結果

問題 No.2873 Kendall's Tau
ユーザー hiro1729hiro1729
提出日時 2024-09-06 22:02:52
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,835 ms / 4,500 ms
コード長 5,363 bytes
コンパイル時間 215 ms
コンパイル使用メモリ 82,764 KB
実行使用メモリ 186,652 KB
最終ジャッジ日時 2024-09-06 22:03:39
合計ジャッジ時間 29,959 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge4
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 69 ms
69,680 KB
testcase_01 AC 61 ms
69,484 KB
testcase_02 AC 61 ms
69,464 KB
testcase_03 AC 57 ms
68,636 KB
testcase_04 AC 58 ms
68,248 KB
testcase_05 AC 59 ms
69,040 KB
testcase_06 AC 57 ms
69,012 KB
testcase_07 AC 1,794 ms
169,684 KB
testcase_08 AC 1,789 ms
186,652 KB
testcase_09 AC 1,835 ms
169,492 KB
testcase_10 AC 1,788 ms
183,144 KB
testcase_11 AC 1,788 ms
172,572 KB
testcase_12 AC 1,697 ms
183,324 KB
testcase_13 AC 590 ms
104,320 KB
testcase_14 AC 1,383 ms
167,420 KB
testcase_15 AC 375 ms
95,296 KB
testcase_16 AC 379 ms
94,328 KB
testcase_17 AC 1,303 ms
146,608 KB
testcase_18 AC 994 ms
126,900 KB
testcase_19 AC 1,295 ms
147,804 KB
testcase_20 AC 384 ms
95,220 KB
testcase_21 AC 1,091 ms
135,804 KB
testcase_22 AC 545 ms
104,112 KB
testcase_23 AC 1,063 ms
136,476 KB
testcase_24 AC 285 ms
84,792 KB
testcase_25 AC 366 ms
92,968 KB
testcase_26 AC 1,299 ms
146,112 KB
testcase_27 AC 825 ms
126,328 KB
testcase_28 AC 1,504 ms
162,568 KB
testcase_29 AC 1,572 ms
171,688 KB
testcase_30 AC 334 ms
90,844 KB
testcase_31 AC 546 ms
99,388 KB
testcase_32 AC 1,067 ms
135,292 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

from collections import defaultdict

N = int(input())
pt = [tuple(map(int, input().split())) for _ in range(N)]

P = 0
pt.sort(key = lambda x: (x[0], -x[1]))
st_P = SortedMultiset()
for i in range(N):
	P += st_P.index(pt[i][1])
	st_P.add(pt[i][1])

Q = 0
pt.sort()
st_Q = SortedMultiset()
for i in range(N):
	Q += st_Q.index(-pt[i][1])
	st_Q.add(-pt[i][1])

R = N * (N - 1) // 2
S = N * (N - 1) // 2
ddx = defaultdict(int)
ddy = defaultdict(int)
for x, y in pt:
	ddx[x] += 1
	ddy[y] += 1

for _, c in ddx.items():
	R -= c * (c - 1) // 2

for _, c in ddy.items():
	S -= c * (c - 1) // 2

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