結果
問題 | No.2074 Product is Square ? |
ユーザー | ruthen |
提出日時 | 2022-09-16 23:04:18 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 168 ms / 2,000 ms |
コード長 | 11,156 bytes |
コンパイル時間 | 3,199 ms |
コンパイル使用メモリ | 238,228 KB |
実行使用メモリ | 6,944 KB |
最終ジャッジ日時 | 2024-06-01 13:59:00 |
合計ジャッジ時間 | 5,960 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge3 |
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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
6,812 KB |
testcase_01 | AC | 40 ms
6,940 KB |
testcase_02 | AC | 38 ms
6,940 KB |
testcase_03 | AC | 40 ms
6,944 KB |
testcase_04 | AC | 40 ms
6,940 KB |
testcase_05 | AC | 39 ms
6,940 KB |
testcase_06 | AC | 41 ms
6,940 KB |
testcase_07 | AC | 40 ms
6,940 KB |
testcase_08 | AC | 40 ms
6,944 KB |
testcase_09 | AC | 40 ms
6,940 KB |
testcase_10 | AC | 39 ms
6,944 KB |
testcase_11 | AC | 15 ms
6,940 KB |
testcase_12 | AC | 43 ms
6,944 KB |
testcase_13 | AC | 162 ms
6,940 KB |
testcase_14 | AC | 29 ms
6,944 KB |
testcase_15 | AC | 15 ms
6,944 KB |
testcase_16 | AC | 41 ms
6,940 KB |
testcase_17 | AC | 168 ms
6,944 KB |
testcase_18 | AC | 30 ms
6,940 KB |
testcase_19 | AC | 15 ms
6,940 KB |
testcase_20 | AC | 43 ms
6,940 KB |
testcase_21 | AC | 160 ms
6,944 KB |
testcase_22 | AC | 27 ms
6,940 KB |
testcase_23 | AC | 16 ms
6,940 KB |
testcase_24 | AC | 44 ms
6,940 KB |
testcase_25 | AC | 162 ms
6,944 KB |
testcase_26 | AC | 29 ms
6,944 KB |
testcase_27 | AC | 15 ms
6,940 KB |
testcase_28 | AC | 46 ms
6,940 KB |
testcase_29 | AC | 161 ms
6,944 KB |
testcase_30 | AC | 28 ms
6,940 KB |
testcase_31 | AC | 6 ms
6,944 KB |
testcase_32 | AC | 2 ms
6,940 KB |
testcase_33 | AC | 3 ms
6,944 KB |
ソースコード
#include <bits/stdc++.h> using namespace std; #ifdef _RUTHEN #include <debug.hpp> #else #define show(...) true #endif using ll = long long; #define rep(i, n) for (int i = 0; i < (n); i++) template <class T> using V = vector<T>; #line 2 "prime/fast-factorize.hpp" #line 2 "inner/inner_math.hpp" namespace inner { using i32 = int32_t; using u32 = uint32_t; using i64 = int64_t; using u64 = uint64_t; template <typename T> T gcd(T a, T b) { while (b) swap(a %= b, b); return a; } template <typename T> T inv(T a, T p) { T b = p, x = 1, y = 0; while (a) { T q = b / a; swap(a, b %= a); swap(x, y -= q * x); } assert(b == 1); return y < 0 ? y + p : y; } template <typename T, typename U> T modpow(T a, U n, T p) { T ret = 1 % p; for (; n; n >>= 1, a = U(a) * a % p) if (n & 1) ret = U(ret) * a % p; return ret; } } // namespace inner #line 2 "misc/rng.hpp" namespace my_rand { using i64 = long long; using u64 = unsigned long long; // [0, 2^64 - 1) u64 rng() { static u64 _x = u64(chrono::duration_cast<chrono::nanoseconds>(chrono::high_resolution_clock::now().time_since_epoch()).count()) * 10150724397891781847ULL; _x ^= _x << 7; return _x ^= _x >> 9; } // [l, r] i64 rng(i64 l, i64 r) { assert(l <= r); return l + rng() % (r - l + 1); } // [l, r) i64 randint(i64 l, i64 r) { assert(l < r); return l + rng() % (r - l); } // choose n numbers from [l, r) without overlapping vector<i64> randset(i64 l, i64 r, i64 n) { assert(l <= r && n <= r - l); unordered_set<i64> s; for (i64 i = n; i; --i) { i64 m = randint(l, r + 1 - i); if (s.find(m) != s.end()) m = r - i; s.insert(m); } vector<i64> ret; for (auto &x : s) ret.push_back(x); return ret; } // [0.0, 1.0) double rnd() { return rng() * 5.42101086242752217004e-20; } template <typename T> void randshf(vector<T> &v) { int n = v.size(); for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]); } } // namespace my_rand using my_rand::randint; using my_rand::randset; using my_rand::randshf; using my_rand::rnd; using my_rand::rng; #line 2 "modint/arbitrary-prime-modint.hpp" struct ArbitraryLazyMontgomeryModInt { using mint = ArbitraryLazyMontgomeryModInt; using i32 = int32_t; using u32 = uint32_t; using u64 = uint64_t; static u32 mod; static u32 r; static u32 n2; static u32 get_r() { u32 ret = mod; for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret; return ret; } static void set_mod(u32 m) { assert(m < (1 << 30)); assert((m & 1) == 1); mod = m; n2 = -u64(m) % m; r = get_r(); assert(r * mod == 1); } u32 a; ArbitraryLazyMontgomeryModInt() : a(0) {} ArbitraryLazyMontgomeryModInt(const int64_t &b) : a(reduce(u64(b % mod + mod) * n2)){}; static u32 reduce(const u64 &b) { return (b + u64(u32(b) * u32(-r)) * mod) >> 32; } mint &operator+=(const mint &b) { if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } mint &operator-=(const mint &b) { if (i32(a -= b.a) < 0) a += 2 * mod; return *this; } mint &operator*=(const mint &b) { a = reduce(u64(a) * b.a); return *this; } mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } mint operator+(const mint &b) const { return mint(*this) += b; } mint operator-(const mint &b) const { return mint(*this) -= b; } mint operator*(const mint &b) const { return mint(*this) *= b; } mint operator/(const mint &b) const { return mint(*this) /= b; } bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } mint operator-() const { return mint() - mint(*this); } mint pow(u64 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = ArbitraryLazyMontgomeryModInt(t); return (is); } mint inverse() const { return pow(mod - 2); } u32 get() const { u32 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static u32 get_mod() { return mod; } }; typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::mod; typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::r; typename ArbitraryLazyMontgomeryModInt::u32 ArbitraryLazyMontgomeryModInt::n2; #line 2 "modint/modint-montgomery64.hpp" struct montgomery64 { using mint = montgomery64; using i64 = int64_t; using u64 = uint64_t; using u128 = __uint128_t; static u64 mod; static u64 r; static u64 n2; static u64 get_r() { u64 ret = mod; for (i64 i = 0; i < 5; ++i) ret *= 2 - mod * ret; return ret; } static void set_mod(u64 m) { assert(m < (1LL << 62)); assert((m & 1) == 1); mod = m; n2 = -u128(m) % m; r = get_r(); assert(r * mod == 1); } u64 a; montgomery64() : a(0) {} montgomery64(const int64_t &b) : a(reduce((u128(b) + mod) * n2)){}; static u64 reduce(const u128 &b) { return (b + u128(u64(b) * u64(-r)) * mod) >> 64; } mint &operator+=(const mint &b) { if (i64(a += b.a - 2 * mod) < 0) a += 2 * mod; return *this; } mint &operator-=(const mint &b) { if (i64(a -= b.a) < 0) a += 2 * mod; return *this; } mint &operator*=(const mint &b) { a = reduce(u128(a) * b.a); return *this; } mint &operator/=(const mint &b) { *this *= b.inverse(); return *this; } mint operator+(const mint &b) const { return mint(*this) += b; } mint operator-(const mint &b) const { return mint(*this) -= b; } mint operator*(const mint &b) const { return mint(*this) *= b; } mint operator/(const mint &b) const { return mint(*this) /= b; } bool operator==(const mint &b) const { return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a); } bool operator!=(const mint &b) const { return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a); } mint operator-() const { return mint() - mint(*this); } mint pow(u128 n) const { mint ret(1), mul(*this); while (n > 0) { if (n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } friend ostream &operator<<(ostream &os, const mint &b) { return os << b.get(); } friend istream &operator>>(istream &is, mint &b) { int64_t t; is >> t; b = montgomery64(t); return (is); } mint inverse() const { return pow(mod - 2); } u64 get() const { u64 ret = reduce(a); return ret >= mod ? ret - mod : ret; } static u64 get_mod() { return mod; } }; typename montgomery64::u64 montgomery64::mod, montgomery64::r, montgomery64::n2; #line 7 "prime/fast-factorize.hpp" namespace fast_factorize { using u64 = uint64_t; template <typename mint> bool miller_rabin(u64 n, vector<u64> as) { if (mint::get_mod() != n) mint::set_mod(n); u64 d = n - 1; while (~d & 1) d >>= 1; mint e{1}, rev{int64_t(n - 1)}; for (u64 a : as) { if (n <= a) break; u64 t = d; mint y = mint(a).pow(t); while (t != n - 1 && y != e && y != rev) { y *= y; t *= 2; } if (y != rev && t % 2 == 0) return false; } return true; } bool is_prime(u64 n) { if (~n & 1) return n == 2; if (n <= 1) return false; if (n < (1LL << 30)) return miller_rabin<ArbitraryLazyMontgomeryModInt>(n, {2, 7, 61}); else return miller_rabin<montgomery64>(n, {2, 325, 9375, 28178, 450775, 9780504, 1795265022}); } template <typename mint, typename T> T pollard_rho(T n) { if (~n & 1) return 2; if (is_prime(n)) return n; if (mint::get_mod() != n) mint::set_mod(n); mint R, one = 1; auto f = [&](mint x) { return x * x + R; }; auto rnd_ = [&]() { return rng() % (n - 2) + 2; }; while (1) { mint x, y, ys, q = one; R = rnd_(), y = rnd_(); T g = 1; constexpr int m = 128; for (int r = 1; g == 1; r <<= 1) { x = y; for (int i = 0; i < r; ++i) y = f(y); for (int k = 0; g == 1 && k < r; k += m) { ys = y; for (int i = 0; i < m && i < r - k; ++i) q *= x - (y = f(y)); g = inner::gcd<T>(q.get(), n); } } if (g == n) do g = inner::gcd<T>((x - (ys = f(ys))).get(), n); while (g == 1); if (g != n) return g; } exit(1); } using i64 = long long; vector<i64> inner_factorize(u64 n) { if (n <= 1) return {}; u64 p; if (n <= (1LL << 30)) p = pollard_rho<ArbitraryLazyMontgomeryModInt, uint32_t>(n); else p = pollard_rho<montgomery64, uint64_t>(n); if (p == n) return {i64(p)}; auto l = inner_factorize(p); auto r = inner_factorize(n / p); copy(begin(r), end(r), back_inserter(l)); return l; } vector<i64> factorize(u64 n) { auto ret = inner_factorize(n); sort(begin(ret), end(ret)); return ret; } map<i64, i64> factor_count(u64 n) { map<i64, i64> mp; for (auto &x : factorize(n)) mp[x]++; return mp; } vector<i64> divisors(u64 n) { if (n == 0) return {}; vector<pair<i64, i64>> v; for (auto &p : factorize(n)) { if (v.empty() || v.back().first != p) { v.emplace_back(p, 1); } else { v.back().second++; } } vector<i64> ret; auto f = [&](auto rc, int i, i64 x) -> void { if (i == (int)v.size()) { ret.push_back(x); return; } for (int j = v[i].second;; --j) { rc(rc, i + 1, x); if (j == 0) break; x *= v[i].first; } }; f(f, 0, 1); sort(begin(ret), end(ret)); return ret; } } // namespace fast_factorize using fast_factorize::divisors; using fast_factorize::factor_count; using fast_factorize::factorize; using fast_factorize::is_prime; /** * @brief 高速素因数分解(Miller Rabin/Pollard's Rho) * @docs docs/prime/fast-factorize.md */ void solve() { int N; cin >> N; V<ll> A(N); rep(i, N) cin >> A[i]; map<ll, int> mp; rep(i, N) { auto p = factorize(A[i]); for (auto &pi : p) mp[pi] ^= 1; } int ans = 0; for (auto a : mp) ans += a.second; cout << (ans == 0 ? "Yes" : "No") << '\n'; } int main() { ios::sync_with_stdio(false); cin.tie(0); int tt; cin >> tt; while (tt--) solve(); return 0; }