int, n) // 深度parent := make([]int, n) // 父结点heavySon := make([]int, n) // 重儿子return &_HLD{Tree: tree,dfn: dfn,dfnToNode: dfnToNode,top: top,SubSize: subSize,Depth: depth,Parent: parent,heavySon: heavySon,}}// 返回树节点 u 对应的 欧拉序区间 [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}// 返回边 u-v 对应的 欧拉序起点编号.func (hld *_HLD) Eid(u, v int) int {id1, _ := hld.Id(u)id2, _ := hld.Id(v)if id1 < id2 {return id2}return id1}// 处理路径上的可换操作.// 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)}}// 处理以 root 为根的子树上的查询.// 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)]}// 寻找以 start 为 top 的重链 ,heavyPath[-1] 即为重链末端节点.func (hld *_HLD) GetHeavyPath(start int) []int {heavyPath := []int{start}cur := startfor 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, -1for _, e := range hld.Tree[cur] {next := e.toif next != pre {nextSize := hld.build(next, cur, dep+1)subSize += nextSizeif nextSize > heavySize {heavySize, heavySon = nextSize, next}}}hld.Depth[cur] = dephld.SubSize[cur] = subSizehld.heavySon[cur] = heavySonhld.Parent[cur] = prereturn subSize}func (hld *_HLD) markTop(cur, top int) {hld.top[cur] = tophld.dfn[cur] = hld.dfnIdhld.dfnId++hld.dfnToNode[hld.dfn[cur]] = curif hld.heavySon[cur] != -1 {hld.markTop(hld.heavySon[cur], top)for _, e := range hld.Tree[cur] {next := e.toif 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] = irank[i] = 1}return &UnionFindArray{Part: n,rank: rank,n: n,parent: parent,}}type UnionFindArray struct {// 连通分量的个数Part intrank []intn intparent []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] = root2ufa.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")}