結果

問題 No.308 素数は通れません
コンテスト
ユーザー heno239
提出日時 2020-08-21 14:45:39
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 651 ms / 1,000 ms
コード長 8,422 bytes
コンパイル時間 2,267 ms
コンパイル使用メモリ 136,548 KB
実行使用メモリ 5,248 KB
最終ジャッジ日時 2024-10-15 00:15:46
合計ジャッジ時間 6,913 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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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 #
raw source code 

#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define stop char nyaa;cin>>nyaa;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
typedef double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-12;
const ld pi = acos(-1.0);

ll mod_pow(ll x, ll n, ll m) {
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
struct modint {
	ll n;
	modint() :n(0) { ; }
	modint(ll m) :n(m) {
		if (n >= mod)n %= mod;
		else if (n < 0)n = (n % mod + mod) % mod;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }

const int max_n = 1 << 2;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}

struct bigint {
	string s;
	bigint() {};
	bigint(ll n) { s = to_string(n); };
	bigint(string t) { s = t; };
};
bool operator==(const bigint& a, const bigint& b) { return a.s == b.s; };
bool operator==(const bigint& a, const int& b) { return a.s == to_string(b); };
bool operator!=(const bigint& a, const bigint& b) { return !(a == b); };
bool operator!=(const bigint& a, const int& b) { return a != to_string(b); };
bool operator<(const bigint& a, const bigint& b) {
	if (a.s.length() != b.s.length())return a.s.length() < b.s.length();
	return a.s < b.s;
}
bool operator>(const bigint& a, const bigint& b) {
	if (a.s.length() != b.s.length())return a.s.length() > b.s.length();
	return a.s > b.s;
}
bool operator>=(const bigint& a, const bigint& b) {
	return !(a < b);
}
bool operator<=(const bigint& a, const bigint& b) {
	return !(a > b);
}
bigint operator+(const bigint& a, const bigint& b) {
	int len = max(a.s.length(), b.s.length());
	bigint ret; bool f = false;
	rep(i, len) {
		int c = 0;
		if (f)c = 1, f = false;
		int j = a.s.length() - 1 - i;
		if (j >= 0)c += a.s[j] - '0';
		j = b.s.length() - 1 - i;
		if (j >= 0)c += b.s[j] - '0';
		if (c >= 10)f = true, c -= 10;
		ret.s.push_back('0' + c);
	}
	if (f)ret.s.push_back('1');
	reverse(ret.s.begin(), ret.s.end()); return ret;
}
bigint operator+(const bigint& a, const int b) {
	return a + bigint(b);
}
bigint operator-(const bigint& a, const bigint& b) {
	int len = max(a.s.length(), b.s.length());
	bigint ret; bool f = false;
	rep(i, len) {
		int c = 0;
		if (f)c = -1, f = false;
		int j = a.s.length() - 1 - i;
		if (j >= 0)c += a.s[j] - '0';
		j = b.s.length() - 1 - i;
		if (j >= 0)c -= b.s[j] - '0';
		if (c < 0)f = true, c += 10;
		ret.s.push_back('0' + c);
	}
	while (ret.s.size() > 1 && ret.s.back() == '0')ret.s.pop_back();
	reverse(ret.s.begin(), ret.s.end());
	return ret;
}
bigint operator/(const bigint& a, const bigint& b) {
	bigint ret(0);
	bigint ans;
	int len = a.s.length();
	rep(i, len) {
		ret = ret + (a.s[i] - '0');
		int cnt = 0;
		while (ret >= b)++cnt, ret = ret - b;
		ans.s.push_back('0' + cnt);
		if (ret != 0)ret.s.push_back('0');
	}
	rep(i, ans.s.length()) {
		if (ans.s[i] != '0') {
			ans.s.erase(ans.s.begin(), ans.s.begin() + i);
			break;
		}
		if (i == (int)ans.s.length() - 1) {
			ans = 0;
		}
	}
	return ans;
}
bigint operator%(const bigint& a, const bigint& b) {
	bigint ret(0);
	int len = a.s.length();
	rep(i, len) {
		ret = ret + (a.s[i] - '0');
		while (ret >= b)ret = ret - b;
		if (ret != 0 && i < len - 1)ret.s.push_back('0');
	}

	rep(i, ret.s.size()) {
		if (ret.s[i] != '0' || i == ret.s.size() - 1) {
			ret.s.erase(ret.s.begin(), ret.s.begin() + i);
			break;
		}
	}
	return ret;
}
bigint multi(const bigint& a, const int& t) {
	bigint ret;
	int c = 0;
	per(i, a.s.length()) {
		c += (a.s[i] - '0') * t;
		ret.s.push_back('0' + (c % 10));
		c /= 10;
	}
	while (c > 0) {
		ret.s.push_back('0' + (c % 10));
		c /= 10;
	}
	while (ret != 0 && ret.s.back() == '0')ret.s.pop_back();
	reverse(ret.s.begin(), ret.s.end());
	return ret;
}
bigint operator*(const bigint& a, const bigint& b) {
	bigint ret(0);
	int l = b.s.length();
	rep(i, b.s.length()) {
		bigint u = multi(a, (b.s[l - 1 - i] - '0'));
		if (u != 0) {
			rep(j, i)u.s.push_back('0');
		}
		ret = ret + u;
	}
	rep(i, ret.s.size()) {
		if (ret.s[i] != '0' || i == ret.s.size() - 1) {
			ret.s.erase(ret.s.begin(), ret.s.begin() + i);
			break;
		}
	}
	return ret;
}
bigint min(const bigint& a, const bigint& b) {
	if (a < b)return a;
	else return b;
}

bigint gcd(bigint a, bigint b) {
	if (a < b)swap(a, b);
	while (b > 0) {
		bigint r = a % b; a = b; b = r;
	}
	return a;
}
bigint mod_pow(bigint x, bigint n, bigint m) {
	bigint ret = 1;
	while (n != 0) {
		if (n % 2 != 0)ret = ret * x % m;
		x = x * x % m; n = n / 2;
	}
	return ret;
}
typedef pair<bigint, bigint> bP;

bool intest(bigint a, bigint d, bigint n, int s) {
	if (mod_pow(a, d, n) == 1)return false;
	rep(r, s) {
		bigint d_ = d; rep(i, r)d_ = d_ * 2;
		if (mod_pow(a, d_, n) == n - 1)return false;
	}
	return true;
}
bool miller_rabin_primality_test(bigint n, int t = 30) {
	if (n.s == "1")return false;
	int s = 0; bigint d = n - 1;
	while (d % 2 == 0) {
		d = d / 2; s++;
	}
	mt19937_64 mt(time(0));
	rep(i, t) {
		ul a = mt(); ul b = mt();
		bigint c(to_string(a) + to_string(b));
		c = c % (n - 1); c = c + 1;
		if (intest(c, d, n, s))return false;
	}
	return true;
}


const int mn = 2001;
bool isp[mn + 1];
void init() {
	fill(isp + 2, isp + mn + 1, true);
	Rep1(i, 2, mn) {
		if (!isp[i])continue;
		for (int j = 2 * i; j <= mn; j += i) {
			isp[j] = false;
		}
	}
}
bool testmincase(int n, int m) {
	if (isp[n])return false;
	vector<bool> used(n, false);
	queue<int> q; q.push(0); used[0] = true;
	rep(i, n) {
		if (isp[i + 1])used[i] = true;
	}
	while (!q.empty()) {
		int id = q.front(); q.pop();
		if (id % m) {
			if (!used[id - 1]) {
				used[id - 1] = true; q.push(id - 1);
			}
		}
		if ((id % m) < m - 1 && id < n - 1) {
			if (!used[id + 1]) {
				used[id + 1] = true; q.push(id + 1);
			}
		}
		if (id - m >= 0) {
			if (!used[id - m]) {
				used[id - m] = true; q.push(id - m);
			}
		}
		if (id + m < n) {
			if (!used[id + m]) {
				used[id + m] = true; q.push(id + m);
			}
		}
	}
	return used[n - 1];
}


void solve() {
	init();
	string s; cin >> s;
	if (s.size() <= 2) {
		int n = stoi(s);
		rep1(i, n) {
			if (testmincase(n, i)) {
				cout << i << "\n"; return;
			}
		}
	}
	else {
		bigint b(s); b = b - 8;
		if (b % 8 == 1 && miller_rabin_primality_test(b))cout << 14 << "\n";
		else cout << 8 << "\n";
	}
}
signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init_f();
	//expr();
	//int t; cin >> t; rep(i, t)
	//while (cin >> n >> m>>s1>>s2>>t, n)
	solve();
	return 0;
}
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