結果

問題 No.308 素数は通れません
ユーザー mkawa2mkawa2
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
このコードへのチャレンジ
(要ログイン)

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 45 ms
54,784 KB
testcase_01 AC 44 ms
54,656 KB
testcase_02 AC 43 ms
54,912 KB
testcase_03 AC 44 ms
54,656 KB
testcase_04 AC 49 ms
54,784 KB
testcase_05 AC 45 ms
55,040 KB
testcase_06 AC 45 ms
54,784 KB
testcase_07 AC 46 ms
55,040 KB
testcase_08 AC 48 ms
54,912 KB
testcase_09 AC 48 ms
54,784 KB
testcase_10 AC 44 ms
55,040 KB
testcase_11 AC 48 ms
54,656 KB
testcase_12 AC 46 ms
55,040 KB
testcase_13 AC 48 ms
54,528 KB
testcase_14 AC 49 ms
54,912 KB
testcase_15 AC 46 ms
54,912 KB
testcase_16 AC 48 ms
55,040 KB
testcase_17 AC 46 ms
54,528 KB
testcase_18 AC 47 ms
55,040 KB
testcase_19 AC 43 ms
55,040 KB
testcase_20 AC 45 ms
55,040 KB
testcase_21 AC 45 ms
54,784 KB
testcase_22 AC 46 ms
54,528 KB
testcase_23 AC 46 ms
54,784 KB
testcase_24 AC 45 ms
54,784 KB
testcase_25 AC 45 ms
54,912 KB
testcase_26 AC 46 ms
54,784 KB
testcase_27 AC 44 ms
54,656 KB
testcase_28 AC 45 ms
54,784 KB
testcase_29 AC 45 ms
54,528 KB
testcase_30 AC 44 ms
54,912 KB
testcase_31 AC 46 ms
55,040 KB
testcase_32 AC 45 ms
54,912 KB
testcase_33 AC 46 ms
54,656 KB
testcase_34 AC 46 ms
54,784 KB
testcase_35 AC 44 ms
54,656 KB
testcase_36 AC 46 ms
55,040 KB
testcase_37 AC 43 ms
55,296 KB
testcase_38 AC 46 ms
55,168 KB
testcase_39 AC 47 ms
54,784 KB
testcase_40 AC 45 ms
55,040 KB
testcase_41 AC 46 ms
55,296 KB
testcase_42 AC 46 ms
55,168 KB
testcase_43 AC 45 ms
55,168 KB
testcase_44 AC 45 ms
55,296 KB
testcase_45 AC 44 ms
55,168 KB
testcase_46 AC 45 ms
55,252 KB
testcase_47 AC 47 ms
55,168 KB
testcase_48 AC 46 ms
54,912 KB
testcase_49 AC 45 ms
54,912 KB
testcase_50 AC 46 ms
55,040 KB
testcase_51 AC 45 ms
55,296 KB
testcase_52 AC 46 ms
54,912 KB
testcase_53 AC 45 ms
54,784 KB
testcase_54 AC 44 ms
55,168 KB
testcase_55 AC 45 ms
54,912 KB
testcase_56 AC 45 ms
55,040 KB
testcase_57 AC 45 ms
55,040 KB
testcase_58 AC 46 ms
55,168 KB
testcase_59 AC 44 ms
55,040 KB
testcase_60 AC 46 ms
55,296 KB
testcase_61 AC 47 ms
55,168 KB
testcase_62 AC 45 ms
54,656 KB
testcase_63 AC 45 ms
55,168 KB
testcase_64 AC 44 ms
55,040 KB
testcase_65 AC 46 ms
54,912 KB
testcase_66 AC 45 ms
55,168 KB
testcase_67 AC 46 ms
54,784 KB
testcase_68 AC 47 ms
58,496 KB
testcase_69 AC 48 ms
57,344 KB
testcase_70 AC 48 ms
58,880 KB
testcase_71 AC 49 ms
58,368 KB
testcase_72 AC 50 ms
58,112 KB
testcase_73 AC 50 ms
58,240 KB
testcase_74 AC 49 ms
59,904 KB
testcase_75 AC 47 ms
57,344 KB
testcase_76 AC 46 ms
55,424 KB
testcase_77 AC 45 ms
54,784 KB
testcase_78 AC 46 ms
55,168 KB
testcase_79 AC 51 ms
55,040 KB
testcase_80 AC 47 ms
55,168 KB
testcase_81 AC 47 ms
55,168 KB
testcase_82 AC 44 ms
55,168 KB
testcase_83 AC 45 ms
54,784 KB
testcase_84 AC 46 ms
55,296 KB
testcase_85 AC 44 ms
55,040 KB
testcase_86 AC 45 ms
54,656 KB
testcase_87 AC 46 ms
55,424 KB
testcase_88 AC 45 ms
55,040 KB
testcase_89 AC 45 ms
54,912 KB
testcase_90 AC 44 ms
55,424 KB
testcase_91 AC 49 ms
58,496 KB
testcase_92 AC 47 ms
58,112 KB
testcase_93 AC 47 ms
59,008 KB
testcase_94 AC 49 ms
57,984 KB
testcase_95 AC 49 ms
58,112 KB
testcase_96 AC 47 ms
54,912 KB
testcase_97 AC 47 ms
58,368 KB
testcase_98 AC 49 ms
57,216 KB
testcase_99 AC 47 ms
57,472 KB
testcase_100 AC 51 ms
57,856 KB
testcase_101 AC 48 ms
58,368 KB
testcase_102 AC 50 ms
58,880 KB
testcase_103 AC 52 ms
58,496 KB
testcase_104 AC 52 ms
58,496 KB
testcase_105 AC 50 ms
59,136 KB
testcase_106 AC 49 ms
57,472 KB
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 #

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...信頼度
    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()
0