結果
問題 | No.2873 Kendall's Tau |
ユーザー |
![]() |
提出日時 | 2024-09-06 23:28:37 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 1,493 ms / 4,500 ms |
コード長 | 5,437 bytes |
コンパイル時間 | 284 ms |
コンパイル使用メモリ | 82,520 KB |
実行使用メモリ | 230,880 KB |
最終ジャッジ日時 | 2024-09-06 23:29:30 |
合計ジャッジ時間 | 24,940 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 30 |
ソースコード
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.pyimport mathfrom bisect import bisect_left, bisect_rightfrom typing import Generic, Iterable, Iterator, List, Tuple, TypeVar, OptionalT = TypeVar('T')class SortedMultiset(Generic[T]):BUCKET_RATIO = 16SPLIT_RATIO = 24def __init__(self, a: Iterable[T] = []) -> None:"Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)"a = list(a)n = self.size = len(a)if any(a[i] > a[i + 1] for i in range(n - 1)):a.sort()num_bucket = int(math.ceil(math.sqrt(n / self.BUCKET_RATIO)))self.a = [a[n * i // num_bucket : n * (i + 1) // num_bucket] for i in range(num_bucket)]def __iter__(self) -> Iterator[T]:for i in self.a:for j in i: yield jdef __reversed__(self) -> Iterator[T]:for i in reversed(self.a):for j in reversed(i): yield jdef __eq__(self, other) -> bool:return list(self) == list(other)def __len__(self) -> int:return self.sizedef __repr__(self) -> str:return "SortedMultiset" + str(self.a)def __str__(self) -> str:s = str(list(self))return "{" + s[1 : len(s) - 1] + "}"def _position(self, x: T) -> Tuple[List[T], int, int]:"return the bucket, index of the bucket and position in which x should be. self must not be empty."for i, a in enumerate(self.a):if x <= a[-1]: breakreturn (a, i, bisect_left(a, x))def __contains__(self, x: T) -> bool:if self.size == 0: return Falsea, _, i = self._position(x)return i != len(a) and a[i] == xdef count(self, x: T) -> int:"Count the number of x."return self.index_right(x) - self.index(x)def add(self, x: T) -> None:"Add an element. / O(√N)"if self.size == 0:self.a = [[x]]self.size = 1returna, b, i = self._position(x)a.insert(i, x)self.size += 1if len(a) > len(self.a) * self.SPLIT_RATIO:mid = len(a) >> 1self.a[b:b+1] = [a[:mid], a[mid:]]def _pop(self, a: List[T], b: int, i: int) -> T:ans = a.pop(i)self.size -= 1if not a: del self.a[b]return ansdef discard(self, x: T) -> bool:"Remove an element and return True if removed. / O(√N)"if self.size == 0: return Falsea, b, i = self._position(x)if i == len(a) or a[i] != x: return Falseself._pop(a, b, i)return Truedef lt(self, x: T) -> Optional[T]:"Find the largest element < x, or None if it doesn't exist."for a in reversed(self.a):if a[0] < x:return a[bisect_left(a, x) - 1]def le(self, x: T) -> Optional[T]:"Find the largest element <= x, or None if it doesn't exist."for a in reversed(self.a):if a[0] <= x:return a[bisect_right(a, x) - 1]def gt(self, x: T) -> Optional[T]:"Find the smallest element > x, or None if it doesn't exist."for a in self.a:if a[-1] > x:return a[bisect_right(a, x)]def ge(self, x: T) -> Optional[T]:"Find the smallest element >= x, or None if it doesn't exist."for a in self.a:if a[-1] >= x:return a[bisect_left(a, x)]def __getitem__(self, i: int) -> T:"Return the i-th element."if i < 0:for a in reversed(self.a):i += len(a)if i >= 0: return a[i]else:for a in self.a:if i < len(a): return a[i]i -= len(a)raise IndexErrordef pop(self, i: int = -1) -> T:"Pop and return the i-th element."if i < 0:for b, a in enumerate(reversed(self.a)):i += len(a)if i >= 0: return self._pop(a, ~b, i)else:for b, a in enumerate(self.a):if i < len(a): return self._pop(a, b, i)i -= len(a)raise IndexErrordef index(self, x: T) -> int:"Count the number of elements < x."ans = 0for a in self.a:if a[-1] >= x:return ans + bisect_left(a, x)ans += len(a)return ansdef index_right(self, x: T) -> int:"Count the number of elements <= x."ans = 0for a in self.a:if a[-1] > x:return ans + bisect_right(a, x)ans += len(a)return ansN = int(input())P,Q,R,S = 0,0,0,0Z = []S = set()Y = SortedMultiset()for _ in range(N):x,y = map(int,input().split())Z.append((x,y))S.add(x)S.add(y)Y.add(y)S = list(S)S.sort()n = len(S)d = {}for i in range(n):d[S[i]] = iG = [[] for i in range(n)]for x,y in Z:G[d[x]].append(y)M = Nfor i in range(n):m = len(G[i])M -= mR += m * (N - m)for y in G[i]:Y.discard(y)for y in G[i]:Q += Y.index(y)P += (M - Y.index_right(y))S = 0G = [0 for i in range(n)]for x,y in Z:G[d[y]] += 1for g in G:S += (N - g) * gP = (P - Q) * 2Q = R * Sans = P * P / Qans = ans ** 0.5if P < 0:ans = -ansprint(ans)