結果

問題 No.2873 Kendall's Tau
ユーザー 👑 seekworserseekworser
提出日時 2024-07-13 17:59:49
言語 Nim
(2.0.2)
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
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 2 ms
6,816 KB
testcase_01 AC 2 ms
6,940 KB
testcase_02 AC 1 ms
6,944 KB
testcase_03 AC 2 ms
6,944 KB
testcase_04 AC 2 ms
6,940 KB
testcase_05 AC 4 ms
6,940 KB
testcase_06 AC 2 ms
6,940 KB
testcase_07 AC 606 ms
48,912 KB
testcase_08 AC 651 ms
56,576 KB
testcase_09 AC 618 ms
49,916 KB
testcase_10 AC 705 ms
78,832 KB
testcase_11 AC 606 ms
46,948 KB
testcase_12 AC 633 ms
58,584 KB
testcase_13 AC 180 ms
16,980 KB
testcase_14 AC 520 ms
54,076 KB
testcase_15 AC 104 ms
12,928 KB
testcase_16 AC 106 ms
13,824 KB
testcase_17 AC 451 ms
44,344 KB
testcase_18 AC 344 ms
40,716 KB
testcase_19 AC 466 ms
45,480 KB
testcase_20 AC 107 ms
15,860 KB
testcase_21 AC 358 ms
30,648 KB
testcase_22 AC 154 ms
17,664 KB
testcase_23 AC 366 ms
32,088 KB
testcase_24 AC 44 ms
6,948 KB
testcase_25 AC 95 ms
12,928 KB
testcase_26 AC 469 ms
34,116 KB
testcase_27 AC 274 ms
25,652 KB
testcase_28 AC 529 ms
45,836 KB
testcase_29 AC 565 ms
54,100 KB
testcase_30 AC 71 ms
10,240 KB
testcase_31 AC 141 ms
14,592 KB
testcase_32 AC 398 ms
40,556 KB
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 # 

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 = 100100111.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/collections/defaultdict.nim
ImportExpand "cplib/collections/defaultdict" <=== "when not declared CPLIB_COLLECTIONS_DEFAULTDICT:\n    const CPLIB_COLLECTIONS_DEFAULTDICT* = 1\n    import 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] =\n        result = 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 = $(d.table)\n"
# source: https://github.com/kemuniku/cplib/tree/main/src/cplib/collections/segtree_var.nim
ImportExpand "cplib/collections/segtree_var" <=== "when not declared CPLIB_COLLECTIONS_SEGTREE_VAR:\n    const CPLIB_COLLECTIONS_SEGTREE_VAR* = 1\n    import algorithm\n    import strutils\n    import sequtils\n    import macros\n    type SegmentTree*[T, Elem] = object\n        default: T\n        merge: proc(x: T, y: T): T\n        arr*: seq[Elem]\n        lastnode: int\n        length: int\n    type SegmentTreeElem[T] = object\n        st: ptr SegmentTree[T, SegmentTreeElem[T]]\n        v: T\n        index: int\n    proc initSegmentTreeElem[T](st: ptr SegmentTree[T, SegmentTreeElem[T]], v: T, index: int): SegmentTreeElem[T] = SegmentTreeElem[T](st: st, v: v, index: index)\n    converter convertTo*[T](self: SegmentTreeElem[T]): T = self.v\n    proc `$`*[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\n        var 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)\n    proc 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)\n    proc `[]=`*[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 =\n        return 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: var SegmentTreeElem[T], v: T) =\n                `op`(self.v, v)\n                self.st[].propagete_update(self.index)\n    declareOperation(`+=`)\n    declareOperation(`-=`)\n    declareOperation(`*=`)\n    declareOperation(`/=`)\n    declareOperation(`^=`)\n    declareOperation(`&=`)\n    declareOperation(`|=`)\n    declareOperation(`%=`)\n    declareOperation(`//=`)\n    declareOperation(`>>=`)\n    declareOperation(`<<=`)\n    declareOperation(`**=`)\n    proc initSegmentTree*[T](v: seq[T], merge: proc(x, y: T): T, default: T): SegmentTree[T, SegmentTreeElem[T]] =\n        var lastnode = 1\n        while lastnode < len(v):\n            lastnode*=2\n        var arr = newSeq[SegmentTreeElem[T]](2*lastnode)\n        result = 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)\n        for i in len(v)..<lastnode:\n            result.arr[lastnode+i] = initSegmentTreeElem(result.addr, default, lastnode+i)\n        for i in countdown(lastnode-1, 1):\n            result.arr[i] = initSegmentTreeElem(result.addr, merge(result.arr[2*i].v, result.arr[2*i+1].v), i)\n    proc 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\n        l += 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\n            sm = 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:\n            r -= 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                while r < 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\n        return 0\n"

# {.checks: off.}

var n = input(int)
var xy = newSeqWith(n, input(int, int))
assert n in 2..200000
var 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 > 1

proc calc_pq(): (int, int) =
    var p, q = 0
    var 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] += 1
    return (p, q)

proc calc_r(x: seq[int]): int =
    var cnt = x.toCountTable
    result = n * (n-1) // 2
    for k, v in cnt:
        result -= v * (v - 1) // 2

var (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 != 0
debug(p, q, r, s)
var ans = float(p - q) / (sqrt(float(r)) * sqrt(float(s)))
print(ans)
0