cp_library/math/conv/superset_zeta_pair_fn.py

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

Required by

• cp_library/math/conv/and_conv_fast_fn.py

Verified with

• test/library-checker/convolution/bitwise_and_convolution_fast.test.py

Code

import cp_library.__header__
import cp_library.math.__header__
import cp_library.math.conv.__header__

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

'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
             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 superset_zeta_pair(A: list[int], B: list[int], N: int):
    Z = len(A)
    for i in range(N):
        m = b = 1<<i
        while m < Z:
            A[m ^ b] += A[m]
            B[m ^ b] += B[m]
            m = m+1|b
    return A

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