cp-library
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cp_library/ds/sorted_multiset_cls.py
- View this file on GitHub
- Last update: 2025-03-30 20:17:47+09:00
- Link: https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py
Code
import cp_library.ds.__header__
from math import ceil, sqrt
from bisect import bisect_left, bisect_right
from typing import Iterable, Iterator, MutableSet
from cp_library.misc.typing import _T
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py
class SortedMultiset(MutableSet[_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(ceil(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):
return list(self) == list(other)
def __len__(self):
return self.size
def __repr__(self):
return "SortedMultiset" + str(self.a)
def __str__(self):
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):
if self.size == 0: return False
a, _, i = self._position(x)
return i != len(a) and a[i] == x
def count(self, x: _T):
"Count the number of x."
return self.index_right(x) - self.index(x)
def add(self, x: _T):
"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):
ans = a.pop(i)
self.size -= 1
if not a: del self.a[b]
return ans
def discard(self, x: _T):
"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):
"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):
"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):
"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):
"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):
"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):
"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 bisect_left(self, x: _T):
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def bisect_right(self, x: _T):
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
https://kobejean.github.io/cp-library
'''
from math import ceil, sqrt
from bisect import bisect_left, bisect_right
from typing import Iterable, Iterator, MutableSet
from typing import TypeVar
_T = TypeVar('T')
# https://github.com/tatyam-prime/SortedSet/blob/main/SortedMultiset.py
class SortedMultiset(MutableSet[_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(ceil(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):
return list(self) == list(other)
def __len__(self):
return self.size
def __repr__(self):
return "SortedMultiset" + str(self.a)
def __str__(self):
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):
if self.size == 0: return False
a, _, i = self._position(x)
return i != len(a) and a[i] == x
def count(self, x: _T):
"Count the number of x."
return self.index_right(x) - self.index(x)
def add(self, x: _T):
"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):
ans = a.pop(i)
self.size -= 1
if not a: del self.a[b]
return ans
def discard(self, x: _T):
"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):
"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):
"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):
"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):
"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):
"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):
"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 bisect_left(self, x: _T):
ans = 0
for a in self.a:
if a[-1] >= x:
return ans + bisect_left(a, x)
ans += len(a)
return ans
def bisect_right(self, x: _T):
ans = 0
for a in self.a:
if a[-1] > x:
return ans + bisect_right(a, x)
ans += len(a)
return ans