#335117 (C++14) No.308 素数は通れません

提出ソース

結果

問題	No.308 素数は通れません
ユーザー	minami
提出日時	2019-04-03 16:38:02
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	87 ms / 1,000 ms
コード長	11,211 bytes
コンパイル時間	4,060 ms
コンパイル使用メモリ	206,744 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-12-21 15:33:23
合計ジャッジ時間	6,050 ms
ジャッジサーバーID （参考情報）	judge5 / judge4

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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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	2 ms 5,248 KB
testcase_03	AC	2 ms 5,248 KB
testcase_04	AC	2 ms 5,248 KB
testcase_05	AC	2 ms 5,248 KB
testcase_06	AC	1 ms 5,248 KB
testcase_07	AC	2 ms 5,248 KB
testcase_08	AC	2 ms 5,248 KB
testcase_09	AC	2 ms 5,248 KB
testcase_10	AC	2 ms 5,248 KB
testcase_11	AC	2 ms 5,248 KB
testcase_12	AC	2 ms 5,248 KB
testcase_13	AC	2 ms 5,248 KB
testcase_14	AC	1 ms 5,248 KB
testcase_15	AC	2 ms 5,248 KB
testcase_16	AC	2 ms 5,248 KB
testcase_17	AC	2 ms 5,248 KB
testcase_18	AC	2 ms 5,248 KB
testcase_19	AC	2 ms 5,248 KB
testcase_20	AC	2 ms 5,248 KB
testcase_21	AC	2 ms 5,248 KB
testcase_22	AC	2 ms 5,248 KB
testcase_23	AC	2 ms 5,248 KB
testcase_24	AC	1 ms 5,248 KB
testcase_25	AC	2 ms 5,248 KB
testcase_26	AC	2 ms 5,248 KB
testcase_27	AC	1 ms 5,248 KB
testcase_28	AC	2 ms 5,248 KB
testcase_29	AC	2 ms 5,248 KB
testcase_30	AC	2 ms 5,248 KB
testcase_31	AC	2 ms 5,248 KB
testcase_32	AC	2 ms 5,248 KB
testcase_33	AC	2 ms 5,248 KB
testcase_34	AC	2 ms 5,248 KB
testcase_35	AC	2 ms 5,248 KB
testcase_36	AC	2 ms 5,248 KB
testcase_37	AC	2 ms 5,248 KB
testcase_38	AC	2 ms 5,248 KB
testcase_39	AC	2 ms 5,248 KB
testcase_40	AC	2 ms 5,248 KB
testcase_41	AC	2 ms 5,248 KB
testcase_42	AC	2 ms 5,248 KB
testcase_43	AC	2 ms 5,248 KB
testcase_44	AC	2 ms 5,248 KB
testcase_45	AC	2 ms 5,248 KB
testcase_46	AC	2 ms 5,248 KB
testcase_47	AC	1 ms 5,248 KB
testcase_48	AC	1 ms 5,248 KB
testcase_49	AC	2 ms 5,248 KB
testcase_50	AC	2 ms 5,248 KB
testcase_51	AC	2 ms 5,248 KB
testcase_52	AC	2 ms 5,248 KB
testcase_53	AC	2 ms 5,248 KB
testcase_54	AC	2 ms 5,248 KB
testcase_55	AC	2 ms 5,248 KB
testcase_56	AC	2 ms 5,248 KB
testcase_57	AC	1 ms 5,248 KB
testcase_58	AC	2 ms 5,248 KB
testcase_59	AC	2 ms 5,248 KB
testcase_60	AC	2 ms 5,248 KB
testcase_61	AC	2 ms 5,248 KB
testcase_62	AC	2 ms 5,248 KB
testcase_63	AC	7 ms 5,248 KB
testcase_64	AC	2 ms 5,248 KB
testcase_65	AC	2 ms 5,248 KB
testcase_66	AC	2 ms 5,248 KB
testcase_67	AC	2 ms 5,248 KB
testcase_68	AC	2 ms 5,248 KB
testcase_69	AC	2 ms 5,248 KB
testcase_70	AC	2 ms 5,248 KB
testcase_71	AC	2 ms 5,248 KB
testcase_72	AC	2 ms 5,248 KB
testcase_73	AC	2 ms 5,248 KB
testcase_74	AC	2 ms 5,248 KB
testcase_75	AC	3 ms 5,248 KB
testcase_76	AC	4 ms 5,248 KB
testcase_77	AC	2 ms 5,248 KB
testcase_78	AC	2 ms 5,248 KB
testcase_79	AC	2 ms 5,248 KB
testcase_80	AC	8 ms 5,248 KB
testcase_81	AC	14 ms 5,248 KB
testcase_82	AC	2 ms 5,248 KB
testcase_83	AC	2 ms 5,248 KB
testcase_84	AC	22 ms 5,248 KB
testcase_85	AC	2 ms 5,248 KB
testcase_86	AC	28 ms 5,248 KB
testcase_87	AC	35 ms 5,248 KB
testcase_88	AC	2 ms 5,248 KB
testcase_89	AC	2 ms 5,248 KB
testcase_90	AC	65 ms 5,248 KB
testcase_91	AC	2 ms 5,248 KB
testcase_92	AC	2 ms 5,248 KB
testcase_93	AC	2 ms 5,248 KB
testcase_94	AC	2 ms 5,248 KB
testcase_95	AC	2 ms 5,248 KB
testcase_96	AC	6 ms 5,248 KB
testcase_97	AC	2 ms 5,248 KB
testcase_98	AC	2 ms 5,248 KB
testcase_99	AC	14 ms 5,248 KB
testcase_100	AC	17 ms 5,248 KB
testcase_101	AC	87 ms 5,248 KB
testcase_102	AC	2 ms 5,248 KB
testcase_103	AC	2 ms 5,248 KB
testcase_104	AC	2 ms 5,248 KB
testcase_105	AC	2 ms 5,248 KB
testcase_106	AC	21 ms 5,248 KB

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ソースコード

raw source code

#include "bits/stdc++.h"
using namespace std;
#ifdef _DEBUG
#include "dump.hpp"
#else
#define dump(...)
#endif

#define rep(i,a,b) for(int i=(a);i<(b);i++)
#define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--)
#define all(c) begin(c),end(c)
const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f;
const int MOD = 1'000'000'007;
template<class Interval> bool chmax(Interval &a, const Interval &b) { if (a < b) { a = b; return true; } return false; }
template<class Interval> bool chmin(Interval &a, const Interval &b) { if (b < a) { a = b; return true; } return false; }

struct BigInt {
	static const int kBase = 1000000000;
	static const int kBaseDigits = 9;
	vector<int> d;
	int sign;
	BigInt() :sign(1) {}
	BigInt(long long v) {
		sign = 1;
		if (v < 0)
			sign = -1, v = -v;
		for (; v > 0; v = v / kBase)
			d.emplace_back(v % kBase);
	}
	BigInt(const string &s) { read(s); }

	bool operator<(const BigInt &v)const {
		if (sign != v.sign)
			return sign < v.sign;
		if (d.size() != v.d.size())
			return d.size() * sign < v.d.size() * v.sign;
		for (int i = d.size() - 1; i >= 0; i--)
			if (d[i] != v.d[i])
				return d[i] * sign < v.d[i] * sign;
		return false;
	}
	bool operator>(const BigInt &v)const { return v < *this; }
	bool operator<=(const BigInt &v)const { return !(v < *this); }
	bool operator>=(const BigInt &v)const { return !(*this < v); }
	bool operator==(const BigInt &v)const { return !(*this < v) && !(v < *this); }
	bool operator!=(const BigInt &v)const { return !(*this == v); }

	BigInt &operator+=(const BigInt &v) {
		if (sign == v.sign) {
			BigInt res = v;
			for (int i = 0, carry = 0; i < (int)max(d.size(), v.d.size()) || carry; ++i) {
				if (i == (int)res.d.size())
					res.d.emplace_back(0);
				res.d[i] += carry + (i < (int)d.size() ? d[i] : 0);
				carry = res.d[i] >= kBase;
				if (carry)
					res.d[i] -= kBase;
			}
			return *this = res;
		}
		else
			return *this -= (-v);
	}
	BigInt &operator-=(const BigInt &v) {
		if (sign == v.sign) {
			BigInt tmp = abs();
			if (abs() >= v.abs()) {
				BigInt res = *this;
				for (int i = 0, carry = 0; i < (int)v.d.size() || carry; ++i) {
					res.d[i] -= carry + (i < (int)v.d.size() ? v.d[i] : 0);
					carry = res.d[i] < 0;
					if (carry)
						res.d[i] += kBase;
				}
				res.trim();
				return *this = res;
			}
			else
				return *this = -(v - *this);
		}
		else
			return *this += -v;
	}
	BigInt &operator*=(const BigInt &v) {
		return *this = *this * v;
	}
	BigInt &operator/=(const BigInt &v) {
		return *this = *this / v;
	}
	BigInt operator-()const {
		BigInt res = *this;
		res.sign = -sign;
		return res;
	}

	BigInt operator+(const BigInt &v)const { return BigInt(*this) += v; }
	BigInt operator-(const BigInt &v)const { return BigInt(*this) -= v; }
	BigInt operator*(int v)const {
		BigInt res = *this;
		res *= v;
		return res;
	}
	BigInt operator*(const BigInt &v)const {
		vector<int> a6 = convertBase(this->d, kBaseDigits, 6);
		vector<int> b6 = convertBase(v.d, kBaseDigits, 6);
		vll a(a6.begin(), a6.end());
		vll b(b6.begin(), b6.end());
		while (a.size() < b.size())
			a.emplace_back(0);
		while (b.size() < a.size())
			b.emplace_back(0);
		while (a.size() & (a.size() - 1))
			a.emplace_back(0), b.emplace_back(0);
		vll c = karatsubaMultiply(a, b);
		BigInt res;
		res.sign = sign * v.sign;
		for (int i = 0, carry = 0; i < (int)c.size(); i++) {
			long long cur = c[i] + carry;
			res.d.emplace_back((int)(cur % 1000000));
			carry = (int)(cur / 1000000);
		}
		res.d = convertBase(res.d, 6, kBaseDigits);
		res.trim();
		return res;
	}

	BigInt operator/(const BigInt &v)const { return divmod(*this, v).first; }
	BigInt operator/(int v)const {
		BigInt res = *this;
		res /= v;
		return res;
	}
	BigInt operator%(const BigInt &v)const {
		return divmod(*this, v).second;
	}
	int operator%(int v)const {
		if (v < 0)
			v = -v;
		int m = 0;
		for (int i = d.size() - 1; i >= 0; --i)
			m = (d[i] + m * (long long)kBase) % v;
		return m * sign;
	}

	BigInt &operator*=(int v) {
		if (v < 0)
			sign = -sign, v = -v;
		for (int i = 0, carry = 0; i < (int)d.size() || carry; ++i) {
			if (i == (int)d.size())
				d.emplace_back(0);
			long long cur = d[i] * (long long)v + carry;
			carry = (int)(cur / kBase);
			d[i] = (int)(cur % kBase);
		}
		trim();
		return *this;
	}
	BigInt &operator/=(int v) {
		if (v < 0)
			sign = -sign, v = -v;
		for (int i = (int)d.size() - 1, rem = 0; i >= 0; --i) {
			long long cur = d[i] + rem * (long long)kBase;
			d[i] = (int)(cur / v);
			rem = (int)(cur % v);
		}
		trim();
		return *this;
	}

	void read(const string &s) {
		sign = 1;
		d.clear();
		int pos = 0;
		while (pos < (int)s.size() && (s[pos] == '-' || s[pos] == '+')) {
			if (s[pos] == '-')
				sign = -sign;
			++pos;
		}
		for (int i = s.size() - 1; i >= pos; i -= kBaseDigits) {
			int x = 0;
			for (int j = max(pos, i - kBaseDigits + 1); j <= i; j++)
				x = x * 10 + s[j] - '0';
			d.emplace_back(x);
		}
		trim();
	}
	friend istream& operator >> (istream &stream, BigInt &v) {
		string s;
		stream >> s;
		v.read(s);
		return stream;
	}
	friend ostream& operator << (ostream &stream, const BigInt &v) {
		if (v.sign == -1)
			stream << '-';
		stream << (v.d.empty() ? 0 : v.d.back());
		for (int i = (int)v.d.size() - 2; i >= 0; --i)
			stream << setw(kBaseDigits) << setfill('0') << v.d[i];
		return stream;
	}

	long long toLongLong()const {
		long long res = 0;
		for (int i = d.size() - 1; i >= 0; i--)
			res = res * kBase + d[i];
		return res * sign;
	}
	string toString()const {
		ostringstream os;
		os << *this;
		return os.str();
	}


	static pair<BigInt, BigInt> divmod(const BigInt &a1, const BigInt &b1) {
		int norm = kBase / (b1.d.back() + 1);
		BigInt a = a1.abs() * norm;
		BigInt b = b1.abs() * norm;
		BigInt q, r;
		q.d.resize(a.d.size());

		for (int i = a.d.size() - 1; i >= 0; i--) {
			r *= kBase;
			r += a.d[i];
			int s1 = r.d.size() <= b.d.size() ? 0 : r.d[b.d.size()];
			int s2 = r.d.size() <= b.d.size() - 1 ? 0 : r.d[b.d.size() - 1];
			int d = ((long long)kBase * s1 + s2) / b.d.back();
			r -= b * d;
			while (r < 0)
				r += b, --d;
			q.d[i] = d;
		}

		q.sign = a1.sign * b1.sign;
		r.sign = a1.sign;
		q.trim();
		r.trim();
		return make_pair(q, r / norm);
	}
	void trim() {
		while (!d.empty() && !d.back())
			d.pop_back();
		if (d.empty())
			sign = 1;
	}
	bool isZero()const {
		return d.empty() || (d.size() == 1 && !d[0]);
	}

	BigInt abs()const {
		BigInt res = *this;
		res.sign *= res.sign;
		return res;
	}

	static vector<int> convertBase(const vector<int> &a, int old_digits, int new_digits) {
		vector<long long> p(max(old_digits, new_digits) + 1);
		p[0] = 1;
		for (int i = 1; i < (int)p.size(); i++)
			p[i] = p[i - 1] * 10;
		vector<int> res;
		long long cur = 0;
		int cur_digits = 0;
		for (int i = 0; i < (int)a.size(); i++) {
			cur += a[i] * p[cur_digits];
			cur_digits += old_digits;
			while (cur_digits >= new_digits) {
				res.emplace_back(int(cur % p[new_digits]));
				cur /= p[new_digits];
				cur_digits -= new_digits;
			}
		}
		res.emplace_back((int)cur);
		while (!res.empty() && !res.back())
			res.pop_back();
		return res;
	}

	using vll = vector<long long>;
	static vll karatsubaMultiply(const vll &a, const vll &b) {
		int n = a.size();
		vll res(n + n);
		if (n <= 32) {
			for (int i = 0; i < n; i++)
				for (int j = 0; j < n; j++)
					res[i + j] += a[i] * b[j];
			return res;
		}

		int k = n >> 1;
		vll a1(a.begin(), a.begin() + k);
		vll a2(a.begin() + k, a.end());
		vll b1(b.begin(), b.begin() + k);
		vll b2(b.begin() + k, b.end());

		vll a1b1 = karatsubaMultiply(a1, b1);
		vll a2b2 = karatsubaMultiply(a2, b2);

		for (int i = 0; i < k; i++)
			a2[i] += a1[i];
		for (int i = 0; i < k; i++)
			b2[i] += b1[i];

		vll r = karatsubaMultiply(a2, b2);
		for (int i = 0; i < (int)a1b1.size(); i++)
			r[i] -= a1b1[i];
		for (int i = 0; i < (int)a2b2.size(); i++)
			r[i] -= a2b2[i];

		for (int i = 0; i < (int)r.size(); i++)
			res[i + k] += r[i];
		for (int i = 0; i < (int)a1b1.size(); i++)
			res[i] += a1b1[i];
		for (int i = 0; i < (int)a2b2.size(); i++)
			res[i + n] += a2b2[i];
		return res;
	}

};

BigInt gcd(const BigInt &x, const BigInt &y) { return y.isZero() ? x : gcd(y, x % y); }
BigInt lcm(const BigInt &x, const BigInt &y) { return x / gcd(x, y) * y; }

// エラトステネスの篩
// O(n log log n)
// Verified: http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=3452809
vector<bool> eratos(int n) {
	vector<bool> is_prime(n + 1, true);
	is_prime[0] = is_prime[1] = false;
	for (int i = 2; i*i <= n; i++) {
		if (!is_prime[i])continue;
		for (int j = i * i; j <= n; j += i)
			is_prime[j] = false;
	}
	return is_prime;
}

// (a*b) % mod 
template<typename Int>
Int modmul(Int a, Int b, Int mod) {
	Int x = 0, y = a % mod;
	while (b > 0) {
		if (b % 2)x = x + y % mod;
		y = y * 2 % mod;
		b /= 2;
	}
	return x % mod;
}

// mod^2 が long long の最大値より大きければオーバーフローするので掛け算に modmul を使う
template<typename Int>
Int modpow(Int a, Int e, Int mod) {
	Int res = 1;
	while (e > 0) {
		if (e % 2)res = modmul(res, a, mod);
		a = modmul(a, a, mod);
		e /= 2;
	}
	dump(a, e, mod, res);
	return res;
}

// 素数判定（Miller-Rabin primality test）
// 2^24程度から
// 2^32以上を判定する場合は modpow で modmul を使う
// millerRabinPrimalityTest(n, 5)
template<typename Int>
bool millerRabinPrimalityTest(Int x, int iteration) {
	if (x < 2)return false;
	if (x != 2 && x % 2 == 0)return false;
	Int s = x - 1;
	dump(s);
	while (s % 2 == 0)s /= 2;
	dump(s);
	for (int i = 0; i < iteration; i++) {
		Int a = BigInt(rand()) % (x - 1) + 1, tmp = s;
		Int mod = modpow(a, tmp, x);
		while (tmp != x - 1 && mod != 1 && mod != x - 1) {
			mod = modmul(mod, mod, x);
			tmp *= 2;
			dump(tmp);
		}
		if (mod != x - 1 && tmp % 2 == 0)return false;
	}
	return true;
}

using Int = BigInt;
signed main() {
	cin.tie(0);
	ios::sync_with_stdio(false);

	Int n; cin >> n;
	if (n < 50) {
		int N = n.d[0];
		auto e = eratos(N);
		static const int di[] = { 1,0,-1,0 };
		static const int dj[] = { 0,1,0,-1 };
		using State = tuple<int, int, int>;
		rep(w, 1, N + 1) {
			dump(w);
			vector<bool> f(N + 1);
			int H = (N - 1) / w + 1, W = w;
			auto inrange = [&](int i, int j) { return i >= 0 && i < H && j >= 0 && j < W; };
			auto bfs = [&](int si, int sj, int gi, int gj) {
				queue<State> q;
				q.emplace(0, si, sj);
				while (q.size()) {
					int d, ci, cj; tie(d, ci, cj) = q.front(); q.pop();
					if (ci == gi && cj == gj)return d;
					rep(i, 0, 4) {
						int ni = ci + di[i], nj = cj + dj[i];
						int nx = ni * w + nj + 1;
						if (!inrange(ni, nj))continue;
						if (nx > N)continue;
						if (e[nx])continue;
						if (f[nx])continue;
						f[nx] = true;
						q.emplace(d + 1, ni, nj);
					}
				}
				return -1;
			};
			auto res = bfs(0, 0, (N - 1) / w, (N - 1) % w);
			dump(res);
			if (res != -1) {
				cout << w << endl;
				break;
			}
		}
	}
	else {
		dump(n);
		for (int w = 8;; w += 2) {
			if (millerRabinPrimalityTest(Int(1 + w), 5))continue;
			if (((n - 1) % w) == 0 && millerRabinPrimalityTest(n - w, 5))continue;
			cout << w << endl;
			break;
		}
	}
	return 0;
}

yukicoder

結果

テストケース

ソースコード