cp-library

This documentation is automatically generated by online-judge-tools/verification-helper

View the Project on GitHub kobejean/cp-library

:warning: cp_library/math/sps/mod/sps_exp_adaptive_fn.py

Depends on

Code

import cp_library.__header__
import cp_library.math.__header__
import cp_library.math.sps.__header__
import cp_library.math.sps.mod.__header__
from cp_library.math.sps.mod.sps_exp_small_fn import sps_exp_small
from cp_library.math.sps.mod.sps_exp_half_fn import sps_exp_half

def sps_exp_adaptive(P, mod): return sps_exp_half(P, mod) if len(P).bit_length() - 1 > 17 else sps_exp_small(P, mod)
'''
╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸
             https://kobejean.github.io/cp-library               
'''




def sps_exp_small(P, mod):
    assert P[0] == 0
    exp = [0]*(Z := 1<<(len(P).bit_length()-1)); exp[0] = 1
    for i in range(1, Z):
        fg, b, j = 0, 1 << (i.bit_length() - 1), i-1&i
        while b <= j: fg += P[j]*exp[i^j]%mod; j = j-1&i
        exp[i] = (P[i]+fg)%mod
    return exp


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

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

def ior_zeta(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 isubset_conv_half(Ar: list[int], B: list[int], n: int, N: int, mod: int, pcnt) -> list[int]:
    Br = [0]*(z := (n+1)*(m := 1<<n))
    for i in range(m): Br[pcnt[i]<<n|i] = B[i]
    ior_zeta(Br, n)
    for i in range(z): Br[i] = Br[i]%mod
    for ij in range(n,-1,-1):
        ij_, i_ = (ij+1)<<N|m, ij<<n
        for k in range(m): Ar[ij_|k] = (Br[i_|k] * Ar[k]) % mod
        for i in range(ij):
            j = ij-i; i_, j_ = i<<n, j<<N
            for k in range(m): Ar[ij_|k] = (Ar[ij_|k] + Br[i_|k] * Ar[j_|k]) % mod
    for i in range(n+1):
        i = i << N
        for k in range(m): Ar[i|k|m] += Ar[i|k]

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 sps_exp_half(P, mod):
    assert P[0] == 0
    N = len(P).bit_length() - 1
    Z = (N+1)*(M := 1<<N)
    exp = [0]*Z; exp[0] = 1
    pcnt = popcnts(N)
    P = view(P); m = 1
    for n in range(N):
        P.set_range(m, m := m<<1)
        isubset_conv_half(exp, P, n, N, mod, pcnt)
    ior_mobius(exp, N)
    return [exp[p<<N|i] % mod for i,p in enumerate(pcnt)]

def sps_exp_adaptive(P, mod): return sps_exp_half(P, mod) if len(P).bit_length() - 1 > 17 else sps_exp_small(P, mod)
Back to top page