floor sum
(NumberTheory/misc/floor_sum.py)

• View this file on GitHub
• Last update: 2021-05-03 22:51:42+09:00

使い方

floor_sum(n: int, m: int, a: int, b: int) -> int:
$\sum_{i = 0}^{n - 1} floor((a \times i + b) / m)$ を返す。計算量 $O(\log m)$

Verified with

• TestCase/LibraryChecker/sum_of_floor_of_linear.test.py

Code

def floor_sum(n, m, a, b):
    ans = 0
    if a >= m:
        ans += (n - 1) * n * (a // m) // 2
        a %= m
    if b >= m:
        ans += n * (b // m)
        b %= m

    y_max = (a * n + b) // m
    x_max = y_max * m - b
    if y_max == 0:
        return ans
    ans += (n - (x_max + a - 1) // a) * y_max
    ans += floor_sum(y_max, a, m, (a - x_max) % a)
    return ans

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

Back to top page