結果

問題 No.2873 Kendall's Tau
ユーザー tassei903tassei903
提出日時 2024-09-07 00:27:01
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,573 ms / 4,500 ms
コード長 5,173 bytes
コンパイル時間 378 ms
コンパイル使用メモリ 82,028 KB
実行使用メモリ 247,512 KB
最終ジャッジ日時 2024-09-07 00:27:28
合計ジャッジ時間 26,407 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge5
このコードへのチャレンジ
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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 63 ms
68,044 KB
testcase_01 AC 64 ms
68,176 KB
testcase_02 AC 63 ms
68,096 KB
testcase_03 AC 63 ms
68,984 KB
testcase_04 AC 67 ms
69,048 KB
testcase_05 AC 64 ms
67,844 KB
testcase_06 AC 65 ms
68,604 KB
testcase_07 AC 1,381 ms
204,392 KB
testcase_08 AC 1,528 ms
234,396 KB
testcase_09 AC 1,340 ms
202,428 KB
testcase_10 AC 1,573 ms
247,512 KB
testcase_11 AC 1,341 ms
199,488 KB
testcase_12 AC 1,421 ms
225,108 KB
testcase_13 AC 602 ms
114,768 KB
testcase_14 AC 1,215 ms
193,524 KB
testcase_15 AC 426 ms
103,684 KB
testcase_16 AC 440 ms
100,104 KB
testcase_17 AC 1,058 ms
174,460 KB
testcase_18 AC 898 ms
160,912 KB
testcase_19 AC 1,103 ms
179,048 KB
testcase_20 AC 416 ms
102,248 KB
testcase_21 AC 823 ms
156,964 KB
testcase_22 AC 455 ms
110,644 KB
testcase_23 AC 884 ms
158,660 KB
testcase_24 AC 315 ms
88,428 KB
testcase_25 AC 414 ms
101,436 KB
testcase_26 AC 990 ms
170,660 KB
testcase_27 AC 759 ms
146,572 KB
testcase_28 AC 1,262 ms
194,312 KB
testcase_29 AC 1,172 ms
202,060 KB
testcase_30 AC 342 ms
93,220 KB
testcase_31 AC 519 ms
109,640 KB
testcase_32 AC 905 ms
161,292 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 sys
input = lambda :sys.stdin.readline()[:-1]
ni = lambda :int(input())
na = lambda :list(map(int,input().split()))
yes = lambda :print("yes");Yes = lambda :print("Yes");YES = lambda : print("YES")
no = lambda :print("no");No = lambda :print("No");NO = lambda : print("NO")
#######################################################################

# https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py
import math
from bisect import bisect_left, bisect_right, insort
from typing import Generic, Iterable, Iterator, TypeVar, Union, List
T = TypeVar('T')

class SortedMultiset(Generic[T]):
    BUCKET_RATIO = 50
    REBUILD_RATIO = 170

    def _build(self, a=None) -> None:
        "Evenly divide `a` into buckets."
        if a is None: a = list(self)
        size = self.size = len(a)
        bucket_size = int(math.ceil(math.sqrt(size / self.BUCKET_RATIO)))
        self.a = [a[size * i // bucket_size : size * (i + 1) // bucket_size] for i in range(bucket_size)]
    
    def __init__(self, a: Iterable[T] = []) -> None:
        "Make a new SortedMultiset from iterable. / O(N) if sorted / O(N log N)"
        a = list(a)
        if not all(a[i] <= a[i + 1] for i in range(len(a) - 1)):
            a = sorted(a)
        self._build(a)

    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 __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 _find_bucket(self, x: T) -> List[T]:
        "Find the bucket which should contain x. self must not be empty."
        for a in self.a:
            if x <= a[-1]: return a
        return a

    def __contains__(self, x: T) -> bool:
        if self.size == 0: return False
        a = self._find_bucket(x)
        i = bisect_left(a, 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 = self._find_bucket(x)
        insort(a, x)
        self.size += 1
        if len(a) > len(self.a) * self.REBUILD_RATIO:
            self._build()

    def discard(self, x: T) -> bool:
        "Remove an element and return True if removed. / O(√N)"
        if self.size == 0: return False
        a = self._find_bucket(x)
        i = bisect_left(a, x)
        if i == len(a) or a[i] != x: return False
        a.pop(i)
        self.size -= 1
        if len(a) == 0: self._build()
        return True

    def lt(self, x: T) -> Union[T, None]:
        "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) -> Union[T, None]:
        "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) -> Union[T, None]:
        "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) -> Union[T, None]:
        "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, x: int) -> T:
        "Return the x-th element, or IndexError if it doesn't exist."
        if x < 0: x += self.size
        if x < 0: raise IndexError
        for a in self.a:
            if x < len(a): return a[x]
            x -= 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

from collections import defaultdict, Counter
def f(p):
    eve = defaultdict(list)
    
    for x, y in p:
        eve[x].append(y)
    ms = SortedMultiset()
    ans = 0
    for x in sorted(eve.keys()):
        for y in eve[x]:
            ans += ms.index(y)
        for y in eve[x]:
            ms.add(y)
    return ans

def g(p):
    c = Counter(p)
    ans = 0
    for i in c:
        ans += c[i] * (c[i] - 1) // 2
    return n * (n - 1) // 2 - ans

n = ni()
xy = [na() for i in range(n)]

P = f(xy)
Q = f([(x, -y) for x, y in xy])
R = g([x for x, y in xy])
S = g([y for x, y in xy])

print((P - Q) /(R*S)**0.5)
0