結果
問題 | No.2873 Kendall's Tau |
ユーザー | ikoma |
提出日時 | 2024-09-06 23:21:20 |
言語 | PyPy3 (7.3.15) |
結果 |
AC
|
実行時間 | 1,574 ms / 4,500 ms |
コード長 | 5,493 bytes |
コンパイル時間 | 263 ms |
コンパイル使用メモリ | 82,444 KB |
実行使用メモリ | 168,592 KB |
最終ジャッジ日時 | 2024-09-06 23:21:55 |
合計ジャッジ時間 | 26,301 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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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 | 58 ms
68,680 KB |
testcase_01 | AC | 60 ms
69,392 KB |
testcase_02 | AC | 63 ms
69,344 KB |
testcase_03 | AC | 59 ms
68,528 KB |
testcase_04 | AC | 56 ms
68,280 KB |
testcase_05 | AC | 60 ms
69,860 KB |
testcase_06 | AC | 56 ms
69,048 KB |
testcase_07 | AC | 1,431 ms
153,084 KB |
testcase_08 | AC | 1,518 ms
162,824 KB |
testcase_09 | AC | 1,452 ms
151,996 KB |
testcase_10 | AC | 1,574 ms
168,592 KB |
testcase_11 | AC | 1,395 ms
151,252 KB |
testcase_12 | AC | 1,455 ms
161,020 KB |
testcase_13 | AC | 520 ms
103,020 KB |
testcase_14 | AC | 1,242 ms
156,804 KB |
testcase_15 | AC | 436 ms
93,952 KB |
testcase_16 | AC | 392 ms
92,956 KB |
testcase_17 | AC | 1,075 ms
134,732 KB |
testcase_18 | AC | 860 ms
129,048 KB |
testcase_19 | AC | 1,064 ms
135,712 KB |
testcase_20 | AC | 419 ms
93,164 KB |
testcase_21 | AC | 894 ms
124,760 KB |
testcase_22 | AC | 464 ms
100,232 KB |
testcase_23 | AC | 936 ms
125,804 KB |
testcase_24 | AC | 289 ms
85,780 KB |
testcase_25 | AC | 380 ms
93,608 KB |
testcase_26 | AC | 1,067 ms
132,848 KB |
testcase_27 | AC | 828 ms
120,884 KB |
testcase_28 | AC | 1,294 ms
148,304 KB |
testcase_29 | AC | 1,255 ms
157,396 KB |
testcase_30 | AC | 321 ms
89,504 KB |
testcase_31 | AC | 480 ms
97,700 KB |
testcase_32 | AC | 934 ms
126,848 KB |
ソースコード
import sys input = sys.stdin.readline from collections import defaultdict,Counter # https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py import math from bisect import bisect_left, bisect_right from typing import Generic, Iterable, Iterator, List, Tuple, TypeVar, Optional T = TypeVar('T') class SortedMultiset(Generic[T]): BUCKET_RATIO = 16 SPLIT_RATIO = 24 def __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 j def __reversed__(self) -> Iterator[T]: for i in reversed(self.a): for j in reversed(i): yield j def __eq__(self, other) -> bool: return list(self) == list(other) def __len__(self) -> int: return self.size def __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]: break return (a, i, bisect_left(a, x)) def __contains__(self, x: T) -> bool: if self.size == 0: return False a, _, i = self._position(x) return i != len(a) and a[i] == x def 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 = 1 return a, b, i = self._position(x) a.insert(i, x) self.size += 1 if len(a) > len(self.a) * self.SPLIT_RATIO: mid = len(a) >> 1 self.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 -= 1 if not a: del self.a[b] return ans def discard(self, x: T) -> bool: "Remove an element and return True if removed. / O(√N)" if self.size == 0: return False a, b, i = self._position(x) if i == len(a) or a[i] != x: return False self._pop(a, b, i) return True def 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 IndexError def 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 IndexError def index(self, x: T) -> int: "Count the number of elements < x." ans = 0 for a in self.a: if a[-1] >= x: return ans + bisect_left(a, x) ans += len(a) return ans def index_right(self, x: T) -> int: "Count the number of elements <= x." ans = 0 for a in self.a: if a[-1] > x: return ans + bisect_right(a, x) ans += len(a) return ans N=int(input()) XY=[list(map(int,input().split())) for _ in range(N)] xy = defaultdict(list) cntY = Counter(list([y for _,y in XY])) for x,y in XY: xy[x].append(y) X = sorted(xy.keys()) P=0 Q=0 ss = SortedMultiset() for x in X[::-1]: y = xy[x] for i in y: P += len(ss) - ss.index_right(i) Q += ss.index(i) for i in y: ss.add(i) ss = SortedMultiset() for x in X[::-1]: y = xy[x] for i in y: P += len(ss) - ss.index_right(i) Q += ss.index(i) for i in y: ss.add(i) R=0 S=0 for x,y in xy.items(): n = len(y) R += n*(N-n) for v in cntY.values(): S += v*(N-v) print((P-Q)/(R*S)**0.5)