結果

問題 No.1322 Totient Bound
ユーザー maspy
提出日時 2020-12-19 15:10:11
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 3,517 ms / 5,000 ms
コード長 2,703 bytes
コンパイル時間 309 ms
コンパイル使用メモリ 82,192 KB
実行使用メモリ 89,960 KB
最終ジャッジ日時 2024-09-21 10:19:29
合計ジャッジ時間 57,867 ms
ジャッジサーバーID
(参考情報)
judge2 / 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 * 36
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ソースコード

diff #
プレゼンテーションモードにする

def prime_count(N):
""" O(N^{0/75}) pi(N//i)
"""
sqN = int(N**.5)
sum_lo = [0] * (sqN+1)
sum_hi = [0] * (sqN+1)
for i in range(1, sqN + 1):
sum_lo[i] = i - 1
sum_hi[i] = N // i - 1
for p in range(2, sqN + 1):
if sum_lo[p] == sum_lo[p - 1]:
continue
sp = sum_lo[p - 1]
pp = p * p
for i in range(1, sqN + 1):
n = N // i
if n < pp:
break
x = sum_hi[i * p] if i * p <= sqN else sum_lo[n // p]
sum_hi[i] -= x - sp
for n in range(sqN, pp - 1, -1):
sum_lo[n] -= sum_lo[n // p] - sp
return sum_lo, sum_hi
def dfs(N, primes):
# 使
stack = [(1,1,0)]
while stack:
n, phi, nxt_i = stack.pop()
yield n, phi, nxt_i
for i in range(nxt_i, len(primes)):
p = primes[i]
if phi * (p-1) * p > N:
break
phi_p = p - 1
n_p=p
while True:
if phi * phi_p * p > N:
break
stack.append((n*n_p, phi * phi_p, i+1))
phi_p *= p
n_p*=p
def main(N):
pi_lo, pi_hi = prime_count(N)
sqN = len(pi_lo) - 1
def pi(x):
if x <= sqN:
return pi_lo[x]
return pi_hi[N//x]
memo = dict()
def isprime(n):
if n <= sqN:
return pi_lo[n] > pi_lo[n-1]
if n == 2:
return True
if n in memo:
return memo[n]
if pow(2, n-1, n) != 1:
memo[n] = False
return False
for p in primes:
if p*p>n:
break
if n%p==0:
memo[n]=False
return False
memo[n] = True
return True
primes = [p for p in range(2, sqN+1) if pi_lo[p] > pi_lo[p-1]]
if isprime(sqN+1):
primes.append(sqN+1)
ans = 1 # N = 1
for n, phi, nxt_i in dfs(N, primes):
cnt = 0
# 2
MAX = N // phi
for i in range(nxt_i, len(primes)):
p = primes[i]
k = 1
phi_p = (p-1)
while phi_p * p <= MAX:
k += 1
phi_p *= p
if k == 1:
break
cnt += k - 1
# (p-1)phi <= N p
# p - 1 <= N//phi
k = pi(N//phi)
if isprime(N//phi+1):
k += 1
k -= nxt_i
cnt += max(k, 0)
ans += cnt
return ans
print(main(int(input())))
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