cp_library/math/conv/mod/ior_conv_fn.py

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• Last update: 2025-08-24 20:27:05+09:00

Depends on

• cp_library/math/conv/ior_mobius_fn.py
• cp_library/math/conv/ior_zeta_pair_fn.py

Code

import cp_library.__header__
import cp_library.math.__header__
import cp_library.math.conv.__header__
from cp_library.math.conv.ior_zeta_pair_fn import ior_zeta_pair
from cp_library.math.conv.ior_mobius_fn import ior_mobius

def ior_conv(A: list[int], B: list[int], N: int, mod: int) -> list[int]:
    assert len(A) == len(B)
    Z = 1 << N
    ior_zeta_pair(A, B, N)
    for i, b in enumerate(B): A[i] = A[i]*b%mod
    ior_mobius(A, N)
    for i, a in enumerate(Z): A[i] = a%mod
    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 ior_zeta_pair(A: list[int], B: list[int], N: int, Z: int = None):
    Z = Z if Z else len(A)
    for i in range(N):
        m = b = 1<<i
        while m < Z: A[m] += A[m^b]; B[m] += B[m^b]; m = m+1|b
    return A, B

def ior_mobius(A: list[int], N: int, Z: int = None):
    Z = Z if Z else 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 ior_conv(A: list[int], B: list[int], N: int, mod: int) -> list[int]:
    assert len(A) == len(B)
    Z = 1 << N
    ior_zeta_pair(A, B, N)
    for i, b in enumerate(B): A[i] = A[i]*b%mod
    ior_mobius(A, N)
    for i, a in enumerate(Z): A[i] = a%mod
    return A

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