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

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• Last update: 2024-05-01 23:44:47+09:00
• Problem: https://judge.yosupo.jp/problem/sqrt_mod

Depends on

• Mod Pow(べき乗) (math/combinatorics/mod-pow.hpp)
• Mod Sqrt (math/combinatorics/mod-sqrt.hpp)
• template/template.hpp

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>

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(forward<F>(f)) {}

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

template <typename F>
inline decltype(auto) MFP(F &&f) {
  return FixPoint<F>{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	AC	6 ms	4 MB
g++	max_random_00	AC	185 ms	4 MB
g++	max_random_01	AC	197 ms	4 MB
g++	max_random_02	AC	147 ms	4 MB
g++	max_random_03	AC	150 ms	4 MB
g++	max_random_04	AC	180 ms	4 MB
g++	mod_998244353_00	AC	265 ms	4 MB
g++	mod_998244353_01	AC	206 ms	4 MB
g++	random_00	AC	33 ms	4 MB
g++	random_01	AC	37 ms	4 MB
g++	random_02	AC	136 ms	4 MB
g++	random_03	AC	44 ms	4 MB
g++	random_04	AC	171 ms	4 MB
clang++	example_00	AC	6 ms	4 MB
clang++	max_random_00	AC	154 ms	4 MB
clang++	max_random_01	AC	149 ms	4 MB
clang++	max_random_02	AC	218 ms	4 MB
clang++	max_random_03	AC	180 ms	4 MB
clang++	max_random_04	AC	189 ms	4 MB
clang++	mod_998244353_00	AC	282 ms	4 MB
clang++	mod_998244353_01	AC	225 ms	4 MB
clang++	random_00	AC	34 ms	4 MB
clang++	random_01	AC	49 ms	4 MB
clang++	random_02	AC	98 ms	4 MB
clang++	random_03	AC	48 ms	4 MB
clang++	random_04	AC	190 ms	4 MB

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