cp_library/math/conv/mod/isubset_deconv_fn.py

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

Depends on

• cp_library/bit/popcnts_fn.py
• cp_library/math/conv/ior_mobius_ranked_fn.py
• cp_library/math/conv/ior_zeta_pair_ranked_fn.py
• cp_library/math/conv/mod/isubset_deconv_ranked_fn.py

Code

import cp_library.__header__
from cp_library.bit.popcnts_fn import popcnts
import cp_library.math.__header__
import cp_library.math.conv.__header__
from cp_library.math.conv.mod.isubset_deconv_ranked_fn import isubset_deconv_ranked
import cp_library.math.conv.mod.__header__

def isubset_deconv(A: list[int], B: list[int], N: int, mod: int) -> list[int]:
    Z = (N+1)*(M:=1<<N)
    Ar, Br, P = [0]*Z, [0]*Z, popcnts(N)
    for i, p in enumerate(P): Ar[p<<N|i], Br[p<<N|i] = A[i], B[i]
    isubset_deconv_ranked(Ar, Br, N, Z, M, mod)
    for i, p in enumerate(P): A[i] = Ar[p<<N|i] % mod
    return A

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


def popcnts(N):
    P = [0]*(1 << N)
    for i in range(N):
        for m in range(b := 1<<i):
            P[m^b] = P[m] + 1
    return P

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


def ior_zeta_pair_ranked(A, B, N, M, Z):
    for i in range(0, Z, M):
        l, r = i+(1<<(i>>N))-1, i+M
        for j in range(N):
            m = l|(b := 1<<j)
            while m < r: A[m] += A[m^b]; B[m] += B[m^b]; m = m+1|b
    return A, B

def ior_mobius_ranked(A: list[int], N: int, M: int, Z: int):
    for i in range(0, Z, M):
        l, r = i, i+M-(1<<(N-(i>>N)))+1
        for j in range(N):
            m = l|(b := 1<<j)
            while m < r: A[m] -= A[m^b]; m = m+1|b
    return A

def isubset_deconv_ranked(Ar, Br, N, Z, M, mod):
    inv = pow(Br[0], -1, mod); ior_zeta_pair_ranked(Ar, Br, N, M, Z)
    for i in range(Z): Br[i], Ar[i] = Br[i]%mod, Ar[i]%mod
    for i in range(0, Z, M):
        for k in range(M): Ar[i|k] = Ar[i|k] * inv % mod
        for j in range(M, Z-i, M):
            ij = i + j; l = (1 << (j>>N))-1
            for k in range(l,M): Ar[ij|k] -= Ar[i|k] * Br[j|k] % mod
    return ior_mobius_ranked(Ar, N, M, Z)

def isubset_deconv(A: list[int], B: list[int], N: int, mod: int) -> list[int]:
    Z = (N+1)*(M:=1<<N)
    Ar, Br, P = [0]*Z, [0]*Z, popcnts(N)
    for i, p in enumerate(P): Ar[p<<N|i], Br[p<<N|i] = A[i], B[i]
    isubset_deconv_ranked(Ar, Br, N, Z, M, mod)
    for i, p in enumerate(P): A[i] = Ar[p<<N|i] % mod
    return A

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