sorted_multiset

ソースコード

from titan_pylib.data_structures.set.sorted_multiset import SortedMultiset

view on github

展開済みコード

# from titan_pylib.data_structures.set.sorted_multiset import SortedMultiset
# 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, 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

仕様

class SortedMultiset(a: Iterable[T] = [])

Bases: Generic[T]

BUCKET_RATIO = 16

SPLIT_RATIO = 24

__getitem__(i: int) → T

Return the i-th element.

add(x: T) → None

Add an element. / O(√N)

count(x: T) → int

Count the number of x.

discard(x: T) → bool

Remove an element and return True if removed. / O(√N)

ge(x: T) → T | None

Find the smallest element >= x, or None if it doesn’t exist.

gt(x: T) → T | None

Find the smallest element > x, or None if it doesn’t exist.

index(x: T) → int

Count the number of elements < x.

index_right(x: T) → int

Count the number of elements <= x.

le(x: T) → T | None

Find the largest element <= x, or None if it doesn’t exist.

lt(x: T) → T | None

Find the largest element < x, or None if it doesn’t exist.

pop(i: int = -1) → T

Pop and return the i-th element.