結果
| 問題 | No.2873 Kendall's Tau |
| ユーザー |
👑  seekworser
|
| 提出日時 | 2024-07-13 17:59:49 |
| 言語 | Nim (2.2.0) |
| 結果 |
AC
|
| 実行時間 | 705 ms / 4,500 ms |
| コード長 | 17,296 bytes |
| コンパイル時間 | 7,737 ms |
| コンパイル使用メモリ | 105,020 KB |
| 実行使用メモリ | 78,832 KB |
| 最終ジャッジ日時 | 2024-07-13 18:00:10 |
| 合計ジャッジ時間 | 20,750 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 30 |
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.nimImportExpand "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 importstd/math\n import sets\n import strutils\n import strformat\n import sugar\n import streams\n import deques\n import bitops\nimport heapqueue\n import options\n import hashes\n const MODINT998244353* = 998244353\n const MODINT1000000007* = 1000000007\nwhen not declared CPLIB_UTILS_CONSTANTS:\n const CPLIB_UTILS_CONSTANTS* = 1\n const INF32*: int32 = 100100111.int32\n constINF64*: 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 yields[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(\" \")\nproc `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\nmacro getSymbolName(x: typed): string = x.toStrLit\n macro debug*(args: varargs[untyped]): untyped =\n when LOCAL_DEBUG:\nresult = newNimNode(nnkStmtList, args)\n template prop(e: string = \"\"): untyped = (f: stderr, sepc: \"\", endc: e, flush: true)\nfor 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\nproc `|`*(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: varSomeInteger, y: SomeInteger): void = x = x // y\n proc `^=`*(x: var SomeInteger, y: SomeInteger): void = x = x ^ y\n proc `&=`*(x: varSomeInteger, y: SomeInteger): void = x = x & y\n proc `|=`*(x: var SomeInteger, y: SomeInteger): void = x = x | y\n proc `>>=`*(x: varSomeInteger, 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 = xxor (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 whennot 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 procchmax*[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: varT, 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 procNO_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 procinitHashSet[T](): Hashset[T] = initHashSet[T](0)\n"# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/collections/defaultdict.nimImportExpand "cplib/collections/defaultdict" <=== "when not declared CPLIB_COLLECTIONS_DEFAULTDICT:\n const CPLIB_COLLECTIONS_DEFAULTDICT* = 1\nimport tables\n import hashes\n type DefaultDict*[K, V] = object\n table: Table[K, V]\n default: V\n proc initDefaultDict*[K, V](default: V): DefaultDict[K, V] = DefaultDict[K, V](table: initTable[K, V](), default: default)\n proc `==`*[K, V](src, dst:DefaultDict[K, V]): bool = src.table == dst.table\n proc `[]=`*[K, V](d: var DefaultDict[K, V], key: K, val: V) = d.table[key] = val\n proc`[]`*[K, V](d: DefaultDict[K, V], key: K): V =\n if key notin d.table: return d.default()\n return d.table[key]\n proc `[]`*[K,V](d: var DefaultDict[K, V], key: K): var V =\n if key notin d.table: d.table[key] = d.default\n return d.table[key]\n proc clear*[K, V](d: var DefaultDict[K, V]) = d.table = initTable[K, V](0)\n proc contains*[K, V](d: var DefaultDict[K, V], key: K): bool = d.table.contains(key)\n proc del*[K, V](d: var DefaultDict[K, V], key: K) = d.table.del(key)\n proc hash*[K, V](d: DefaultDict[K, V]): Hash = d.table.hash\n proc hasKey*[K, V](d: DefaultDict[K, V], key: K): bool = d.table.hasKey(key)\n proc len*[K, V](d: DefaultDict[K, V]): int = d.table.len\n proc pop*[K, V](d: var DefaultDict, key: K, val: var V): bool = d.table.pop(key, val)\n proc take*[K, V](d: var DefaultDict,key: K, val: var V): bool = d.table.pop(key, val)\n proc toDefaultDict*[K, V](pairs: openArray[(K, V)], default: V): DefaultDict[K, V] =\nresult = initDefaultDict[K, V](default)\n result.table = pairs.toTable\n proc toDefaultDict*[K, V](table: Table[K, V], default: V):DefaultDict[K, V] =\n result = initDefaultDict[K, V](default)\n result.table = table\n iterator pairs*[K, V](d: DefaultDict[K, V]): (K, V) =\n for k, v in d.table: yield (k, v)\n iterator mpairs*[K, V](d: var DefaultDict[K, V]): (K, var V) =\n for k, v in d.table.mpairs: yield (k, v)\n iterator keys*[K, V](d: DefaultDict[K, V]): K =\n for k in d.table.keys: yield k\n iterator values*[K,V](d: DefaultDict[K, V]): V =\n for v in d.table.values: yield v\n proc `$`*[K, V](d: DefaultDict[K, V]): string = $(d.table)\n"# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/collections/segtree_var.nimImportExpand "cplib/collections/segtree_var" <=== "when not declared CPLIB_COLLECTIONS_SEGTREE_VAR:\n const CPLIB_COLLECTIONS_SEGTREE_VAR* = 1\nimport algorithm\n import strutils\n import sequtils\n import macros\n type SegmentTree*[T, Elem] = object\n default: T\nmerge: proc(x: T, y: T): T\n arr*: seq[Elem]\n lastnode: int\n length: int\n type SegmentTreeElem[T] = object\nst: ptr SegmentTree[T, SegmentTreeElem[T]]\n v: T\n index: int\n proc initSegmentTreeElem[T](st: ptr SegmentTree[T,SegmentTreeElem[T]], v: T, index: int): SegmentTreeElem[T] = SegmentTreeElem[T](st: st, v: v, index: index)\n converter convertTo*[T](self:SegmentTreeElem[T]): T = self.v\n proc `$`*[T](self: SegmentTreeElem[T]): string = $(self.v)\n proc get*[T](self: var SegmentTree[T,SegmentTreeElem[T]], q_left: Natural, q_right: Natural): T =\n assert q_left <= q_right and 0 <= q_left and q_right <= self.length\nvar q_left = q_left\n var q_right = q_right\n q_left += self.lastnode\n q_right += self.lastnode\n var (lres, rres) =(self.default, self.default)\n while q_left < q_right:\n if (q_left and 1) > 0:\n lres = self.merge(lres, self.arr[q_left].v)\n q_left += 1\n if (q_right and 1) > 0:\n q_right -= 1\n rres = self.merge(self.arr[q_right].v, rres)\n q_left = q_left shr 1\n q_right = q_right shr 1\n return self.merge(lres, rres)\nproc get*[T](self: var SegmentTree[T, SegmentTreeElem[T]], segment: HSlice[int, int]): T =\n assert segment.a <= segment.b + 1 and 0 <=segment.a and segment.b+1 <= self.length\n return self.get(segment.a, segment.b+1)\n proc `[]`*[T](self: var SegmentTree[T,SegmentTreeElem[T]], segment: HSlice[int, int]): T = self.get(segment)\n proc `[]`*[T](self: var SegmentTree[T, SegmentTreeElem[T]], index:Natural): var SegmentTreeElem[T] =\n assert index < self.length\n return self.arr[index+self.lastnode]\n proc propagete_update[T](self: var SegmentTree[T, SegmentTreeElem[T]], x: Natural) =\n var x = x\n while x > 1:\n x = x shr 1\n self.arr[x].v = self.merge(self.arr[2*x].v, self.arr[2*x+1].v)\n proc update*[T](self: var SegmentTree[T, SegmentTreeElem[T]], index: Natural, val:T) =\n assert index < self.length\n self.arr[self.lastnode+index].v = val\n self.propagete_update(index + self.lastnode)\nproc `[]=`*[T](self: var SegmentTree[T, SegmentTreeElem[T]], index: Natural, val: T) = self.update(index, val)\n proc get_all*[T](self:SegmentTree[T, SegmentTreeElem[T]]): T =\n return self.arr[1].v\n proc len*[T](self: SegmentTree[T, SegmentTreeElem[T]]): int =\nreturn self.length\n proc `$`*[T](self: SegmentTree[T, SegmentTreeElem[T]]): string =\n var s = self.arr.len div 2\n return self.arr[s..<s+self.len].mapIt(it.v).join(\" \")\n macro declareOperation(op) =\n quote do:\n proc `op`*[T](self: varSegmentTreeElem[T], v: T) =\n `op`(self.v, v)\n self.st[].propagete_update(self.index)\n declareOperation(`+=`)\ndeclareOperation(`-=`)\n declareOperation(`*=`)\n declareOperation(`/=`)\n declareOperation(`^=`)\n declareOperation(`&=`)\ndeclareOperation(`|=`)\n declareOperation(`%=`)\n declareOperation(`//=`)\n declareOperation(`>>=`)\n declareOperation(`<<=`)\ndeclareOperation(`**=`)\n proc initSegmentTree*[T](v: seq[T], merge: proc(x, y: T): T, default: T): SegmentTree[T, SegmentTreeElem[T]] =\nvar lastnode = 1\n while lastnode < len(v):\n lastnode*=2\n var arr = newSeq[SegmentTreeElem[T]](2*lastnode)\nresult = SegmentTree[T, SegmentTreeElem[T]](default: default, merge: merge, arr: arr, lastnode: lastnode, length: len(v))\n #1-indexedで作成する\n for i in 0..<len(v):\n result.arr[lastnode+i] = initSegmentTreeElem(result.addr, v[i], lastnode+i)\nfor i in len(v)..<lastnode:\n result.arr[lastnode+i] = initSegmentTreeElem(result.addr, default, lastnode+i)\n for i incountdown(lastnode-1, 1):\n result.arr[i] = initSegmentTreeElem(result.addr, merge(result.arr[2*i].v, result.arr[2*i+1].v), i)\nproc initSegmentTree*[T](n: int, merge: proc(x, y: T): T, default: T): SegmentTree[T, SegmentTreeElem[T]] = initSegmentTree(newSeqWith(n, default), merge, default)\n template newSegWith*(V, merge, default: untyped): untyped =\n initSegmentTree(V, proc (l{.inject.}, r{.inject.}:typeof(default)): typeof(default) = merge, default)\n proc max_right*[T](self: SegmentTree[T, SegmentTreeElem[T]], l: int, f: proc(l: T): bool): int =\n assert 0 <= l and l <= self.len\n assert f(self.default)\n if l == self.len: return self.len\n var l = l\nl += self.lastnode\n var sm = self.default\n while true:\n while l mod 2 == 0: l = (l shr 1)\n if not f(self.merge(sm, self.arr[l])):\n while l < self.lastnode:\n l *= 2\n if f(self.merge(sm, self.arr[l])):\n sm = self.merge(sm, self.arr[l])\n l += 1\n return l - self.lastnode\nsm = self.merge(sm, self.arr[l])\n l += 1\n if (l and -l) == l: break\n return self.len\n proc min_left*[T](self: SegmentTree[T, SegmentTreeElem[T]], r: int, f: proc(l: T): bool): int =\n assert 0 <= r and r <= self.len\n assert f(self.default)\n if r == 0: return 0\n var r = r\n r += self.lastnode\n var sm = self.default\n while true:\nr -= 1\n while (r > 1 and r mod 2 != 0): r = (r shr 1)\n if not f(self.merge(self.arr[r], sm)):\n whiler < self.lastnode:\n r = 2 * r + 1\n if f(self.merge(self.arr[r], sm)):\n sm = self.merge(self.arr[r], sm)\n r -= 1\n return r + 1 - self.lastnode\n if (r and -r) == r: break\nreturn 0\n"# {.checks: off.}var n = input(int)var xy = newSeqWith(n, input(int, int))assert n in 2..200000var xst = initHashSet[int]()var yst = initHashSet[int]()for (x, y) in xy:assert abs(x) in 0..pow(10, 9)assert abs(y) in 0..pow(10, 9)xst.incl(x)yst.incl(y)assert xst.len > 1 and yst.len > 1proc calc_pq(): (int, int) =var p, q = 0var c = xy.mapIt(it[1]).sorted.deduplicate(true)var cx = xy.mapIt(it[0]).sorted.deduplicate(true)var seg = newSegWith(c.len, l+r, 0)var d = initDefaultDict[int, seq[int]](newSeq[int]())for (x, y) in xy: d[x].add(y)for x in cx:for y in d[x]:var pos = c.lowerBound(y)p += seg[0..<pos]q += seg[pos+1..<c.len]for y in d[x]:var pos = c.lowerBound(y)seg[pos] += 1return (p, q)proc calc_r(x: seq[int]): int =var cnt = x.toCountTableresult = n * (n-1) // 2for k, v in cnt:result -= v * (v - 1) // 2var (p, q) = calc_pq()var r = calc_r(xy.mapIt(it[0]))var s = calc_r(xy.mapIt(it[1]))assert r != 0 and s != 0debug(p, q, r, s)var ans = float(p - q) / (sqrt(float(r)) * sqrt(float(s)))print(ans)