#288609 (C++14) No.308 素数は通れません

• 問題: No.308 素数は通れません
• ユーザー: Yang33
• 提出日時: 2018-09-30 17:03:02
• 言語: C++14 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 88 ms / 1,000 ms
• コード長: 3,454 bytes
• コンパイル時間: 1,713 ms
• コンパイル使用メモリ: 176,556 KB
• 実行使用メモリ: 5,248 KB
• 最終ジャッジ日時: 2024-10-12 09:13:10
• 合計ジャッジ時間: 4,791 ms
• ジャッジサーバーID （参考情報）: judge3 / judge4

ファイルパターン	結果
other	AC * 107

ソースコード

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#include <bits/stdc++.h>
using namespace std;
using VS = vector<string>;    using LL = long long;
using VI = vector<int>;       using VVI = vector<VI>;
using PII = pair<int, int>;   using PLL = pair<LL, LL>;
using VL = vector<LL>;        using VVL = vector<VL>;
#define ALL(a)  begin((a)),end((a))
#define RALL(a) (a).rbegin(), (a).rend()
#define SZ(a) int((a).size())
#define SORT(c) sort(ALL((c)))
#define RSORT(c) sort(RALL((c)))
#define UNIQ(c) (c).erase(unique(ALL((c))), end((c)))
#define FOR(i, s, e) for (int(i) = (s); (i) < (e); (i)++)
#define FORR(i, s, e) for (int(i) = (s); (i) > (e); (i)--)
#define debug(x) cerr << #x << ": " << x << endl
const int INF = 1e9;                          const LL LINF = 1e16;
const LL MOD = 1000000007;                    const double PI = acos(-1.0);
int DX[8] = { 0, 0, 1, -1, 1, 1, -1, -1 };    int DY[8] = { 1, -1, 0, 0, 1, -1, 1, -1 };
/* -----  2018/09/30  Problem: yukicoder 308  / Link: http://yukicoder.me/problems/no/308  ----- */
/* ------問題------
-----問題ここまで----- */
/* -----解説等-----
オーバーフロー…
----解説ここまで---- */
using LLL = __int128;
__int128 parse(string &s) {
    __int128 ret = 0;
    for (int i = 0; i < (int)s.length(); i++)
        if (isdigit(s[i]))
            ret = 10 * ret + s[i] - '0';
    if (s[0] == '-')ret = -ret;
    return ret;
}
std::istream &operator>>(std::istream &is, __int128 &value) {
    string s; cin >> s;
    value = parse(s);
    return is;
}
vector<int> make_prime(LL N) {
    vector<int> prime(N + 1, 1);
    prime[0] = prime[1] = 0;
    for (int i = 2; i <= N; i++) {
        if (prime[i]) {
            for (int j = i * 2; j <= N; j += i)
                prime[j] = 0;
        }
    }
    return prime;
}
LLL mul(const LLL a, const LLL b, const LLL mod) {
    if (b == 0) { return 0; }
    if (b % 2 == 1) {
        return (mul(a, b - 1, mod) + a) % mod;
    }
    else {
        const LLL pp = mul(a, b / 2, mod);
        return (pp + pp) % mod;
    }
}
LLL power(const LLL a, const LLL n, const LLL mod) {
    if (n == 0) { return 1; }
    if (n % 2 == 1) {
        return mul(power(a, n - 1, mod), a, mod);
    }
    else {
        const LLL aa = power(a, n / 2, mod);
        return mul(aa, aa, mod);
    }
}
int main() {
    cin.tie(0);
    ios_base::sync_with_stdio(false);
    LLL N;
    cin >> N;
    int ans = 0;
    if (N <= 1000) {
        VI is_prime = make_prime(N + 1);
        for (int w = 3; ; w++) {
            VI masu(N + 1, 0);
            masu[1] = 1;
            queue<int>q;
            q.push(1);
#define IN(a,b,c) (a<=b&&b<c)
            vector<int> ds({ -w,w,-1,1 });
            while (!q.empty()) {
                int pos = q.front(); q.pop();
                FOR(k, 0, 4) {
                    if (k == 3 && pos%w == 0)continue;
                    if (k == 2 && pos%w == 1)continue;
                    int nx = pos + ds[k];
                    if (IN(1, nx, N + 1) && !masu[nx] && !is_prime[nx]) {
                        masu[nx] = 1;
                        q.push(nx);
                    }
                }
            }
            if (masu[N]) { ans = w; break; }
        }
    }
    else {
        auto f = [](LLL n) {
            if (n == 1) { return 0; }
            LLL s = 0, d = n - 1;
            while (!(d & 1))s++, d >>= 1;
            mt19937_64 rand_src(random_device{}());
            FOR(i, 0, 100) {
                const LLL a = (rand_src() % (n - 2)) + 1;
                if (power(a, n - 1, n) != 1) { return 0; }
                LLL num = power(a, d, n);
                if (num != 1) {
                    bool comp = true;
                    FOR(_, 0, s) {
                        if (num == n - 1) {
                            comp = 0;
                            break;
                        }
                        num = mul(num, num, n);
                    }
                    if (comp) return 0;
                }
            }
            return 1;
        };
        if (N % 8 == 1) {
            // if N-8 prime : ans = 14 
            if (f(N - 8))ans = 14;
            else ans = 8;
        }
        else {
            ans = 8;
        }
    }
    cout << ans << "\n";
    return 0;
}
 
 
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