区間加算・区間和取得
(DataStructure/BinaryIndexedTree/RangeAddRangeSum.py)

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• Last update: 2021-07-18 03:57:07+09:00

概要

列に対する区間加算、区間和取得を計算量 $O(\log n)$ 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 を配列 array で初期化する。計算量 $O(n)$

• 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 $O(\log n)$

• sum(l: int, r: int) -> int
  $\lbrack l, r)$ 番目の要素の総和を返す。計算量 $O(\log n)$

Verified with

• TestCase/AOJ/2667.test.py
• TestCase/AOJ/DSL_2_G.test.py
• TestCase/AOJ/GRL_5_E.test.py

Code

class BinaryIndexedTree:
    def __init__(self, n):
        self.size = n
        self.bit0 = [0] * (self.size + 1)
        self.bit1 = [0] * (self.size + 1)

    def build(self, array):
        for i, val in enumerate(array):
            self.bit0[i + 1] = val
        for i in range(1, self.size):
            if i + (i & -i) > self.size:
                continue
            self.bit0[i + (i & -i)] += self.bit0[i]
        self.bit1 = [0] * (self.size + 1)

    def _add(self, bit, i, val):
        i = i + 1
        while i <= self.size:
            bit[i] += val
            i += i & -i

    def _sum(self, bit, i):
        s = 0
        while i > 0:
            s += bit[i]
            i -= i & -i
        return s

    def add(self, l, r, val):
        """add value in range [l, r)"""
        self._add(self.bit0, l, -val * l)
        self._add(self.bit0, r, val * r)
        self._add(self.bit1, l, val)
        self._add(self.bit1, r, -val)

    def sum(self, l, r):
        """sum of values in range [l, r)"""
        return (self._sum(self.bit0, r) + r * self._sum(self.bit1, r)
                - self._sum(self.bit0, l) - l * self._sum(self.bit1, l))

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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