結果

問題 No.308 素数は通れません
ユーザー mkawa2
提出日時 2023-03-21 18:04:21
言語 PyPy3
(7.3.15)
結果
AC  
実行時間 52 ms / 1,000 ms
コード長 3,204 bytes
コンパイル時間 223 ms
コンパイル使用メモリ 82,704 KB
実行使用メモリ 59,904 KB
最終ジャッジ日時 2024-09-18 14:25:57
合計ジャッジ時間 7,547 ms
ジャッジサーバーID
(参考情報)
judge4 / judge1
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ファイルパターン 結果
other AC * 107
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 sys
# sys.setrecursionlimit(200005)
int1 = lambda x: int(x)-1
pDB = lambda *x: print(*x, end="\n", file=sys.stderr)
p2D = lambda x: print(*x, sep="\n", end="\n\n", file=sys.stderr)
def II(): return int(sys.stdin.readline())
def LI(): return list(map(int, sys.stdin.readline().split()))
def LLI(rows_number): return [LI() for _ in range(rows_number)]
def LI1(): return list(map(int1, sys.stdin.readline().split()))
def LLI1(rows_number): return [LI1() for _ in range(rows_number)]
def SI(): return sys.stdin.readline().rstrip()
dij = [(0, 1), (-1, 0), (0, -1), (1, 0)]
# dij = [(0, 1), (-1, 0), (0, -1), (1, 0), (1, 1), (1, -1), (-1, 1), (-1, -1)]
inf = (1 << 63)-1
# inf = (1 << 31)-1
# md = 10**9+7
md = 998244353
from random import randrange
def is_prime(n):
# K...
K = 20
if n == 2: return True
if n == 1 or n & 1 == 0: return False
d = (n-1) >> 1
while d & 1 == 0: d >>= 1
for k in range(K):
a = randrange(1, n)
t = d
y = pow(a, t, n)
while t != n-1 and y != 1 and y != n-1:
y = pow(y, 2, n)
t <<= 1
if y != n-1 and t & 1 == 0: return False
return True
primes = set(
[2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107,
109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229,
233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359,
367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491,
499])
def ok(w):
def push(ij):
if fin[ij]: return
fin[ij] = 1
st.append(ij)
fin = [0]*n
for p in primes:
if p-1 >= n: break
fin[p-1] = 1
fin[0] = 1
st = [0]
while st:
ij = st.pop()
if ij == n-1: return True
i, j = divmod(ij, w)
if i: push(ij-w)
if j: push(ij-1)
if ij+w < n: push(ij+w)
if j+1 < w: push(ij+1)
return False
def ok1(w):
def push(ij):
if ij in fin: return
fin.add(ij)
if ij+1 in primes: return
st.append(ij)
fin = set()
st = [0]
while st:
ij = st.pop()
i, j = divmod(ij, w)
if i > d or j > d:
return True
if i: push(ij-w)
if j: push(ij-1)
if ij+w < n: push(ij+w)
if j+1 < w: push(ij+1)
return False
def ok2(w):
def push(ij):
if ij in fin: return
fin.add(ij)
if is_prime(ij+1): return
st.append(ij)
fin = set()
gi, gj = divmod(n-1, w)
st = [n-1]
while st:
ij = st.pop()
i, j = divmod(ij, w)
if abs(i-gi) > d or abs(j-gj) > d:
return True
if i: push(ij-w)
if j: push(ij-1)
if ij+w < n: push(ij+w)
if j+1 < w and ij+1 < n: push(ij+1)
return False
d = 9
n = II()
if n < 500:
for w in range(3, n+1):
if ok(w):
print(w)
exit()
else:
for w in range(8, 1000):
if ok1(w) and ok2(w):
print(w)
exit()
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