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
(3.12.2 + numpy 1.26.4 + scipy 1.12.0)
結果
AC  
実行時間 139 ms / 2,000 ms
コード長 3,670 bytes
コンパイル時間 94 ms
コンパイル使用メモリ 13,184 KB
実行使用メモリ 15,048 KB
最終ジャッジ日時 2024-06-01 17:46:32
合計ジャッジ時間 2,081 ms
ジャッジサーバーID
(参考情報)
judge4 / judge3
このコードへのチャレンジ
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 46 ms
12,160 KB
testcase_01 AC 43 ms
12,160 KB
testcase_02 AC 138 ms
14,720 KB
testcase_03 AC 42 ms
12,160 KB
testcase_04 AC 43 ms
12,288 KB
testcase_05 AC 45 ms
12,288 KB
testcase_06 AC 51 ms
12,416 KB
testcase_07 AC 55 ms
12,544 KB
testcase_08 AC 91 ms
13,312 KB
testcase_09 AC 85 ms
13,440 KB
testcase_10 AC 78 ms
13,220 KB
testcase_11 AC 116 ms
14,720 KB
testcase_12 AC 69 ms
12,672 KB
testcase_13 AC 139 ms
15,032 KB
testcase_14 AC 136 ms
15,048 KB
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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

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)
0