結果

問題 No.2873 Kendall's Tau
ユーザー nikoro256nikoro256
提出日時 2024-09-06 22:36:52
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,795 ms / 4,500 ms
コード長 5,384 bytes
コンパイル時間 296 ms
コンパイル使用メモリ 82,364 KB
実行使用メモリ 183,340 KB
最終ジャッジ日時 2024-09-06 22:37:32
合計ジャッジ時間 29,705 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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 66 ms
68,912 KB
testcase_01 AC 64 ms
68,708 KB
testcase_02 AC 64 ms
69,308 KB
testcase_03 AC 65 ms
69,076 KB
testcase_04 AC 64 ms
68,952 KB
testcase_05 AC 65 ms
68,620 KB
testcase_06 AC 65 ms
68,924 KB
testcase_07 AC 1,700 ms
157,464 KB
testcase_08 AC 1,740 ms
174,452 KB
testcase_09 AC 1,690 ms
155,648 KB
testcase_10 AC 1,795 ms
183,340 KB
testcase_11 AC 1,673 ms
153,140 KB
testcase_12 AC 1,688 ms
169,532 KB
testcase_13 AC 608 ms
97,692 KB
testcase_14 AC 1,355 ms
149,664 KB
testcase_15 AC 392 ms
93,252 KB
testcase_16 AC 425 ms
93,044 KB
testcase_17 AC 1,302 ms
135,140 KB
testcase_18 AC 993 ms
123,888 KB
testcase_19 AC 1,248 ms
138,348 KB
testcase_20 AC 431 ms
92,484 KB
testcase_21 AC 1,015 ms
122,244 KB
testcase_22 AC 534 ms
96,956 KB
testcase_23 AC 1,053 ms
121,940 KB
testcase_24 AC 295 ms
84,668 KB
testcase_25 AC 413 ms
91,960 KB
testcase_26 AC 1,229 ms
132,204 KB
testcase_27 AC 848 ms
115,432 KB
testcase_28 AC 1,457 ms
153,368 KB
testcase_29 AC 1,481 ms
151,284 KB
testcase_30 AC 369 ms
87,900 KB
testcase_31 AC 504 ms
95,080 KB
testcase_32 AC 1,022 ms
123,584 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 = 50
    REBUILD_RATIO = 170

    def _build(self, a: Optional[List[T]] = None) -> None:
        "Evenly divide `a` into buckets."
        if a is None: a = list(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)
        self.size = len(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 __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]:
        "Find the bucket and position which x should be inserted. self must not be empty."
        for a in self.a:
            if x <= a[-1]: break
        return (a, 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, i = self._position(x)
        a.insert(i, x)
        self.size += 1
        if len(a) > len(self.a) * self.REBUILD_RATIO:
            self._build()
    
    def _pop(self, a: List[T], i: int) -> T:
        ans = a.pop(i)
        self.size -= 1
        if not a: self._build()
        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, i = self._position(x)
        if i == len(a) or a[i] != x: return False
        self._pop(a, 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 a in reversed(self.a):
                i += len(a)
                if i >= 0: return self._pop(a, i)
        else:
            for a in self.a:
                if i < len(a): return self._pop(a, 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())
xd=defaultdict(int)
yd=defaultdict(int)
dic=defaultdict(list)
lis=[]
for _ in range(N):
    x,y=map(int,input().split())
    xd[x]+=1
    yd[y]+=1
    dic[x].append(y)
    lis.append((x,y))
P,Q,R,S=0,0,0,0
for k in xd.keys():
    R+=(N-xd[k])*xd[k]
for k in yd.keys():
    S+=(N-yd[k])*yd[k]
R//=2
S//=2
lis.sort()
smt=SortedMultiset()
for x in sorted(list(dic.keys())):
    for y in dic[x]:
        P+=smt.index(y)
        Q+=len(smt)-smt.index_right(y)
    for y in dic[x]:
        smt.add(y)
print((P-Q)/math.sqrt(R*S))
0