結果
| 問題 | No.2 素因数ゲーム |
| コンテスト | |
| ユーザー |
 lif4635
|
| 提出日時 | 2025-10-16 20:03:15 |
| 言語 | PyPy3 (7.3.15) |
| 結果 |
AC
|
| 実行時間 | 47 ms / 5,000 ms |
| コード長 | 6,003 bytes |
| コンパイル時間 | 396 ms |
| コンパイル使用メモリ | 82,396 KB |
| 実行使用メモリ | 58,912 KB |
| 最終ジャッジ日時 | 2025-10-16 20:03:19 |
| 合計ジャッジ時間 | 3,164 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 31 |
ソースコード
# input
import sys
input = sys.stdin.readline
II = lambda : int(input())
MI = lambda : map(int, input().split())
LI = lambda : [int(a) for a in input().split()]
SI = lambda : input().rstrip()
LLI = lambda n : [[int(a) for a in input().split()] for _ in range(n)]
LSI = lambda n : [input().rstrip() for _ in range(n)]
MI_1 = lambda : map(lambda x:int(x)-1, input().split())
LI_1 = lambda : [int(a)-1 for a in input().split()]
mod = 998244353
inf = 1001001001001001001
ordalp = lambda s : ord(s)-65 if s.isupper() else ord(s)-97
ordallalp = lambda s : ord(s)-39 if s.isupper() else ord(s)-97
yes = lambda : print("Yes")
no = lambda : print("No")
yn = lambda flag : print("Yes" if flag else "No")
prinf = lambda ans : print(ans if ans < 1000001001001001001 else -1)
alplow = "abcdefghijklmnopqrstuvwxyz"
alpup = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"
alpall = "abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"
URDL = {'U':(-1,0), 'R':(0,1), 'D':(1,0), 'L':(0,-1)}
DIR_4 = [[-1,0],[0,1],[1,0],[0,-1]]
DIR_8 = [[-1,0],[-1,1],[0,1],[1,1],[1,0],[1,-1],[0,-1],[-1,-1]]
DIR_BISHOP = [[-1,1],[1,1],[1,-1],[-1,-1]]
prime60 = [2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59]
sys.set_int_max_str_digits(0)
# sys.setrecursionlimit(10**6)
# import pypyjit
# pypyjit.set_param('max_unroll_recursion=-1')
from collections import defaultdict,deque
from heapq import heappop,heappush
from bisect import bisect_left,bisect_right
DD = defaultdict
BSL = bisect_left
BSR = bisect_right
from math import isqrt
from random import randint
def gcd(x, y):
""" x < y """
while y:
x, y = y, x%y
return x
def is_prime(num):
""" 1 <= x < 1<<64 """
if num < 4: return num > 1
if not num&1: return False
d, s = num-1, 0
while not d&1:
d >>= 1
s += 1
tests = (2,7,61) if num < 4759123141 else (2,325,9375,28178,450775,9780504,1795265022)
for test in tests:
if test >= num: return True
t = pow(test, d, num)
if 1 < t < num-1:
for _ in range(s-1):
t = t*t%num
if t == num-1: break
else:
return False
return True
def find_prime(n):
b = n.bit_length() - 1
b = (b >> 2) << 2
m = (1 << (b >> 3)) << 1
while True:
c = randint(1, n - 1)
y = 0
g = q = r = 1
while g == 1:
x = y
for _ in range(r):
y = (y * y + c) % n
k = 0
while k < r and g == 1:
ys = y
for _ in range(min(m, r - k)):
y = (y * y + c) % n
q = q * abs(x - y) % n
g = gcd(q, n)
k += m
r <<= 1
if g == n:
g = 1
y = ys
while g == 1:
y = (y * y + c) % n
g = gcd(abs(x - y), n)
if g == n:
continue
if is_prime(g):
return g
elif is_prime(n // g):
return n // g
else:
n = g
def _primefactor(n):
result = []
for p in range(2, 500):
if p * p > n:
break
c = 0
while n%p == 0:
n //= p
c += 1
if c:
result.append(p)
while n > 1 and not is_prime(n):
p = find_prime(n)
while n % p == 0:
n //= p
result.append(p)
if n > 1: result.append(p)
return result
def primefact(n, deduplicate = True):
if deduplicate == False:
return _primefactor(n)
result = dict()
for p in range(2, 500):
if p * p > n:
break
c = 0
while n%p == 0:
n //= p
c += 1
if c:
result[p] = c
while n > 1 and not is_prime(n):
p = find_prime(n)
c = 0
while n % p == 0:
n //= p
c += 1
result[p] = c
if n > 1: result[n] = 1
return result
def divisors_naive(n):
divs_small, divs_big = [], []
i = 1
while i*i <= n:
if n % i == 0:
divs_small.append(i)
if i != n//i:
divs_big.append(n//i)
i += 1
return divs_small + divs_big[::-1]
def divisors(n):
if n == 1: return [1]
if n <= 100_000_000: # 10 ** 8
return divisors_naive(n)
pf = primefact(n)
ps = list(pf.keys())
es = list(pf.values())
us = [p ** e for p,e in zip(ps, es)]
l = len(es)
nes = [0] * (l + 1)
r = 1
res = [1]
while True:
nes[0] += 1
for i in range(l):
if nes[i] > es[i]:
if i+1 == l:
res.sort()
return res
nes[i] = 0
nes[i+1] += 1
r //= us[i]
else:
r *= ps[i]
break
res.append(r)
def totient(n):
"""
totient(n) = #{ m | (m,n) = 1, 1 <= m <= n }
"""
pf = _primefactor(n)
for p in pf:
n //= p
n *= p - 1
return n
def mobius(n):
pf = primefact(n)
r = 1
for p,e in pf.items():
if e >= 2: return 0
r *= -1
return r
def primitive_root(p):
""" p : prime """
if p == 2: return 1
r = p - 1
tests = []
for q in range(2, 500):
if q * q > r:
break
if r % q == 0:
while r % q == 0:
r //= q
tests.append((p - 1) // q)
while r > 1 and not is_prime(r):
q = find_prime(r)
while r % q == 0:
r //= q
tests.append((p - 1) // q)
if r > 1: tests.append((p - 1) // r)
res = 2
while True:
for test in tests:
if pow(res, test, p) == 1:
break
else:
return res
res = randint(3, p - 2)
n = II()
pf = primefact(n)
nim = 0
for x in pf.values():
nim ^= x
print("Alice" if nim else "Bob")