結果

問題 No.2075 GCD Subsequence
ユーザー vwxyzvwxyz
提出日時 2023-11-29 17:48:57
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 1,102 ms / 4,000 ms
コード長 4,073 bytes
コンパイル時間 310 ms
コンパイル使用メモリ 81,884 KB
実行使用メモリ 120,832 KB
最終ジャッジ日時 2024-09-26 13:33:22
合計ジャッジ時間 22,322 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge5
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 28
権限があれば一括ダウンロードができます

ソースコード

diff # 

import bisect
import copy
import decimal
import fractions
import heapq
import itertools
import math
import random
import sys
import time
from collections import Counter,deque,defaultdict
from functools import lru_cache,reduce
from heapq import heappush,heappop,heapify,heappushpop,_heappop_max,_heapify_max
def _heappush_max(heap,item):
    heap.append(item)
    heapq._siftdown_max(heap, 0, len(heap)-1)
def _heappushpop_max(heap, item):
    if heap and item < heap[0]:
        item, heap[0] = heap[0], item
        heapq._siftup_max(heap, 0)
    return item
from math import gcd as GCD
read=sys.stdin.read
readline=sys.stdin.readline
readlines=sys.stdin.readlines
write=sys.stdout.write
#import pypyjit
#pypyjit.set_param('max_unroll_recursion=-1')
#sys.set_int_max_str_digits(10**9)

def Factorize(N):
    assert N>=1
    factors=defaultdict(int)
    for p in range(2,N):
        if p**2>N:
            break
        while N%p==0:
            factors[p]+=1
            N//=p
    if N!=1:
        factors[N]+=1
    return factors

class Prime:
    def __init__(self,N):
        assert N<=10**8
        self.smallest_prime_factor=[None]*(N+1)
        for i in range(2,N+1,2):
            self.smallest_prime_factor[i]=2
        n=int(N**.5)+1
        for p in range(3,n,2):
            if self.smallest_prime_factor[p]==None:
                self.smallest_prime_factor[p]=p
                for i in range(p**2,N+1,2*p):
                    if self.smallest_prime_factor[i]==None:
                        self.smallest_prime_factor[i]=p
        for p in range(n,N+1):
            if self.smallest_prime_factor[p]==None:
                self.smallest_prime_factor[p]=p
        self.primes=[p for p in range(N+1) if p==self.smallest_prime_factor[p]]

    def Factorize(self,N):
        assert N>=1
        factors=defaultdict(int)
        if N<=len(self.smallest_prime_factor)-1:
            while N!=1:
                factors[self.smallest_prime_factor[N]]+=1
                N//=self.smallest_prime_factor[N]
        else:
            for p in self.primes:
                while N%p==0:
                    N//=p
                    factors[p]+=1
                if N<p*p:
                    if N!=1:
                        factors[N]+=1
                    break
                if N<=len(self.smallest_prime_factor)-1:
                    while N!=1:
                        factors[self.smallest_prime_factor[N]]+=1
                        N//=self.smallest_prime_factor[N]
                    break
            else:
                if N!=1:
                    factors[N]+=1
        return factors

    def Divisors(self,N):
        assert N>0
        divisors=[1]
        for p,e in self.Factorize(N).items():
            pow_p=[1]
            for _ in range(e):
                pow_p.append(pow_p[-1]*p)
            divisors=[i*j for i in divisors for j in pow_p]
        return divisors

    def Is_Prime(self,N):
        return N==self.smallest_prime_factor[N]

    def Totient(self,N):
        for p in self.Factorize(N).keys():
            N*=p-1
            N//=p
        return N

    def Mebius(self,N):
        fact=self.Factorize(N)
        for e in fact.values():
            if e>=2:
                return 0
        else:
            if len(fact)%2==0:
                return 1
            else:
                return -1

N=int(readline())
A=list(map(int,readline().split()))
mod=998244353
for i in range(N):
    a=1
    for p in Factorize(A[i]):
        a*=p
    A[i]=a
max_A=max(A)
Pr=Prime(max_A)
ans=0
dp=[0]*(max_A+1)
for a in A:
    cnt=1
    P=list(Pr.Factorize(a).keys())
    le=len(P)
    dp_p=[None]*(1<<le)
    dp_sgn=[None]*(1<<le)
    dp_p[0]=1
    dp_sgn[0]=0
    for bit in range(1,1<<le):
        i=(bit&-bit).bit_length()-1
        dp_p[bit]=dp_p[bit^1<<i]*P[i]
        dp_sgn[bit]=dp_sgn[bit^1<<i]^1
        if dp_sgn[bit]:
            cnt+=dp[dp_p[bit]]
        else:
            cnt-=dp[dp_p[bit]]
    cnt%=mod
    ans+=cnt
    ans%=mod
    for bit in range(1<<le):
        dp[dp_p[bit]]+=cnt
        dp[dp_p[bit]]%=mod
print(ans)
0