区間加算・一点取得
(DataStructure/BinaryIndexedTree/RangeAddPointGet.py)

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• Last update: 2021-01-02 01:31:17+09:00

概要

列に対する区間加算、一点取得を計算量 $O(\log n)$ で行えるデータ構造。

使い方

BinaryIndexedTree(n: int)
長さ $n$ の Binary Indexed Tree を構築する。初期値はすべて $0$ である。計算量 $O(n)$

• build(array: Sequence[int]) -> None
  Binary Indexed Tree を array で初期化する。計算量 $O(n)$

• __getitem__(i: int) -> int
  $i$ 番目の要素を返す。計算量 $O(\log n)$

• add(l: int, r: int, val: int) -> None
  $\lbrack l, r)$ 番目の要素に val を加える。計算量 $O(\log n)$

Verified with

• TestCase/AOJ/DSL_2_E.test.py

Code

class BinaryIndexedTree:
    def __init__(self, n):
        self.size = n
        self.bit = [0] * (self.size + 1)

    def build(self, array):
        for i, val in enumerate(array):
            self.bit[i + 1] = val
        for i in range(1, self.size):
            if i + (i & -i) > self.size:
                continue
            self.bit[i] -= self.bit[i + (i & -i)]

    def __getitem__(self, i):
        i = i + 1
        s = 0
        while i <= self.size:
            s += self.bit[i]
            i += i & -i
        return s

    def _add(self, i, val):
        while i > 0:
            self.bit[i] += val
            i -= i & -i

    def add(self, l, r, val):
        """add value in range [l, r)"""
        self._add(r, val)
        self._add(l, -val)

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.12.4/x64/lib/python3.12/site-packages/onlinejudge_verify/documentation/build.py", line 71, in _render_source_code_stat
    bundled_code = language.bundle(stat.path, basedir=basedir, options={'include_paths': [basedir]}).decode()
                   ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.12.4/x64/lib/python3.12/site-packages/onlinejudge_verify/languages/python.py", line 96, in bundle
    raise NotImplementedError
NotImplementedError

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