結果
| 問題 | No.308 素数は通れません |
| コンテスト | |
| ユーザー |
 minami
|
| 提出日時 | 2019-04-03 16:38:02 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 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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| ファイルパターン | 結果 |
|---|---|
| other | AC * 107 |
ソースコード
#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;
}