cp-library

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View the Project on GitHub kobejean/cp-library

:warning: cp_library/math/sps/sps_exp_fn.py

Depends on

Code

import cp_library.__header__
from cp_library.ds.list.elist_fn import elist
from cp_library.ds.view.view_cls import view
import cp_library.math.__header__
from cp_library.math.conv.subset_conv_fn import subset_conv
import cp_library.math.sps.__header__

def sps_exp(P):
    N = len(P).bit_length()-1; P = view(P); m = 1; exp = elist(1 << N); exp.append(1)
    for n in range(N): P.set_range(m, m := m<<1); exp.extend(subset_conv(exp, P, n))
    return exp
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
             https://kobejean.github.io/cp-library               
'''



def elist(hint: int) -> list: ...
try:
    from __pypy__ import newlist_hint
except:
    def newlist_hint(hint): return []
elist = newlist_hint
    

from typing import Generic
from typing import TypeVar

_S = TypeVar('S'); _T = TypeVar('T'); _U = TypeVar('U'); _T1 = TypeVar('T1'); _T2 = TypeVar('T2'); _T3 = TypeVar('T3'); _T4 = TypeVar('T4'); _T5 = TypeVar('T5'); _T6 = TypeVar('T6')
import sys

def list_find(lst: list, value, start = 0, stop = sys.maxsize):
    try:
        return lst.index(value, start, stop)
    except:
        return -1


class view(Generic[_T]):
    __slots__ = 'A', 'l', 'r'
    def __init__(V, A: list[_T], l: int = 0, r: int = 0): V.A, V.l, V.r = A, l, r
    def __len__(V): return V.r - V.l
    def __getitem__(V, i: int): 
        if 0 <= i < V.r - V.l: return V.A[V.l+i]
        else: raise IndexError
    def __setitem__(V, i: int, v: _T): V.A[V.l+i] = v
    def __contains__(V, v: _T): return list_find(V.A, v, V.l, V.r) != -1
    def set_range(V, l: int, r: int): V.l, V.r = l, r
    def index(V, v: _T): return V.A.index(v, V.l, V.r) - V.l
    def reverse(V):
        l, r = V.l, V.r-1
        while l < r: V.A[l], V.A[r] = V.A[r], V.A[l]; l += 1; r -= 1
    def sort(V, /, *args, **kwargs):
        A = V.A[V.l:V.r]; A.sort(*args, **kwargs)
        for i,a in enumerate(A,V.l): V.A[i] = a
    def pop(V): V.r -= 1; return V.A[V.r]
    def append(V, v: _T): V.A[V.r] = v; V.r += 1
    def popleft(V): V.l += 1; return V.A[V.l-1]
    def appendleft(V, v: _T): V.l -= 1; V.A[V.l] = v; 
    def validate(V): return 0 <= V.l <= V.r <= len(V.A)



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

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) -> list[int]:
    ior_zeta_pair_ranked(Ar, Br, N, M, Z)
    for ij in range(Z-M,-1,-M):
        for k in range(M): Ar[ij|k] *= Br[k]
        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]
    return ior_mobius_ranked(Ar, N, M, Z)

def subset_conv(A: list[int], B: list[int], N: 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_conv_ranked(Ar, Br, N, M, Z)
    return [Ar[p<<N|i] for i, p in enumerate(P)]


def sps_exp(P):
    N = len(P).bit_length()-1; P = view(P); m = 1; exp = elist(1 << N); exp.append(1)
    for n in range(N): P.set_range(m, m := m<<1); exp.extend(subset_conv(exp, P, n))
    return exp
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