#798654 (C++23) No.2074 Product is Square ?

提出ソース

結果

問題	No.2074 Product is Square ?
ユーザー	hitonanode
提出日時	2022-09-17 12:56:45
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,613 ms / 2,000 ms
コード長	10,389 bytes
コンパイル時間	2,318 ms
コンパイル使用メモリ	191,328 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-06-01 15:05:54
合計ジャッジ時間	17,183 ms
ジャッジサーバーID （参考情報）	judge3 / judge2

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	2 ms 5,248 KB
testcase_01	AC	310 ms 5,248 KB
testcase_02	AC	303 ms 5,376 KB
testcase_03	AC	303 ms 5,376 KB
testcase_04	AC	295 ms 5,376 KB
testcase_05	AC	324 ms 5,376 KB
testcase_06	AC	323 ms 5,376 KB
testcase_07	AC	327 ms 5,376 KB
testcase_08	AC	295 ms 5,376 KB
testcase_09	AC	290 ms 5,376 KB
testcase_10	AC	291 ms 5,376 KB
testcase_11	AC	55 ms 5,376 KB
testcase_12	AC	275 ms 5,376 KB
testcase_13	AC	1,613 ms 5,376 KB
testcase_14	AC	144 ms 5,376 KB
testcase_15	AC	54 ms 5,376 KB
testcase_16	AC	286 ms 5,376 KB
testcase_17	AC	1,593 ms 5,376 KB
testcase_18	AC	185 ms 5,376 KB
testcase_19	AC	54 ms 5,376 KB
testcase_20	AC	283 ms 5,376 KB
testcase_21	AC	1,521 ms 5,376 KB
testcase_22	AC	155 ms 5,376 KB
testcase_23	AC	54 ms 5,376 KB
testcase_24	AC	317 ms 5,376 KB
testcase_25	AC	1,574 ms 5,376 KB
testcase_26	AC	157 ms 5,376 KB
testcase_27	AC	51 ms 5,376 KB
testcase_28	AC	298 ms 5,376 KB
testcase_29	AC	1,591 ms 5,376 KB
testcase_30	AC	168 ms 5,376 KB
testcase_31	AC	29 ms 5,376 KB
testcase_32	AC	2 ms 5,376 KB
testcase_33	AC	3 ms 5,376 KB

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ソースコード

raw source code

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <deque>
#include <forward_list>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iostream>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <tuple>
#include <type_traits>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
using namespace std;
using lint = long long;
using pint = pair<int, int>;
using plint = pair<lint, lint>;
struct fast_ios { fast_ios(){ cin.tie(nullptr), ios::sync_with_stdio(false), cout << fixed << setprecision(20); }; } fast_ios_;
#define ALL(x) (x).begin(), (x).end()
#define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++)
#define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--)
#define REP(i, n) FOR(i,0,n)
#define IREP(i, n) IFOR(i,0,n)
template <typename T, typename V>
void ndarray(vector<T>& vec, const V& val, int len) { vec.assign(len, val); }
template <typename T, typename V, typename... Args> void ndarray(vector<T>& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); }
template <typename T> bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; }
template <typename T> bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; }
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class T> int arglb(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); }
template <class T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); }
template <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);

template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
#if __cplusplus >= 201703L
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
#endif
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
#ifdef HITONANODE_LOCAL
const string COLOR_RESET = "\033[0m", BRIGHT_GREEN = "\033[1;32m", BRIGHT_RED = "\033[1;31m", BRIGHT_CYAN = "\033[1;36m", NORMAL_CROSSED = "\033[0;9;37m", RED_BACKGROUND = "\033[1;41m", NORMAL_FAINT = "\033[0;2m";
#define dbg(x) std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl
#define dbgif(cond, x) ((cond) ? std::cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << std::endl : std::cerr)
#else
#define dbg(x) ((void)0)
#define dbgif(cond, x) ((void)0)
#endif

namespace SPRP {
// http://miller-rabin.appspot.com/
const std::vector<std::vector<__int128>> bases{
    {126401071349994536},                              // < 291831
    {336781006125, 9639812373923155},                  // < 1050535501 (1e9)
    {2, 2570940, 211991001, 3749873356},               // < 47636622961201 (4e13)
    {2, 325, 9375, 28178, 450775, 9780504, 1795265022} // <= 2^64
};
inline int get_id(long long n) {
    if (n < 291831) {
        return 0;
    } else if (n < 1050535501) {
        return 1;
    } else if (n < 47636622961201)
        return 2;
    else {
        return 3;
    }
}
} // namespace SPRP

// Miller-Rabin primality test
// https://ja.wikipedia.org/wiki/%E3%83%9F%E3%83%A9%E3%83%BC%E2%80%93%E3%83%A9%E3%83%93%E3%83%B3%E7%B4%A0%E6%95%B0%E5%88%A4%E5%AE%9A%E6%B3%95
// Complexity: O(lg n) per query
struct {
    long long modpow(__int128 x, __int128 n, long long mod) noexcept {
        __int128 ret = 1;
        for (x %= mod; n; x = x * x % mod, n >>= 1) ret = (n & 1) ? ret * x % mod : ret;
        return ret;
    }
    bool operator()(long long n) noexcept {
        if (n < 2) return false;
        if (n % 2 == 0) return n == 2;
        int s = __builtin_ctzll(n - 1);

        for (__int128 a : SPRP::bases[SPRP::get_id(n)]) {
            if (a % n == 0) continue;
            a = modpow(a, (n - 1) >> s, n);
            bool may_composite = true;
            if (a == 1) continue;
            for (int r = s; r--; a = a * a % n) {
                if (a == n - 1) may_composite = false;
            }
            if (may_composite) return false;
        }
        return true;
    }
} is_prime;

struct {
    // Pollard's rho algorithm: find factor greater than 1
    long long find_factor(long long n) {
        assert(n > 1);
        if (n % 2 == 0) return 2;
        if (is_prime(n)) return n;
        long long c = 1;
        auto f = [&](__int128 x) -> long long { return (x * x + c) % n; };

        for (int t = 1;; t++) {
            long long x0 = t, m = std::max(n >> 3, 1LL), x, ys, y = x0, r = 1, g, q = 1;
            do {
                x = y;
                for (int i = r; i--;) y = f(y);
                long long k = 0;
                do {
                    ys = y;
                    for (int i = std::min(m, r - k); i--;)
                        y = f(y), q = __int128(q) * std::abs(x - y) % n;
                    g = std::__gcd<long long>(q, n);
                    k += m;
                } while (k < r and g <= 1);
                r <<= 1;
            } while (g <= 1);
            if (g == n) {
                do {
                    ys = f(ys);
                    g = std::__gcd(std::abs(x - ys), n);
                } while (g <= 1);
            }
            if (g != n) return g;
        }
    }

    std::vector<long long> operator()(long long n) {
        std::vector<long long> ret;
        while (n > 1) {
            long long f = find_factor(n);
            if (f < n) {
                auto tmp = operator()(f);
                ret.insert(ret.end(), tmp.begin(), tmp.end());
            } else
                ret.push_back(n);
            n /= f;
        }
        std::sort(ret.begin(), ret.end());
        return ret;
    }
} FactorizeLonglong;

bool solve() {
    int N;
    cin >> N;
    set<lint> s;
    while (N--) {
        lint a;
        cin >> a;
        for (lint p : FactorizeLonglong(a)) {
            if (s.count(p)) {
                s.erase(p);
            } else {
                s.insert(p);
            }
        }
    }
    return s.empty();
}

int main() {
    int T;
    cin >> T;
    while (T--) {
        cout << (solve() ? "Yes" : "No") << endl;
    }
}

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結果

テストケース

ソースコード