結果

問題 No.2873 Kendall's Tau
ユーザー PNJPNJ
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
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 65 ms
68,584 KB
testcase_01 AC 66 ms
69,028 KB
testcase_02 AC 65 ms
69,848 KB
testcase_03 AC 64 ms
68,436 KB
testcase_04 AC 64 ms
68,364 KB
testcase_05 AC 65 ms
69,392 KB
testcase_06 AC 64 ms
68,568 KB
testcase_07 AC 1,422 ms
190,376 KB
testcase_08 AC 1,435 ms
225,280 KB
testcase_09 AC 1,404 ms
188,304 KB
testcase_10 AC 1,493 ms
230,880 KB
testcase_11 AC 1,390 ms
183,960 KB
testcase_12 AC 1,420 ms
200,628 KB
testcase_13 AC 482 ms
112,160 KB
testcase_14 AC 1,184 ms
196,412 KB
testcase_15 AC 357 ms
102,412 KB
testcase_16 AC 361 ms
97,836 KB
testcase_17 AC 981 ms
156,464 KB
testcase_18 AC 816 ms
153,152 KB
testcase_19 AC 1,012 ms
169,080 KB
testcase_20 AC 371 ms
101,528 KB
testcase_21 AC 854 ms
146,020 KB
testcase_22 AC 443 ms
106,400 KB
testcase_23 AC 837 ms
143,704 KB
testcase_24 AC 254 ms
85,656 KB
testcase_25 AC 345 ms
99,464 KB
testcase_26 AC 981 ms
151,276 KB
testcase_27 AC 655 ms
132,940 KB
testcase_28 AC 1,149 ms
198,580 KB
testcase_29 AC 1,255 ms
208,428 KB
testcase_30 AC 300 ms
91,836 KB
testcase_31 AC 407 ms
104,016 KB
testcase_32 AC 818 ms
146,408 KB
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ソースコード

diff # 

# 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())
P,Q,R,S = 0,0,0,0
Z = []
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]] = i
G = [[] for i in range(n)]

for x,y in Z:
  G[d[x]].append(y)

M = N
for i in range(n):
    m = len(G[i])
    M -= m
    R += 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 = 0
G = [0 for i in range(n)]
for x,y in Z:
    G[d[y]] += 1
for g in G:
    S += (N - g) * g

P = (P - Q) * 2
Q = R * S
ans = P * P / Q
ans = ans ** 0.5
if P < 0:
    ans = -ans
print(ans)
0