結果
| 問題 | No.2873 Kendall's Tau |
| ユーザー |
 Shirotsume
|
| 提出日時 | 2024-09-06 21:56:38 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 1,350 ms / 4,500 ms |
| コード長 | 5,071 bytes |
| コンパイル時間 | 316 ms |
| コンパイル使用メモリ | 82,584 KB |
| 実行使用メモリ | 176,240 KB |
| 最終ジャッジ日時 | 2024-09-06 21:57:39 |
| 合計ジャッジ時間 | 24,354 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
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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
70,132 KB |
| testcase_01 | AC | 67 ms
70,332 KB |
| testcase_02 | AC | 65 ms
69,728 KB |
| testcase_03 | AC | 65 ms
69,528 KB |
| testcase_04 | AC | 65 ms
70,472 KB |
| testcase_05 | AC | 66 ms
69,320 KB |
| testcase_06 | AC | 69 ms
69,252 KB |
| testcase_07 | AC | 1,300 ms
153,880 KB |
| testcase_08 | AC | 1,350 ms
169,540 KB |
| testcase_09 | AC | 1,248 ms
151,980 KB |
| testcase_10 | AC | 1,323 ms
175,184 KB |
| testcase_11 | AC | 1,279 ms
152,468 KB |
| testcase_12 | AC | 1,326 ms
176,240 KB |
| testcase_13 | AC | 487 ms
100,388 KB |
| testcase_14 | AC | 1,088 ms
161,480 KB |
| testcase_15 | AC | 409 ms
93,000 KB |
| testcase_16 | AC | 402 ms
92,272 KB |
| testcase_17 | AC | 963 ms
134,720 KB |
| testcase_18 | AC | 871 ms
127,636 KB |
| testcase_19 | AC | 975 ms
136,888 KB |
| testcase_20 | AC | 391 ms
92,640 KB |
| testcase_21 | AC | 785 ms
126,080 KB |
| testcase_22 | AC | 453 ms
99,216 KB |
| testcase_23 | AC | 868 ms
126,544 KB |
| testcase_24 | AC | 277 ms
84,716 KB |
| testcase_25 | AC | 364 ms
90,568 KB |
| testcase_26 | AC | 954 ms
135,092 KB |
| testcase_27 | AC | 705 ms
117,444 KB |
| testcase_28 | AC | 1,164 ms
149,840 KB |
| testcase_29 | AC | 1,211 ms
165,600 KB |
| testcase_30 | AC | 309 ms
87,920 KB |
| testcase_31 | AC | 428 ms
95,844 KB |
| testcase_32 | AC | 850 ms
126,372 KB |
ソースコード
import sys, time, random
from collections import deque, Counter, defaultdict
def debug(*x):print('debug:',*x, file=sys.stderr)
input = lambda: sys.stdin.readline().rstrip()
ii = lambda: int(input())
mi = lambda: map(int, input().split())
li = lambda: list(mi())
inf = 2 ** 61 - 1
mod = 998244353
# 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
n = ii()
XY = [li() for _ in range(n)]
cntx = Counter()
cnty = Counter()
S = SortedMultiset()
buff = []
bef = -1
XY.sort(key = lambda x: x[0])
ans = 0
for x, y in XY:
cntx[x] += 1
cnty[y] += 1
if bef == x:
buff.append(y)
else:
for y2 in buff:
S.add(y2)
buff = [y]
bef = x
ans += S.index(y)
ans -= len(S) - S.index_right(y)
r = n * (n - 1) // 2
s = n * (n - 1) // 2
for x in cntx.values():
r -= x * (x - 1) // 2
for x in cnty.values():
s -= x * (x - 1) // 2
ans /= (r * s) ** 0.5
print(ans)