cp_library/math/conv/or_conv_fast_fn.py

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• Last update: 2025-03-30 20:17:47+09:00

Depends on

• cp_library/math/conv/subset_mobius_fn.py
• cp_library/math/conv/subset_zeta_fn.py

Code

import cp_library.__header__
import cp_library.math.__header__
import cp_library.math.conv.__header__
from cp_library.math.conv.subset_zeta_fn import subset_zeta
from cp_library.math.conv.subset_mobius_fn import subset_mobius

def or_conv(A: list[int], B: list[int], N: int) -> list[int]:
    assert len(A) == len(B)
    subset_zeta(A, N), subset_zeta(B, N)
    for i, b in enumerate(B): A[i] *= b
    return subset_mobius(A, N)

'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
             https://kobejean.github.io/cp-library               
'''

'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
    x₀ ────────●─●────────●───●────────●───────●────────► X₀
                ╳          ╲ ╱          ╲     ╱          
    x₄ ────────●─●────────●─╳─●────────●─╲───╱─●────────► X₁
                           ╳ ╳          ╲ ╲ ╱ ╱          
    x₂ ────────●─●────────●─╳─●────────●─╲─╳─╱─●────────► X₂
                ╳          ╱ ╲          ╲ ╳ ╳ ╱          
    x₆ ────────●─●────────●───●────────●─╳─╳─╳─●────────► X₃
                                        ╳ ╳ ╳ ╳         
    x₁ ────────●─●────────●───●────────●─╳─╳─╳─●────────► X₄
                ╳          ╲ ╱          ╱ ╳ ╳ ╲          
    x₅ ────────●─●────────●─╳─●────────●─╱─╳─╲─●────────► X₅
                           ╳ ╳          ╱ ╱ ╲ ╲          
    x₃ ────────●─●────────●─╳─●────────●─╱───╲─●────────► X₆
                ╳          ╱ ╲          ╱     ╲          
    x₇ ────────●─●────────●───●────────●───────●────────► X₇
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
                      Math - Convolution                     
'''

def subset_zeta(A: list[int], N: int):
    Z = len(A)
    for i in range(N):
        m = b = 1<<i
        while m < Z:
            A[m] += A[m^b]
            m = m+1|b
    return A

def subset_mobius(A: list[int], N: int):
    Z = len(A)
    for i in range(N):
        m = b = 1<<i
        while m < Z:
            A[m] -= A[m^b]
            m = m+1|b
    return A

def or_conv(A: list[int], B: list[int], N: int) -> list[int]:
    assert len(A) == len(B)
    subset_zeta(A, N), subset_zeta(B, N)
    for i, b in enumerate(B): A[i] *= b
    return subset_mobius(A, N)

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