#426600 (C++17) No.3056 量子コンピュータで素因数分解 Easy

提出ソース
結果

問題	No.3056 量子コンピュータで素因数分解 Easy
ユーザー	👑 emthrm
提出日時	2020-02-06 02:23:14
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	TLE (最新) AC (最初)
実行時間	-
コード長	12,125 bytes
コンパイル時間	3,821 ms
コンパイル使用メモリ	233,412 KB
実行使用メモリ	36,220 KB
平均クエリ数	0.08
最終ジャッジ日時	2023-08-30 06:52:49
合計ジャッジ時間	7,541 ms
ジャッジサーバーID （参考情報）	judge15 / judge12
このコードへのチャレンジ
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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	44 ms 23,544 KB
testcase_01	TLE	-
testcase_02	--	-
testcase_03	--	-
testcase_04	--	-
testcase_05	--	-
testcase_06	--	-
testcase_07	--	-
testcase_08	--	-
testcase_09	--	-
testcase_10	--	-
testcase_11	--	-
testcase_12	--	-
testcase_13	--	-
testcase_14	--	-
testcase_15	--	-
testcase_16	--	-
testcase_17	--	-
testcase_18	--	-
testcase_19	--	-
testcase_20	--	-
testcase_21	--	-
testcase_22	--	-
testcase_23	--	-
testcase_24	--	-
testcase_25	--	-
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ソースコード

raw source code
#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
using namespace std;
#define FOR(i,m,n) for(int i=(m);i<(n);++i)
#define REP(i,n) FOR(i,0,n)
#define ALL(v) (v).begin(),(v).end()
using ll = long long;
template <typename T> using posteriority_queue = priority_queue<T, vector<T>, greater<T> >;
const int INF = 0x3f3f3f3f;
const ll LINF = 0x3f3f3f3f3f3f3f3fLL;
const double EPS = 1e-8;
const int MOD = 1000000007;
// const int MOD = 998244353;
const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1};
const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1};
template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; }
template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; }
template <typename T> void unique(vector<T> &a) { a.erase(unique(ALL(a)), a.end()); }
struct IOSetup {
  IOSetup() {
    cin.tie(nullptr);
    ios_base::sync_with_stdio(false);
    cout << fixed << setprecision(20);
  }
} iosetup;

// "base" must be a power of 10.
const int lg10_base = 9, base = static_cast<int>(round(pow(10, lg10_base)));
struct BigInt {
  int sign; vector<int> dat;
  BigInt(ll val = 0) { *this = val; }
  BigInt(const string &s) { *this = s; }
  vector<ll> convert_base(int new_lg10_base, ll new_base) const {
    // assert(new_base == static_cast<int>(round(pow(10, new_lg10_base))))
    int mx_base = max(lg10_base, new_lg10_base);
    vector<ll> p(mx_base + 1, 1);
    FOR(i, 1, mx_base + 1) p[i] = p[i - 1] * 10;
    vector<ll> res;
    ll now_val = 0;
    int now_lg10_base = 0;
    for (int e : dat) {
      now_val += p[now_lg10_base] * e;
      now_lg10_base += lg10_base;
      while (now_lg10_base >= new_lg10_base) {
        res.emplace_back(now_val % new_base);
        now_val /= new_base;
        now_lg10_base -= new_lg10_base;
      }
    }
    res.emplace_back(now_val);
    while (!res.empty() && res.back() == 0) res.pop_back();
    return res;
  }
  int digit_sum() {
    assert(sign == 1);
    string s = to_string();
    int res = 0;
    for (char c : s) res += c - '0';
    return res;
  }
  int length() {
    if (dat.empty()) return 1;
    int res = lg10_base * (dat.size() - 1);
    int tmp = dat.back();
    while (tmp > 0) { ++res; tmp /= 10; }
    return res;
  }
  BigInt pow(BigInt exponent) {
    BigInt res = 1, tmp = *this;
    while (exponent > 0) {
      if (exponent.dat[0] & 1) res *= tmp;
      tmp *= tmp;
      exponent /= 2;
    }
    return res;
  }
  ll to_llong() const {
    assert(*this >= LLONG_MIN && *this <= LLONG_MAX);
    ll res = 0;
    for (int i = static_cast<int>(dat.size()) - 1; i >= 0; --i) (res *= base) += dat[i];
    return res;
  }
  string to_string() { stringstream ss; ss << *this; string res; ss >> res; return res; }
  void trim() {
    while (!dat.empty() && dat.back() == 0) dat.pop_back();
    if (dat.empty()) sign = 1;
  }
  BigInt &operator=(ll val) {
    sign = 1;
    if (val < 0) { sign = -1; val *= -1;}
    dat.clear();
    for (; val > 0; val /= base) dat.emplace_back(val % base);
    return *this;
  }
  BigInt &operator=(const string &s) {
    sign = 1;
    dat.clear();
    if (!s.empty()) {
      int tail = 0;
      if (s[tail] == '-' || s[tail] == '+') {
        if (s[tail] == '-') sign = -1;
        ++tail;
      }
      for (int i = s.length() - 1; i >= tail; i -= lg10_base) {
        int val = 0;
        for (int j = max(tail, i - lg10_base + 1); j <= i; ++j) val = val * 10 + (s[j] - '0');
        dat.emplace_back(val);
      }
    }
    trim();
    return *this;
  }
  BigInt &operator=(const BigInt &x) {
    sign = x.sign;
    dat.resize(x.dat.size());
    copy(ALL(x.dat), dat.begin());
    return *this;
  }
  BigInt &operator+=(const BigInt &x) {
    if (sign == x.sign) {
      bool carry = false;
      for (int i = 0; i < max(dat.size(), x.dat.size()) || carry; ++i) {
        if (i == dat.size()) dat.emplace_back(0);
        dat[i] += (i < x.dat.size() ? x.dat[i] : 0) + carry;
        carry = dat[i] >= base;
        if (carry) dat[i] -= base;
      }
    } else {
      *this -= -x;
    }
    return *this;
  }
  BigInt &operator-=(const BigInt &x) {
    if (sign == x.sign) {
      BigInt abs_this = *this, abs_x = x;
      abs_this.sign = 1; abs_x.sign = 1;
      if (abs_this >= abs_x) {
        bool carry = false;
        for (int i = 0; i < dat.size() || carry; ++i) {
          dat[i] -= (i < x.dat.size() ? x.dat[i] : 0) + carry;
          carry = dat[i] < 0;
          if (carry) dat[i] += base;
        }
        trim();
      } else {
        *this = -(x - *this);
      }
    } else {
      *this += -x;
    }
    return *this;
  }
  BigInt &operator*=(const BigInt &x) {
    const int new_log10_base = 6, new_base = 1000000;
    vector<ll> this6 = convert_base(new_log10_base, new_base), x6 = x.convert_base(new_log10_base, new_base);
    vector<ll> res = karatsuba(this6, 0, this6.size(), x6, 0, x6.size());
    REP(i, res.size()) {
      ll quo = res[i] / new_base;
      if (quo > 0) {
        if (i + 1 == res.size()) res.emplace_back(0);
        res[i + 1] += quo;
      }
      res[i] %= new_base;
    }
    string s = (sign * x.sign == 1 ? "+" : "-");
    for (int i = static_cast<int>(res.size()) - 1; i >= 0; --i) {
      string tmp = std::to_string(res[i]);
      REP(_, new_log10_base - tmp.size()) s += '0';
      s += tmp;
    }
    return *this = s;
  }
  BigInt &operator/=(int x) { return *this = divide(x).first; }
  BigInt &operator/=(const BigInt &x) { return *this = divide(x).first; }
  BigInt &operator%=(int x) { return *this = divide(x).second; }
  BigInt &operator%=(const BigInt &x) { return *this = divide(x).second; }
  bool operator==(const BigInt &x) const {
    if (sign != x.sign || dat.size() != x.dat.size()) return false;
    int sz = dat.size();
    REP(i, sz) if (dat[i] != x.dat[i]) return false;
    return true;
  }
  bool operator!=(const BigInt &x) const { return !(*this == x); }
  bool operator<(const BigInt &x) const {
    if (sign != x.sign) return sign < x.sign;
    if (dat.size() != x.dat.size()) return sign * dat.size() < x.sign * x.dat.size();
    for (int i = static_cast<int>(dat.size()) - 1; i >= 0; --i) {
      if (dat[i] != x.dat[i]) return dat[i] * sign < x.dat[i] * x.sign;
    }
    return false;
  }
  bool operator<=(const BigInt &x) const { return !(x < *this); }
  bool operator>(const BigInt &x) const { return x < *this; }
  bool operator>=(const BigInt &x) const { return !(*this < x); }
  BigInt &operator++() { return *this += 1; }
  BigInt operator++(int) { BigInt res = *this; ++*this; return res; }
  BigInt &operator--() { return *this -= 1; }
  BigInt operator--(int) { BigInt res = *this; --*this; return res; }
  BigInt operator+() const { return *this; }
  BigInt operator-() const { BigInt res = *this; res.sign *= -1; return res; }
  BigInt operator+(const BigInt &x) const { return BigInt(*this) += x; }
  BigInt operator-(const BigInt &x) const { return BigInt(*this) -= x; }
  BigInt operator*(const BigInt &x) const { return BigInt(*this) *= x; }
  BigInt operator/(int x) const { return BigInt(*this) /= x; }
  BigInt operator/(const BigInt &x) const { return BigInt(*this) /= x; }
  BigInt operator%(int x) const { return BigInt(*this) %= x; }
  BigInt operator%(const BigInt &x) const { return BigInt(*this) %= x; }
  friend ostream &operator<<(ostream &os, const BigInt &x) {
    if (x.sign == -1) os << '-';
    os << (x.dat.empty() ? 0 : x.dat.back());
    for (int i = static_cast<int>(x.dat.size()) - 2; i >= 0; --i) os << setw(lg10_base) << setfill('0') << x.dat[i];
    return os;
  }
  friend istream &operator>>(istream &is, BigInt &x) { string s; is >> s; x = s; return is; }
private:
  vector<ll> karatsuba(vector<ll> &a, int a_l, int a_r, vector<ll> &b, int b_l, int b_r) {
    int a_len = a_r - a_l, b_len = b_r - b_l;
    if (a_len < b_len) return karatsuba(b, b_l, b_r, a, a_l, a_r);
    vector<ll> res(a_len + b_len, 0);
    if (b_len <= 32) {
      FOR(i, a_l, a_r) FOR(j, b_l, b_r) res[(i - a_l) + (j - b_l)] += a[i] * b[j];
    } else {
      int mid = (a_len + 1) / 2, n = min(a_len, mid);
      for (int i = a_l; i + mid < a_r; ++i) a[i] += a[i + mid];
      for (int i = b_l; i + mid < b_r; ++i) b[i] += b[i + mid];
      vector<ll> tmp = karatsuba(a, a_l, a_l + mid, b, b_l, b_l + n);
      REP(i, tmp.size()) res[mid + i] = tmp[i];
      for (int i = a_l; i + mid < a_r; ++i) a[i] -= a[i + mid];
      for (int i = b_l; i + mid < b_r; ++i) b[i] -= b[i + mid];
      tmp = karatsuba(a, a_l, a_l + mid, b, b_l, b_l + n);
      REP(i, tmp.size()) { res[i] += tmp[i]; res[mid + i] -= tmp[i]; }
      tmp = karatsuba(a, a_l + mid, a_r, b, b_l + n, b_r);
      REP(i, tmp.size()) { res[mid + i] -= tmp[i]; res[(mid << 1) + i] += tmp[i]; }
    }
    while (!res.empty() && res.back() == 0) res.pop_back();
    return res;
  }
  pair<BigInt, int> divide(int x) {
    // assert(!x.dat.empty());
    BigInt dividend = *this;
    if (x < 0) { dividend.sign *= -1; x *= -1; }
    ll rem = 0;
    for (int i = static_cast<int>(dividend.dat.size()) - 1; i >= 0; --i) {
      ll tmp = rem * base + dividend.dat[i];
      dividend.dat[i] = static_cast<int>(tmp / x);
      rem = tmp % x;
    }
    dividend.trim();
    return {dividend, static_cast<int>(rem)};
  }
  pair<BigInt, BigInt> divide(const BigInt &x) {
    // assert(!x.dat.empty());
    int k = base / (x.dat.back() + 1);
    BigInt dividend = *this, divisor = x;
    dividend.sign = 1; divisor.sign = 1;
    dividend *= k; divisor *= k;
    BigInt quo, rem = 0;
    quo.dat.resize(dividend.dat.size());
    int sz = divisor.dat.size();
    for (int i = static_cast<int>(dividend.dat.size()) - 1; i >= 0; --i) {
      rem.dat.insert(rem.dat.begin(), dividend.dat[i]);
      quo.dat[i] = static_cast<int>(((sz < rem.dat.size() ? 1LL * rem.dat[sz] * base : 0) + (sz - 1 < rem.dat.size() ? rem.dat[sz - 1] : 0)) / divisor.dat.back());
      rem -= divisor * quo.dat[i];
      while (rem.sign == -1) { rem += divisor; --quo.dat[i];  }
    }
    quo.sign = sign * x.sign; rem.sign = sign;
    quo.trim(); rem.trim();
    return {quo, rem / k};
  }
};
BigInt __gcd(BigInt a, BigInt b) { while (!b.dat.empty()) swap(a %= b, b); return a; }
BigInt __lcm(const BigInt &a, const BigInt &b) { return a / __gcd(a, b) * b; }
BigInt abs(const BigInt &x) { BigInt res = x; res.sign = 1; return res; }
BigInt max(const BigInt &a, const BigInt &b) { return a < b ? b : a; }
BigInt min(const BigInt &a, const BigInt &b) { return a < b ? a : b; }

struct Xor128 {
  int rand() {
    unsigned t = x ^ (x << 11);
    x = y; y = z; z = w; w = (w ^ (w >> 19)) ^ (t ^ (t >> 8));
    return static_cast<int>(w);
  }
  int rand(int ub) {
    int res = rand() % ub;
    return (res < 0 ? res + ub : res);
  }
  int rand(int lb, int ub) { return lb + rand(ub - lb); }
  ll randll() {
    unsigned long long res = static_cast<unsigned long long>(rand()) << 32;
    return static_cast<ll>(res | rand());
  }
  ll randll(ll ub) {
    ll res = randll() % ub;
    return (res < 0 ? res + ub : res);
  }
  ll randll(ll lb, ll ub) { return lb + rand(ub - lb); }
private:
  unsigned x = 123456789, y = 362436069, z = 521288629, w = static_cast<unsigned>(time(nullptr));
} xor128;

BigInt mod_pow(BigInt base, BigInt exponent, BigInt md) {
  BigInt res = 1;
  while (exponent > 0) {
    if (exponent % 2 == 1) (res *= base) %= md;
    (base *= base) %= md;
    exponent /= 2;
  }
  return res;
}

// https://core.ac.uk/download/pdf/35426875.pdf
int main() {
  BigInt n; cin >> n;
  int p = 0;
  BigInt tmp = 1;
  for (; tmp < n; ++p) tmp *= 2;
  BigInt a, r;
  while (true) {
    string s = "";
    REP(_, p) s += '0' + xor128.rand(2);
    a = s;
    if (a >= n) continue;
    if (BigInt g = __gcd(a, n); g > 1) {
      cout << g << ' ' << n / g << endl;
      return 0;
    }
    cout << "? " << a << endl;
    cin >> r;
    if (r % 2 == 0) {
      tmp = mod_pow(a, r / 2, n);
      BigInt p = __gcd(tmp + 1, n), q = __gcd(tmp == 0 ? n - 1 : tmp - 1, n);
      if (p == n || q == n) continue;
      cout << "! " << p << ' ' << q << endl;
      return 0;
    }
  }
}
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結果

テストケース

ソースコード
