結果

問題 No.811 約数の個数の最大化
ユーザー McGregorsh
提出日時 2022-07-04 20:09:30
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 538 ms / 2,000 ms
コード長 4,470 bytes
コンパイル時間 291 ms
コンパイル使用メモリ 82,352 KB
実行使用メモリ 96,544 KB
最終ジャッジ日時 2024-12-14 12:43:38
合計ジャッジ時間 6,423 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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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 # 

###素因数分解###

def prime_factorize(n: int) -> list:
   return_list = []
   while n % 2 == 0:
   	  return_list.append(2)
   	  n //= 2
   f = 3
   while f * f <= n:
   	  if n % f == 0:
   	  	  return_list.append(f)
   	  	  n //= f
   	  else:
   	  	  f += 2
   if n != 1:
   	  return_list.append(n)
   return return_list


###ある数が素数かどうかの判定###

import math

def is_prime(n):
	  sqrt_n = math.ceil(math.sqrt(n))
	  for i in range(2, sqrt_n):
	  	  if n % i == 0:
	  	  	  return False
	  return True


###N以下の素数列挙###

import math 
def sieve_of_eratosthenes(n):
	  prime = [True for i in range(n+1)]
	  prime[0] = False
	  prime[1] = False
	  
	  sqrt_n = math.ceil(math.sqrt(n))
	  for i in range(2, sqrt_n+1):
	  	  if prime[i]:
	  	  	  for j in range(2*i, n+1, i):
	  	  	  	  prime[j] = False
	  return prime


###N以上K以下の素数列挙###

import math

def segment_sieve(a, b):
	  sqrt_b = math.ceil(math.sqrt(b))
	  prime_small = [True for i in range(sqrt_b)]
	  prime = [True for i in range(b-a+1)]
	  
	  for i in range(2, sqrt_b):
	  	  if prime_small[i]:
	  	  	  for j in range(2*i, sqrt_b, i):
	  	  	  	  prime_small[j] = False
	  	  	  for j in range((a+i-1)//i*i, b+1, i):
	  	  	  	  #print('j: ', j)
	  	  	  	  prime[j-a] = False
	  return prime


###n進数から10進数変換###

def base_10(num_n,n):
	  num_10 = 0
	  for s in str(num_n):
	  	  num_10 *= n
	  	  num_10 += int(s)
	  return num_10


###10進数からn進数変換###

def base_n(num_10,n):
	  str_n = ''
	  while num_10:
	  	  if num_10%n>=10:
	  	  	  return -1
	  	  str_n += str(num_10%n)
	  	  num_10 //= n
	  return int(str_n[::-1])


###複数の数の最大公約数、最小公倍数###

from functools import reduce

# 最大公約数
def gcd_list(num_list: list) -> int:
	  return reduce(gcd, num_list)

# 最小公倍数
def lcm_base(x: int, y: int) -> int:
	  return (x * y) // gcd(x, y)
def lcm_list(num_list: list):
	  return reduce(lcm_base, num_list, 1)


###約数列挙###

def make_divisors(n):
	  lower_divisors, upper_divisors = [], []
	  i = 1
	  while i * i <= n:
	  	  if n % i == 0:
	  	  	  lower_divisors.append(i)
	  	  	  if i != n // i:
	  	  	  	  upper_divisors.append(n//i)
	  	  i += 1
	  return lower_divisors + upper_divisors[::-1]


###順列###

def nPr(n, r):
	  npr = 1
	  for i in range(n, n-r, -1):
	  	  npr *= i
	  return npr


###組合せ###

def nCr(n, r):
	  factr = 1
	  r = min(r, n - r)
	  for i in range(r, 1, -1):
	  	  factr *= i
	  return nPr(n, r)/factr



import sys, re
from math import ceil, floor, sqrt, pi, factorial, gcd
from copy import deepcopy
from collections import Counter, deque, defaultdict
from heapq import heapify, heappop, heappush
from itertools import accumulate, product, combinations, combinations_with_replacement, permutations
from bisect import bisect, bisect_left, bisect_right
from functools import reduce
from decimal import Decimal, getcontext
def i_input(): return int(input())
def i_map(): return map(int, input().split())
def i_list(): return list(i_map())
def i_row(N): return [i_input() for _ in range(N)]
def i_row_list(N): return [i_list() for _ in range(N)]
def s_input(): return input()
def s_map(): return input().split()
def s_list(): return list(s_map())
def s_row(N): return [s_input for _ in range(N)]
def s_row_str(N): return [s_list() for _ in range(N)]
def s_row_list(N): return [list(s_input()) for _ in range(N)]
def lcm(a, b): return a * b // gcd(a, b)
def get_distance(x1, y1, x2, y2):
	  d = sqrt((x2 - x1) ** 2 + (y2 - y1) ** 2)
	  return d
def rotate(table):
   	  n_fild = []
   	  for x in zip(*table[::-1]):
   	  	  n_fild.append(x)
   	  return n_fild
sys.setrecursionlimit(10 ** 7)
INF = float('inf')
MOD = 10 ** 9 + 7
MOD2 = 998244353


def main():
   
   n, k = i_map()
   nums = prime_factorize(n)
   count = Counter(nums)
   
   ans = INF
   base = 0
   for i in range(n-1, 0, -1):
   	  lines = prime_factorize(i)
   	  score = 0
   	  new_nums = deepcopy(count)
   	  for j in range(len(lines)):
   	  	  if new_nums[lines[j]] > 0:
   	  	  	  score += 1
   	  	  	  new_nums[lines[j]] -= 1
   	  if score >= k:
   	  	  total = 1
   	  	  cou_line = Counter(lines)
   	  	  for key, value in cou_line.items():
   	  	  	  total *= (value+1)
   	  	  
   	  	  base = max(base, total)
   	  	  if base == total:
   	  	  	  ans = min(ans, i)
   print(ans)
   
   
if __name__ == '__main__':
    main()
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