結果

問題 No.811 約数の個数の最大化
ユーザー vwxyzvwxyz
提出日時 2022-09-22 05:29:37
言語 Python3
(3.13.1 + numpy 2.2.1 + scipy 1.14.1)
結果
AC  
実行時間 142 ms / 2,000 ms
コード長 3,670 bytes
コンパイル時間 172 ms
コンパイル使用メモリ 13,184 KB
実行使用メモリ 15,036 KB
最終ジャッジ日時 2024-12-22 04:40:24
合計ジャッジ時間 2,176 ms
ジャッジサーバーID
(参考情報)
judge4 / judge2
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 12
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 #
プレゼンテーションモードにする

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
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
def Divisor_Counts(N):
divisor_counts=[float('inf')]+[1]*N
for p in range(2,N+1):
if divisor_counts[p]!=1:
continue
pp=p
e=1
while pp<=N:
for i in range(pp,N+1,pp):
divisor_counts[i]+=divisor_counts[i]//e
e+=1
pp*=p
return divisor_counts
N,K=map(int,readline().split())
P=Prime(N)
DC=Divisor_Counts(N)
cnt=[0]*(N+1)
for p,e in P.Factorize(N).items():
for i in range(1,e+1):
for n in range(p**i,N+1,p**i):
cnt[n]+=1
m=max(DC[M] for M in range(1,N) if cnt[M]>=K)
for M in range(1,N):
if cnt[M]>=K and DC[M]==m:
break
print(M)
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