cp_library/math/conv/mod/isubset_conv_ranked_fn.py

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

Depends on

• cp_library/alg/dp/max2_fn.py
• cp_library/math/conv/ior_mobius_ranked_fn.py
• cp_library/math/conv/ior_zeta_pair_ranked_fn.py

Required by

• cp_library/math/conv/mod/isubset_conv_fn.py
• cp_library/math/conv/mod/subset_conv_fn.py
• cp_library/math/sps/mod/sps_exp_fn.py
• cp_library/math/sps/mod/sps_mul_fn.py
• cp_library/math/sps/mod/sps_pow_proj_fn.py
• cp_library/math/sps/mod/sps_pow_proj_poly_fn.py

Verified with

• test/library-checker/set-power-series/exp_of_set_power_series.test.py
• test/library-checker/set-power-series/power_projection_of_set_power_series.test.py
• test/library-checker/set-power-series/subset_convolution.test.py
• test/library-checker/set-power-series/subset_convolution_all.test.py

Code

import cp_library.__header__
from cp_library.alg.dp.max2_fn import max2
import cp_library.math.__header__
import cp_library.math.conv.__header__
import cp_library.math.conv.mod.__header__
from cp_library.math.conv.ior_zeta_pair_ranked_fn import ior_zeta_pair_ranked
from cp_library.math.conv.ior_mobius_ranked_fn import ior_mobius_ranked

def isubset_conv_ranked(Ar, Br, N, M, Z, mod) -> list[int]:
    ior_zeta_pair_ranked(Ar, Br, N, M, Z)
    for i in range(Z): Ar[i], Br[i] = Ar[i]%mod, Br[i]%mod
    for ij in range(Z-M,-1,-M):
        for k in range(M): Ar[ij|k] = (Ar[ij|k] * Br[k]) % mod
        r = M-(1 << (N-(ij>>N)))+1
        for i in range(0,ij,M):
            j = ij-i; l = (1 << (max2(i,j)>>N))-1
            for k in range(l,r): Ar[ij|k] += Ar[i|k] * Br[j|k] % mod
    return ior_mobius_ranked(Ar, N, M, Z)

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



def max2(a, b): return a if a > b else b

'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
    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_conv_ranked(Ar, Br, N, M, Z, mod) -> list[int]:
    ior_zeta_pair_ranked(Ar, Br, N, M, Z)
    for i in range(Z): Ar[i], Br[i] = Ar[i]%mod, Br[i]%mod
    for ij in range(Z-M,-1,-M):
        for k in range(M): Ar[ij|k] = (Ar[ij|k] * Br[k]) % mod
        r = M-(1 << (N-(ij>>N)))+1
        for i in range(0,ij,M):
            j = ij-i; l = (1 << (max2(i,j)>>N))-1
            for k in range(l,r): Ar[ij|k] += Ar[i|k] * Br[j|k] % mod
    return ior_mobius_ranked(Ar, N, M, Z)

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