AtCoderBeginnerContest241 D 問題 400 点 「Sequence Query」
AtCoderBeginnerContest241 D 問題 400 点 「Sequence Query」
問題概要
制約
解法
k が十分小さいので，配列から x のインデックスが見つけられさえすれば問題ない。Python には順序付き集合がないので工夫が必要になるが，強い人が Python の実装を公開しているので，とても簡単に解くことができる。問題文にある通り，条件を満たす値がない場合は -1 を出力することに注意。
お気持ち
AC コード
# 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
Q = int(input())
st = SortedMultiset()
for _ in range(Q):
query = tuple(map(int, input().split()))
if query[0] == 1:
st.add(query[1])
if query[0] == 2:
_, x, k = query
idx = st.index_right(x)
if idx < k:
ans = -1
else:
ans = st[idx - k]
print(ans)
if query[0] == 3:
_, x, k = query
idx = st.index(x)
if idx + k > len(st):
ans = -1
else:
ans = st[idx + k - 1]
print(ans)