結果
| 問題 | No.3405 Engineering University of Tree |
| コンテスト | |
| ユーザー |
 seekworser
|
| 提出日時 | 2025-12-01 08:09:42 |
| 言語 | Nim (2.2.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 29,237 bytes |
| 記録 | |
| コンパイル時間 | 6,400 ms |
| コンパイル使用メモリ | 101,472 KB |
| 実行使用メモリ | 142,908 KB |
| 最終ジャッジ日時 | 2025-12-11 23:30:59 |
| 合計ジャッジ時間 | 19,777 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge5 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 16 WA * 5 |
ソースコード
import macros;macro ImportExpand(s:untyped):untyped = parseStmt($s[2])
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/tmpl/citrus.nim
ImportExpand "cplib/tmpl/citrus" <=== "when not declared CPLIB_TMPL_CITRUS:\n const CPLIB_TMPL_CITRUS* = 1\n {.warning[UnusedImport]: off.}\n {.hint[XDeclaredButNotUsed]: off.}\n import os\n import algorithm\n import sequtils\n import tables\n import macros\n import std/math\n import sets\n import strutils\n import strformat\n import sugar\n import streams\n import deques\n import bitops\n import heapqueue\n import options\n import hashes\n const MODINT998244353* = 998244353\n const MODINT1000000007* = 1000000007\n when not declared CPLIB_UTILS_CONSTANTS:\n const CPLIB_UTILS_CONSTANTS* = 1\n const INF32*: int32 = 1001000027.int32\n const INF64*: int = int(3300300300300300491)\n \n const INFL = INF64\n type double* = float64\n let readNext = iterator(getsChar: bool = false): string {.closure.} =\n while true:\n var si: string\n try: si = stdin.readLine\n except EOFError: yield \"\"\n for s in si.split:\n if getsChar:\n for i in 0..<s.len():\n yield s[i..i]\n else:\n if s.isEmptyOrWhitespace: continue\n yield s\n proc input*(t: typedesc[string]): string = readNext()\n proc input*(t: typedesc[char]): char = readNext(true)[0]\n proc input*(t: typedesc[int]): int = readNext().parseInt\n proc input*(t: typedesc[float]): float = readNext().parseFloat\n macro input*(t: typedesc, n: varargs[int]): untyped =\n var repStr = \"\"\n for arg in n:\n repStr &= &\"({arg.repr}).newSeqWith \"\n parseExpr(&\"{repStr}input({t})\")\n macro input*(ts: varargs[auto]): untyped =\n var tupStr = \"\"\n for t in ts:\n tupStr &= &\"input({t.repr}),\"\n parseExpr(&\"({tupStr})\")\n macro input*(n: int, ts: varargs[auto]): untyped =\n for typ in ts:\n if typ.typeKind != ntyAnything:\n error(\"Expected typedesc, got \" & typ.repr, typ)\n parseExpr(&\"({n.repr}).newSeqWith input({ts.repr})\")\n proc `fmtprint`*(x: int or string or char or bool): string = return $x\n proc `fmtprint`*(x: float or float32 or float64): string = return &\"{x:.16f}\"\n proc `fmtprint`*[T](x: seq[T] or Deque[T] or HashSet[T] or set[T]): string = return x.toSeq.join(\" \")\n proc `fmtprint`*[T, N](x: array[T, N]): string = return x.toSeq.join(\" \")\n proc `fmtprint`*[T](x: HeapQueue[T]): string =\n var q = x\n while q.len != 0:\n result &= &\"{q.pop()}\"\n if q.len != 0: result &= \" \"\n proc `fmtprint`*[T](x: CountTable[T]): string =\n result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n proc `fmtprint`*[K, V](x: Table[K, V]): string =\n result = x.pairs.toSeq.mapIt(&\"{it[0]}: {it[1]}\").join(\" \")\n proc print*(prop: tuple[f: File, sepc: string, endc: string, flush: bool], args: varargs[string, `fmtprint`]) =\n for i in 0..<len(args):\n prop.f.write(&\"{args[i]}\")\n if i != len(args) - 1: prop.f.write(prop.sepc) else: prop.f.write(prop.endc)\n if prop.flush: prop.f.flushFile()\n proc print*(args: varargs[string, `fmtprint`]) = print((f: stdout, sepc: \" \", endc: \"\\n\", flush: false), args)\n const LOCAL_DEBUG{.booldefine.} = false\n macro getSymbolName(x: typed): string = x.toStrLit\n macro debug*(args: varargs[untyped]): untyped =\n when LOCAL_DEBUG:\n result = newNimNode(nnkStmtList, args)\n template prop(e: string = \"\"): untyped = (f: stderr, sepc: \"\", endc: e, flush: true)\n for i, arg in args:\n if arg.kind == nnkStrLit:\n result.add(quote do: print(prop(), \"\\\"\", `arg`, \"\\\"\"))\n else:\n result.add(quote do: print(prop(\": \"), getSymbolName(`arg`)))\n result.add(quote do: print(prop(), `arg`))\n if i != args.len - 1: result.add(quote do: print(prop(), \", \"))\n else: result.add(quote do: print(prop(), \"\\n\"))\n else:\n return (quote do: discard)\n proc `%`*(x: SomeInteger, y: SomeInteger): int =\n result = x mod y\n if y > 0 and result < 0: result += y\n if y < 0 and result > 0: result += y\n proc `//`*(x: SomeInteger, y: SomeInteger): int =\n result = x div y\n if y > 0 and result * y > x: result -= 1\n if y < 0 and result * y < x: result -= 1\n proc `^`*(x: SomeInteger, y: SomeInteger): int = x xor y\n proc `&`*(x: SomeInteger, y: SomeInteger): int = x and y\n proc `|`*(x: SomeInteger, y: SomeInteger): int = x or y\n proc `>>`*(x: SomeInteger, y: SomeInteger): int = x shr y\n proc `<<`*(x: SomeInteger, y: SomeInteger): int = x shl y\n proc `%=`*(x: var SomeInteger, y: SomeInteger): void = x = x % y\n proc `//=`*(x: var SomeInteger, y: SomeInteger): void = x = x // y\n proc `^=`*(x: var SomeInteger, y: SomeInteger): void = x = x ^ y\n proc `&=`*(x: var SomeInteger, y: SomeInteger): void = x = x & y\n proc `|=`*(x: var SomeInteger, y: SomeInteger): void = x = x | y\n proc `>>=`*(x: var SomeInteger, y: SomeInteger): void = x = x >> y\n proc `<<=`*(x: var SomeInteger, y: SomeInteger): void = x = x << y\n proc `[]`*(x, n: int): bool = (x and (1 shl n)) != 0\n proc `[]=`*(x: var int, n: int, i: bool) =\n if i: x = x or (1 << n)\n else: (if x[n]: x = x xor (1 << n))\n proc pow*(a, n: int, m = INF64): int =\n var\n rev = 1\n a = a\n n = n\n while n > 0:\n if n % 2 != 0: rev = (rev * a) mod m\n if n > 1: a = (a * a) mod m\n n >>= 1\n return rev\n when not declared CPLIB_MATH_ISQRT:\n const CPLIB_MATH_ISQRT* = 1\n proc isqrt*(n: int): int =\n var x = n\n var y = (x + 1) shr 1\n while y < x:\n x = y\n y = (x + n div x) shr 1\n return x\n \n proc chmax*[T](x: var T, y: T): bool {.discardable.} = (if x < y: (x = y; return true; ) return false)\n proc chmin*[T](x: var T, y: T): bool {.discardable.} = (if x > y: (x = y; return true; ) return false)\n proc `max=`*[T](x: var T, y: T) = x = max(x, y)\n proc `min=`*[T](x: var T, y: T) = x = min(x, y)\n proc at*(x: char, a = '0'): int = int(x) - int(a)\n proc Yes*(b: bool = true): void = print(if b: \"Yes\" else: \"No\")\n proc No*(b: bool = true): void = Yes(not b)\n proc YES_upper*(b: bool = true): void = print(if b: \"YES\" else: \"NO\")\n proc NO_upper*(b: bool = true): void = Yes_upper(not b)\n const DXY* = [(0, -1), (0, 1), (-1, 0), (1, 0)]\n const DDXY* = [(1, -1), (1, 0), (1, 1), (0, -1), (0, 1), (-1, -1), (-1, 0), (-1, 1)]\n macro exit*(statement: untyped): untyped = (quote do: (`statement`; quit()))\n proc initHashSet[T](): Hashset[T] = initHashSet[T](0)\n"
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/graph/graph.nim
ImportExpand "cplib/graph/graph" <=== "when not declared CPLIB_GRAPH_GRAPH:\n const CPLIB_GRAPH_GRAPH* = 1\n\n import sequtils\n import math\n type DynamicGraph*[T] = ref object of RootObj\n edges*: seq[seq[(int32, T)]]\n len*: int\n type StaticGraph*[T] = ref object of RootObj\n src*, dst*: seq[int32]\n cost*: seq[T]\n elist*: seq[(int32, T)]\n start*: seq[int32]\n len*: int\n\n type WeightedDirectedGraph*[T] = ref object of DynamicGraph[T]\n type WeightedUnDirectedGraph*[T] = ref object of DynamicGraph[T]\n type UnWeightedDirectedGraph* = ref object of DynamicGraph[int]\n type UnWeightedUnDirectedGraph* = ref object of DynamicGraph[int]\n type WeightedDirectedStaticGraph*[T] = ref object of StaticGraph[T]\n type WeightedUnDirectedStaticGraph*[T] = ref object of StaticGraph[T]\n type UnWeightedDirectedStaticGraph* = ref object of StaticGraph[int]\n type UnWeightedUnDirectedStaticGraph* = ref object of StaticGraph[int]\n\n type GraphTypes*[T] = DynamicGraph[T] or StaticGraph[T]\n type DirectedGraph* = WeightedDirectedGraph or UnWeightedDirectedGraph or WeightedDirectedStaticGraph or UnWeightedDirectedStaticGraph\n type UnDirectedGraph* = WeightedUnDirectedGraph or UnWeightedUnDirectedGraph or WeightedUnDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n type WeightedGraph*[T] = WeightedDirectedGraph[T] or WeightedUnDirectedGraph[T] or WeightedDirectedStaticGraph[T] or WeightedUnDirectedStaticGraph[T]\n type UnWeightedGraph* = UnWeightedDirectedGraph or UnWeightedUnDirectedGraph or UnWeightedDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n type DynamicGraphTypes* = WeightedDirectedGraph or UnWeightedDirectedGraph or WeightedUnDirectedGraph or UnWeightedUnDirectedGraph\n type StaticGraphTypes* = WeightedDirectedStaticGraph or UnWeightedDirectedStaticGraph or WeightedUnDirectedStaticGraph or UnWeightedUnDirectedStaticGraph\n\n proc add_edge_dynamic_impl*[T](g: DynamicGraph[T], u, v: int, cost: T, directed: bool) =\n g.edges[u].add((v.int32, cost))\n if not directed: g.edges[v].add((u.int32, cost))\n\n proc initWeightedDirectedGraph*(N: int, edgetype: typedesc = int): WeightedDirectedGraph[edgetype] =\n result = WeightedDirectedGraph[edgetype](edges: newSeq[seq[(int32, edgetype)]](N), len: N)\n proc add_edge*[T](g: var WeightedDirectedGraph[T], u, v: int, cost: T) =\n g.add_edge_dynamic_impl(u, v, cost, true)\n\n proc initWeightedUnDirectedGraph*(N: int, edgetype: typedesc = int): WeightedUnDirectedGraph[edgetype] =\n result = WeightedUnDirectedGraph[edgetype](edges: newSeq[seq[(int32, edgetype)]](N), len: N)\n proc add_edge*[T](g: var WeightedUnDirectedGraph[T], u, v: int, cost: T) =\n g.add_edge_dynamic_impl(u, v, cost, false)\n\n proc initUnWeightedDirectedGraph*(N: int): UnWeightedDirectedGraph =\n result = UnWeightedDirectedGraph(edges: newSeq[seq[(int32, int)]](N), len: N)\n proc add_edge*(g: var UnWeightedDirectedGraph, u, v: int) =\n g.add_edge_dynamic_impl(u, v, 1, true)\n\n proc initUnWeightedUnDirectedGraph*(N: int): UnWeightedUnDirectedGraph =\n result = UnWeightedUnDirectedGraph(edges: newSeq[seq[(int32, int)]](N), len: N)\n proc add_edge*(g: var UnWeightedUnDirectedGraph, u, v: int) =\n g.add_edge_dynamic_impl(u, v, 1, false)\n\n proc len*[T](G: WeightedGraph[T]): int = G.len\n proc len*(G: UnWeightedGraph): int = G.len\n\n iterator `[]`*[T](g: WeightedDirectedGraph[T] or WeightedUnDirectedGraph[T], x: int): (int, T) =\n for e in g.edges[x]: yield (e[0].int, e[1])\n iterator `[]`*(g: UnWeightedDirectedGraph or UnWeightedUnDirectedGraph, x: int): int =\n for e in g.edges[x]: yield e[0].int\n\n proc add_edge_static_impl*[T](g: StaticGraph[T], u, v: int, cost: T, directed: bool) =\n g.src.add(u.int32)\n g.dst.add(v.int32)\n g.cost.add(cost)\n if not directed:\n g.src.add(v.int32)\n g.dst.add(u.int32)\n g.cost.add(cost)\n\n proc build_impl*[T](g: StaticGraph[T]) =\n g.start = newSeqWith(g.len + 1, 0.int32)\n for i in 0..<g.src.len:\n g.start[g.src[i]] += 1\n g.start.cumsum\n g.elist = newSeq[(int32, T)](g.start[^1])\n for i in countdown(g.src.len - 1, 0):\n var u = g.src[i]\n var v = g.dst[i]\n g.start[u] -= 1\n g.elist[g.start[u]] = (v, g.cost[i])\n proc build*(g: StaticGraphTypes) = g.build_impl()\n\n proc initWeightedDirectedStaticGraph*(N: int, edgetype: typedesc = int, capacity: int = 0): WeightedDirectedStaticGraph[edgetype] =\n result = WeightedDirectedStaticGraph[edgetype](\n src: newSeqOfCap[int32](capacity),\n dst: newSeqOfCap[int32](capacity),\n cost: newSeqOfCap[edgetype](capacity),\n elist: newSeq[(int32, edgetype)](0),\n start: newSeq[int32](0),\n len: N\n )\n proc add_edge*[T](g: var WeightedDirectedStaticGraph[T], u, v: int, cost: T) =\n g.add_edge_static_impl(u, v, cost, true)\n\n proc initWeightedUnDirectedStaticGraph*(N: int, edgetype: typedesc = int, capacity: int = 0): WeightedUnDirectedStaticGraph[edgetype] =\n result = WeightedUnDirectedStaticGraph[edgetype](\n src: newSeqOfCap[int32](capacity*2),\n dst: newSeqOfCap[int32](capacity*2),\n cost: newSeqOfCap[edgetype](capacity*2),\n elist: newSeq[(int32, edgetype)](0),\n start: newSeq[int32](0),\n len: N\n )\n proc add_edge*[T](g: var WeightedUnDirectedStaticGraph[T], u, v: int, cost: T) =\n g.add_edge_static_impl(u, v, cost, false)\n\n proc initUnWeightedDirectedStaticGraph*(N: int, capacity: int = 0): UnWeightedDirectedStaticGraph =\n result = UnWeightedDirectedStaticGraph(\n src: newSeqOfCap[int32](capacity),\n dst: newSeqOfCap[int32](capacity),\n cost: newSeqOfCap[int](capacity),\n elist: newSeq[(int32, int)](0),\n start: newSeq[int32](0),\n len: N\n )\n proc add_edge*(g: var UnWeightedDirectedStaticGraph, u, v: int) =\n g.add_edge_static_impl(u, v, 1, true)\n\n proc initUnWeightedUnDirectedStaticGraph*(N: int, capacity: int = 0): UnWeightedUnDirectedStaticGraph =\n result = UnWeightedUnDirectedStaticGraph(\n src: newSeqOfCap[int32](capacity*2),\n dst: newSeqOfCap[int32](capacity*2),\n cost: newSeqOfCap[int](capacity*2),\n elist: newSeq[(int32, int)](0),\n start: newSeq[int32](0),\n len: N\n )\n proc add_edge*(g: var UnWeightedUnDirectedStaticGraph, u, v: int) =\n g.add_edge_static_impl(u, v, 1, false)\n\n proc static_graph_initialized_check*[T](g: StaticGraph[T]) = assert g.start.len > 0, \"Static Graph must be initialized before use.\"\n\n iterator `[]`*[T](g: WeightedDirectedStaticGraph[T] or WeightedUnDirectedStaticGraph[T], x: int): (int, T) =\n g.static_graph_initialized_check()\n for i in g.start[x]..<g.start[x+1]: yield (g.elist[i][0].int, g.elist[i][1])\n iterator `[]`*(g: UnWeightedDirectedStaticGraph or UnWeightedUnDirectedStaticGraph, x: int): int =\n g.static_graph_initialized_check()\n for i in g.start[x]..<g.start[x+1]: yield g.elist[i][0].int\n\n iterator to_and_cost*[T](g: DynamicGraph[T], x: int): (int, T) =\n for e in g.edges[x]: yield (e[0].int, e[1])\n iterator to_and_cost*[T](g: StaticGraph[T], x: int): (int, T) =\n g.static_graph_initialized_check()\n for i in g.start[x]..<g.start[x+1]: yield (g.elist[i][0].int, g.elist[i][1])\n \n import tables\n\n type UnWeightedUnDirectedTableGraph*[T] = object \n toi* : Table[T,int]\n v* : seq[T]\n graph* : UnWeightedUnDirectedGraph\n\n type UnWeightedDirectedTableGraph*[T] = object \n toi* : Table[T,int]\n v* : seq[T]\n graph* : UnWeightedDirectedGraph\n\n type WeightedUnDirectedTableGraph*[T,S] = object \n toi* : Table[T,int]\n v* : seq[T]\n graph* : WeightedUnDirectedGraph[S]\n\n type WeightedDirectedTableGraph*[T,S] = object \n toi* : Table[T,int]\n v* : seq[T]\n graph* : WeightedDirectedGraph[S]\n\n type UnWeightedTableGraph*[T] = UnWeightedUnDirectedTableGraph[T] or UnWeightedDirectedTableGraph[T]\n type WeightedTableGraph*[T,S] = WeightedUnDirectedTableGraph[T,S] or WeightedDirectedTableGraph[T,S]\n\n proc initUnWeightedUnDirectedTableGraph*[T](V:seq[T]):UnWeightedUnDirectedTableGraph[T]=\n for i in 0..<len(V):\n result.toi[V[i]] = i\n result.graph = initUnWeightedUnDirectedGraph(len(V))\n result.v = V\n\n proc initUnWeightedDirectedTableGraph*[T](V:seq[T]):UnWeightedDirectedTableGraph[T]=\n for i in 0..<len(V):\n result.toi[V[i]] = i\n result.graph = initUnWeightedDirectedGraph(len(V))\n result.v = V\n\n proc initWeightedUnDirectedTableGraph*[T](V:seq[T],S:typedesc = int):WeightedUnDirectedTableGraph[T,S]=\n for i in 0..<len(V):\n result.toi[V[i]] = i\n result.graph = initWeightedUnDirectedGraph(len(V),S)\n result.v = V\n\n proc initWeightedDirectedTableGraph*[T](V:seq[T],S:typedesc = int):WeightedDirectedTableGraph[T,S]=\n for i in 0..<len(V):\n result.toi[V[i]] = i\n result.graph = initWeightedDirectedGraph(len(V),S)\n result.v = V\n\n proc add_edge*[T](g: var UnWeightedTableGraph[T],u,v:int)=\n g.graph.add_edge(g.toi[u],g.toi[v])\n\n proc add_edge*[T,S](g: var WeightedTableGraph[T,S],u,v:int,cost:S)=\n g.graph.add_edge(g.toi[u],g.toi[v],cost)\n\n iterator `[]`*[T,S](g: WeightedDirectedTableGraph[T,S] or WeightedUnDirectedTableGraph[T,S], x: T): (T, S) = \n for (x,y) in g.graph[g.toi[x]]:\n yield (g.v[x],y)\n iterator `[]`*[T](g: UnWeightedDirectedTableGraph[T] or UnWeightedUnDirectedTableGraph[T], x: T): T = \n for x in g.graph[g.toi[x]]:\n yield g.v[x]\n\n"
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/tree/heavylightdecomposition.nim
ImportExpand "cplib/tree/heavylightdecomposition" <=== "when not declared CPLIB_TREE_HLD:\n const CPLIB_TREE_HLD* = 1\n import sequtils\n import algorithm\n import sets\n # https://atcoder.jp/contests/abc337/submissions/50216964\n # ↑上記の提出より引用\n type HeavyLightDecomposition* = ref object \n N*: int\n P*, PP*, PD*, D*, I*, rangeL*, rangeR*: seq[int]\n proc initHld*(g: UnDirectedGraph, root: int): HeavyLightDecomposition =\n var hld = HeavyLightDecomposition()\n var n: int = g.len\n hld.N = n\n hld.P = newSeqWith(n, -1)\n hld.I = newSeqWith(n, 0)\n hld.I[0] = root\n var iI = 1\n for i in 0..<n:\n var p = hld.I[i]\n for e in g[p]:\n if hld.P[p] != e:\n hld.I[iI] = e\n hld.P[e] = p\n iI += 1\n var Z = newSeqWith(n, 1)\n var nx = newSeqWith(n, -1)\n hld.PP = newSeqWith(n, 0)\n for i in 0..<n:\n hld.PP[i] = i\n for i in 1..<n:\n var p = hld.I[n-i]\n Z[hld.P[p]] += Z[p]\n if nx[hld.P[p]] == -1 or Z[nx[hld.P[p]]] < Z[p]:\n nx[hld.P[p]] = p\n for p in hld.I:\n if nx[p] != -1:\n hld.PP[nx[p]] = p\n hld.PD = newSeqWith(n, n)\n hld.PD[root] = 0\n hld.D = newSeqWith(n, 0)\n for p in hld.I:\n if p != root:\n hld.PP[p] = hld.PP[hld.PP[p]]\n hld.PD[p] = min(hld.PD[hld.PP[p]], hld.PD[hld.P[p]]+1)\n hld.D[p] = hld.D[hld.P[p]]+1\n hld.rangeL = newSeqWith(n, 0)\n hld.rangeR = newSeqWith(n, 0)\n for p in hld.I:\n hld.rangeR[p] = hld.rangeL[p] + Z[p]\n var ir = hld.rangeR[p]\n for e in g[p]:\n if hld.P[p] != e and e != nx[p]:\n ir -= Z[e]\n hld.rangeL[e] = ir\n if nx[p] != -1:\n hld.rangeL[nx[p]] = hld.rangeL[p] + 1\n for i in 0..<n:\n hld.I[hld.rangeL[i]] = i\n return hld\n proc initHld*(g: DirectedGraph, root: int): HeavyLightDecomposition =\n var n = g.len\n var gn = initUnWeightedUnDirectedStaticGraph(n)\n var seen = initHashSet[(int, int)]()\n for i in 0..<n:\n for (j, _) in g[i]:\n if (i, j) notin seen:\n gn.add_edge(i, j)\n seen.incl((i, j))\n seen.incl((j, i))\n gn.build\n return initHld(gn, root)\n proc initHld*(adj: seq[seq[int]], root: int): HeavyLightDecomposition =\n var n = adj.len\n var gn = initUnWeightedUnDirectedStaticGraph(n)\n var seen = initHashSet[(int, int)]()\n for i in 0..<n:\n for j in adj[i]:\n if (i, j) notin seen:\n gn.add_edge(i, j)\n seen.incl((i, j))\n seen.incl((j, i))\n gn.build\n return initHld(gn, root)\n proc numVertices*(hld: HeavyLightDecomposition): int = hld.N\n proc depth*(hld: HeavyLightDecomposition, p: int): int = hld.D[p]\n proc toSeq*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeL[vtx]\n proc toVtx*(hld: HeavyLightDecomposition, seqidx: int): int = hld.I[seqidx]\n proc toSeq2In*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeL[vtx] * 2 - hld.D[vtx]\n proc toSeq2Out*(hld: HeavyLightDecomposition, vtx: int): int = hld.rangeR[vtx] * 2 - hld.D[vtx] - 1\n proc parentOf*(hld: HeavyLightDecomposition, v: int): int = hld.P[v]\n proc heavyRootOf*(hld: HeavyLightDecomposition, v: int): int = hld.PP[v]\n proc heavyChildOf*(hld: HeavyLightDecomposition, v: int): int =\n if hld.toSeq(v) == hld.N-1:\n return -1\n var cand = hld.toVtx(hld.toSeq(v) + 1)\n if hld.PP[v] == hld.PP[cand]:\n return cand\n -1\n proc lca*(hld: HeavyLightDecomposition, u: int, v: int): int =\n var (u, v) = (u, v)\n if hld.PD[u] < hld.PD[v]:\n swap(u, v)\n while hld.PD[u] > hld.PD[v]:\n u = hld.P[hld.PP[u]]\n while hld.PP[u] != hld.PP[v]:\n u = hld.P[hld.PP[u]]\n v = hld.P[hld.PP[v]]\n if hld.D[u] > hld.D[v]:\n return v\n u\n proc dist*(hld: HeavyLightDecomposition, u: int, v: int): int =\n hld.depth(u) + hld.depth(v) - hld.depth(hld.lca(u, v)) * 2\n proc path*(hld: HeavyLightDecomposition, r: int, c: int, include_root: bool, reverse_path: bool): seq[(int, int)] =\n var (r, c) = (r, c)\n var k = hld.PD[c] - hld.PD[r] + 1\n if k <= 0:\n return @[]\n var res = newSeqWith(k, (0, 0))\n for i in 0..<k-1:\n res[i] = (hld.rangeL[hld.PP[c]], hld.rangeL[c] + 1)\n c = hld.P[hld.PP[c]]\n if hld.PP[r] != hld.PP[c] or hld.D[r] > hld.D[c]:\n return @[]\n var root_off = int(not include_root)\n res[^1] = (hld.rangeL[r]+root_off, hld.rangeL[c]+1)\n if res[^1][0] == res[^1][1]:\n discard res.pop()\n k -= 1\n if reverse_path:\n for i in 0..<k:\n res[i] = (hld.N - res[i][1], hld.N - res[i][0])\n else:\n res.reverse()\n res\n proc subtree*(hld: HeavyLightDecomposition, p: int): (int, int) = (hld.rangeL[p], hld.rangeR[p])\n iterator subtreeV*(hld: HeavyLightDecomposition, p: int):int=\n for i in hld.rangeL[p]..<hld.rangeR[p]:\n yield hld.toVtx(i)\n proc median*(hld: HeavyLightDecomposition, x: int, y: int, z: int): int =\n hld.lca(x, y) xor hld.lca(y, z) xor hld.lca(x, z)\n proc la*(hld: HeavyLightDecomposition, starting: int, goal: int, d: int): int =\n var (u, v, d) = (starting, goal, d)\n if d < 0:\n return -1\n var g = hld.lca(u, v)\n var dist0 = hld.D[u] - hld.D[g] * 2 + hld.D[v]\n if dist0 < d:\n return -1\n var p = u\n if hld.D[u] - hld.D[g] < d:\n p = v\n d = dist0 - d\n while hld.D[p] - hld.D[hld.PP[p]] < d:\n d -= hld.D[p] - hld.D[hld.PP[p]] + 1\n p = hld.P[hld.PP[p]]\n hld.I[hld.rangeL[p] - d]\n iterator children*(hld: HeavyLightDecomposition, v: int): int =\n var s = hld.rangeL[v] + 1\n while s < hld.rangeR[v]:\n var w = hld.toVtx(s)\n yield w\n s += hld.rangeR[w] - hld.rangeL[w]\n \n\n proc initAuxiliaryTree*(hld:HeavyLightDecomposition,v:seq[int]):UnWeightedUnDirectedTableGraph[int]=\n var v = v.sortedByit(hld.toseq(it))\n for i in 0..<(len(v)-1):\n v.add(hld.lca(v[i],v[i+1]))\n v = v.sortedByIt(hld.toseq(it)).deduplicate(true)\n var stack :seq[int]\n result = initUnWeightedUnDirectedTableGraph[int](v)\n stack.add(v[0])\n \n for i in 1..<len(v):\n while len(stack) > 0 and hld.toSeq2Out(stack[^1]) < hld.toseq2In(v[i]):\n discard stack.pop()\n if len(stack) != 0:\n result.add_edge(stack[^1],v[i])\n stack.add(v[i])\n \n proc initAuxiliaryWeightedTree*(hld:HeavyLightDecomposition,v:seq[int]):WeightedUnDirectedTableGraph[int,int]=\n var v = v.sortedByit(hld.toseq(it))\n for i in 0..<(len(v)-1):\n v.add(hld.lca(v[i],v[i+1]))\n v = v.sortedByIt(hld.toseq(it)).deduplicate(true)\n var stack :seq[int]\n result = initWeightedUnDirectedTableGraph(v,int)\n stack.add(v[0])\n for i in 1..<len(v):\n while len(stack) > 0 and hld.toSeq2Out(stack[^1]) < hld.toseq2In(v[i]):\n discard stack.pop()\n if len(stack) != 0:\n result.add_edge(stack[^1],v[i],hld.depth(v[i])-hld.depth(stack[^1]))\n stack.add(v[i])\n\n"
# {.checks: off.}
# 与えられた k については木DPでこの問題を解くことができる。
# k = 1,2,...,N-1 について愚直に木DPをするのは間に合わないが、
# 次数 k 未満の頂点はシンボルを描くことができないので
# 次数 k 以上の頂点で auxiliary tree を構築して木DPできそう
# 次数 k 以上の頂点の個数の最大値は 2N/k なので、総和が O(N log N) でおさえられる。
# おさえられるし、最悪ケースが作りにくそうなので実際にはもっと少ない？
# (雑に考えるとN^(1/2)をN^(1/2)個とかくらいが限界そう）
var n = input(int)
var edges = newSeqWith(n-1, newSeq[int]())
var deg = newSeq[int](n)
for i in 0..<n:
deg[i] = input(int)
for _ in 0..<deg[i]:
var eid = input(int) - 1
edges[eid].add(i)
var g = initUnWeightedUnDirectedStaticGraph(n)
for i in 0..<n-1:
g.add_edge(edges[i][0], edges[i][1])
g.build
var hld = g.initHld(0)
var preorder = newSeqWith(n, -1)
block:
var cnt = 0
proc calc_preorder(u, par: int) =
preorder[u] = cnt
cnt += 1
for v in g[u]:
if v == par: continue
calc_preorder(v, u)
calc_preorder(0, -1)
proc create_auxiliary_tree(v: seq[int]): (WeightedUnDirectedStaticGraph[int], seq[int]) =
var v = v.sortedByIt(preorder[it])
var t = v.len
for i in 0..<t-1:
v.add(hld.lca(v[i], v[i+1]))
v = v.sortedByIt(preorder[it]).deduplicate(true)
t = v.len
var stack = @[0]
var edges = newSeq[(int, int, int)]()
for i in 1..<t:
var u = v[i]
while hld.lca(v[stack[^1]], u) != v[stack[^1]]:
var ln = hld.D[v[stack[^1]]] - hld.D[v[stack[^2]]]
edges.add((stack[^1], stack[^2], ln))
discard stack.pop
stack.add(i)
while stack.len > 1:
var ln = hld.D[v[stack[^1]]] - hld.D[v[stack[^2]]]
edges.add((stack[^1], stack[^2], ln))
discard stack.pop
var g = initWeightedUnDirectedStaticGraph(t)
for (u, v, cost) in edges:
g.add_edge(u, v, cost)
g.build
return (g, v)
var r = (0..<n).toSeq
var ans = newSeq[int]()
for k in 1..(n-1):
var rn = newSeq[int]()
for u in r:
if deg[u] < k: continue
rn.add(u)
swap(r, rn)
if r.len == 0:
ans.add(0)
continue
var (tree, node_map) = create_auxiliary_tree(r)
# if k != 2: continue
# debug(r)
# debug(node_map)
proc calc_dp(u, par: int): (int, int) =
var s = node_map[u]
var w0 = deg[s] - 1 - k
var w1 = deg[s] - k
var dpi = newSeq[(int, int)]()
for (v, cost) in tree[u]:
if v == par: continue
dpi.add(calc_dp(v, u))
if cost > 1:
dpi[^1] = (dpi[^1][1], dpi[^1][1])
dpi = dpi.sortedByIt(it[0] - it[1])
if deg[s] < k:
var ans = dpi.mapIt(it[1]).sum
return (ans, ans)
debug(dpi, w0, w1)
# w0.min = dpi.len
# w1.min = dpi.len
var ans0_1 = dpi.mapIt(it[1]).sum
var ans0_2 = 1
var ans1 = 1
for i in 0..<dpi.len:
var (a, b) = dpi[i]
ans0_2 += (if i < w0: b else: a)
ans1 += (if i < w1: b else: a)
if w0 < 0: ans0_2 = -INFL
debug(u, s, ans0_1, ans0_2, ans1)
var a = max(ans0_1, ans0_2)
var b = max(a, ans1)
return (a, b)
var (ans0, ans1) = calc_dp(0, -1)
if r[0] == 0:
ans.add(ans0)
else:
ans.add(ans1)
print(ans)