BIT
(expansion/data_structure/BIT.py)

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• Last update: 2023-06-10 15:38:57+09:00

概要

Binary Indexed Tree / Fenwick Tree です．1点加算区間和取得を高速に行います．

使い方

• __init__(n) := 長さ $N$ の配列 A を作成します．
• sum(r) := 区間 $[0, r)$ の総和を返します．
• sum(l, r) := 区間 $[l, r)$ の総和を返します．
• get(i) := A[i] の値を求めます．
• add(i, x) := A[i] に $x$ を加算します．
• lower_bound(x) := 区間 $[0, r)$ の総和が $x$ 以上となるような最小の $k$ を返します．

Code

class BIT:
    def __init__(self, n):
        self.n = n
        self.data = [0] * (n + 1)
        if n == 0:
            self.n0 = 0
        else:
            self.n0 = 1 << (n.bit_length() - 1)

    def sum_(self, i):
        s = 0
        while i > 0:
            s += self.data[i]
            i -= i & -i
        return s

    def sum(self, l, r=-1):
        if r == -1:
            return self.sum_(l)
        else:
            return self.sum_(r) - self.sum_(l)

    def get(self, i):
        return self.sum(i, i + 1)

    def add(self, i, x):
        i += 1
        while i <= self.n:
            self.data[i] += x
            i += i & -i

    def lower_bound(self, x):
        if x <= 0:
            return 0
        i = 0
        k = self.n0
        while k > 0:
            if i + k <= self.n and self.data[i + k] < x:
                x -= self.data[i + k]
                i += k
            k //= 2
        return i + 1

Traceback (most recent call last):
  File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/documentation/build.py", line 81, in _render_source_code_stat
    bundled_code = language.bundle(
                   ^^^^^^^^^^^^^^^^
  File "/opt/hostedtoolcache/Python/3.11.4/x64/lib/python3.11/site-packages/onlinejudge_verify/languages/python.py", line 108, in bundle
    raise NotImplementedError
NotImplementedError

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