Luzhiled's Library

This documentation is automatically generated by competitive-verifier/competitive-verifier

View the Project on GitHub ei1333/library

:heavy_check_mark: test/verify/yosupo-sqrt-mod.test.cpp

Depends on

Code

// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/sqrt_mod

#include "../../template/template.hpp"

#include "../../math/combinatorics/mod-pow.hpp"
#include "../../math/combinatorics/mod-sqrt.hpp"

int main() {
  int T;
  cin >> T;
  while(T--) {
    int64_t Y, P;
    cin >> Y >> P;
    cout << mod_sqrt(Y, P) << endl;
  }
}
#line 1 "test/verify/yosupo-sqrt-mod.test.cpp"
// competitive-verifier: PROBLEM https://judge.yosupo.jp/problem/sqrt_mod

#line 1 "template/template.hpp"
#include <bits/stdc++.h>
#if __has_include(<atcoder/all>)
#include <atcoder/all>
#endif

using namespace std;

using int64 = long long;

const int64 infll = (1LL << 62) - 1;
const int inf = (1 << 30) - 1;

struct IoSetup {
  IoSetup() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);
    cerr << fixed << setprecision(10);
  }
} iosetup;

template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << p.first << " " << p.second;
  return os;
}

template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  for (int i = 0; i < (int)v.size(); i++) {
    os << v[i] << (i + 1 != v.size() ? " " : "");
  }
  return os;
}

template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (T &in : v) is >> in;
  return is;
}

template <typename T1, typename T2>
inline bool chmax(T1 &a, T2 b) {
  return a < b && (a = b, true);
}

template <typename T1, typename T2>
inline bool chmin(T1 &a, T2 b) {
  return a > b && (a = b, true);
}

template <typename T = int64>
vector<T> make_v(size_t a) {
  return vector<T>(a);
}

template <typename T, typename... Ts>
auto make_v(size_t a, Ts... ts) {
  return vector<decltype(make_v<T>(ts...))>(a, make_v<T>(ts...));
}

template <typename T, typename V>
typename enable_if<is_class<T>::value == 0>::type fill_v(T &t, const V &v) {
  t = v;
}

template <typename T, typename V>
typename enable_if<is_class<T>::value != 0>::type fill_v(T &t, const V &v) {
  for (auto &e : t) fill_v(e, v);
}

template <typename F>
struct FixPoint : F {
  explicit FixPoint(F &&f) : F(std::forward<F>(f)) {}

  template <typename... Args>
  decltype(auto) operator()(Args &&...args) const {
    return F::operator()(*this, std::forward<Args>(args)...);
  }
};

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{std::forward<F>(f)};
}
#line 4 "test/verify/yosupo-sqrt-mod.test.cpp"

#line 1 "math/combinatorics/mod-pow.hpp"
/**
 * @brief Mod Pow(べき乗)
 *
 */
template <typename T>
T mod_pow(T x, int64_t n, const T &p) {
  T ret = 1;
  while (n > 0) {
    if (n & 1) (ret *= x) %= p;
    (x *= x) %= p;
    n >>= 1;
  }
  return ret % p;
}
#line 1 "math/combinatorics/mod-sqrt.hpp"
/**
 * @brief Mod Sqrt
 */
template <typename T>
T mod_sqrt(const T &a, const T &p) {
  if (a == 0) return 0;
  if (p == 2) return a;
  if (mod_pow(a, (p - 1) >> 1, p) != 1) return -1;
  T b = 1;
  while (mod_pow(b, (p - 1) >> 1, p) == 1) ++b;
  T e = 0, m = p - 1;
  while (m % 2 == 0) m >>= 1, ++e;
  T x = mod_pow(a, (m - 1) >> 1, p);
  T y = a * (x * x % p) % p;
  (x *= a) %= p;
  T z = mod_pow(b, m, p);
  while (y != 1) {
    T j = 0, t = y;
    while (t != 1) {
      j += 1;
      (t *= t) %= p;
    }
    z = mod_pow(z, T(1) << (e - j - 1), p);
    (x *= z) %= p;
    (z *= z) %= p;
    (y *= z) %= p;
    e = j;
  }
  return x;
}
#line 7 "test/verify/yosupo-sqrt-mod.test.cpp"

int main() {
  int T;
  cin >> T;
  while(T--) {
    int64_t Y, P;
    cin >> Y >> P;
    cout << mod_sqrt(Y, P) << endl;
  }
}

Test cases

Env Name Status Elapsed Memory
g++ example_00 :heavy_check_mark: AC 6 ms 3 MB
g++ max_random_00 :heavy_check_mark: AC 148 ms 3 MB
g++ max_random_01 :heavy_check_mark: AC 147 ms 3 MB
g++ max_random_02 :heavy_check_mark: AC 136 ms 3 MB
g++ max_random_03 :heavy_check_mark: AC 151 ms 3 MB
g++ max_random_04 :heavy_check_mark: AC 147 ms 3 MB
g++ mod_998244353_00 :heavy_check_mark: AC 239 ms 3 MB
g++ mod_998244353_01 :heavy_check_mark: AC 209 ms 3 MB
g++ random_00 :heavy_check_mark: AC 29 ms 3 MB
g++ random_01 :heavy_check_mark: AC 36 ms 3 MB
g++ random_02 :heavy_check_mark: AC 109 ms 3 MB
g++ random_03 :heavy_check_mark: AC 40 ms 3 MB
g++ random_04 :heavy_check_mark: AC 134 ms 3 MB
clang++ example_00 :heavy_check_mark: AC 5 ms 3 MB
clang++ max_random_00 :heavy_check_mark: AC 135 ms 3 MB
clang++ max_random_01 :heavy_check_mark: AC 155 ms 3 MB
clang++ max_random_02 :heavy_check_mark: AC 152 ms 3 MB
clang++ max_random_03 :heavy_check_mark: AC 138 ms 3 MB
clang++ max_random_04 :heavy_check_mark: AC 147 ms 3 MB
clang++ mod_998244353_00 :heavy_check_mark: AC 182 ms 3 MB
clang++ mod_998244353_01 :heavy_check_mark: AC 189 ms 3 MB
clang++ random_00 :heavy_check_mark: AC 34 ms 3 MB
clang++ random_01 :heavy_check_mark: AC 36 ms 3 MB
clang++ random_02 :heavy_check_mark: AC 97 ms 3 MB
clang++ random_03 :heavy_check_mark: AC 49 ms 3 MB
clang++ random_04 :heavy_check_mark: AC 175 ms 3 MB
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