cp_library/math/conv/subset_conv_fn.py

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

Depends on

• cp_library/bit/popcnts_fn.py
• cp_library/math/conv/subset_mobius_fn.py
• cp_library/math/conv/subset_zeta_pair_fn.py

Verified with

• test/library-checker/set-power-series/subset_convolution_all.test.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.subset_zeta_pair_fn import subset_zeta_pair
from cp_library.math.conv.subset_mobius_fn import subset_mobius

def subset_conv(A,B,N):
    assert len(A) == len(B)
    Z = (N+1)*(M := 1<<N)
    Ar,Br,Cr,P = [0]*Z, [0]*Z, [0]*Z, popcnts(N)
    for i,p in enumerate(P): Ar[p<<N|i], Br[p<<N|i] = A[i], B[i]
    subset_zeta_pair(Ar, Br, N)
    for i in range(0,Z,M):
        for j in range(0,Z-i,M):
            ij = i+j
            for k in range(M): Cr[ij|k] += Ar[i|k] * Br[j|k]
    subset_mobius(Cr, N)
    for i,p in enumerate(P): A[i] = Cr[p<<N|i]
    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 subset_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] += A[m^b]
            B[m] += B[m^b]
            m = m+1|b
    return A, B

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 subset_conv(A,B,N):
    assert len(A) == len(B)
    Z = (N+1)*(M := 1<<N)
    Ar,Br,Cr,P = [0]*Z, [0]*Z, [0]*Z, popcnts(N)
    for i,p in enumerate(P): Ar[p<<N|i], Br[p<<N|i] = A[i], B[i]
    subset_zeta_pair(Ar, Br, N)
    for i in range(0,Z,M):
        for j in range(0,Z-i,M):
            ij = i+j
            for k in range(M): Cr[ij|k] += Ar[i|k] * Br[j|k]
    subset_mobius(Cr, N)
    for i,p in enumerate(P): A[i] = Cr[p<<N|i]
    return A

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