#833033 (C++23) No.2192 平方数の下１４桁

提出ソース

結果

問題	No.2192 平方数の下１４桁
ユーザー	hitonanode
提出日時	2023-01-13 23:14:03
言語	C++23 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	114 ms / 2,000 ms
コード長	17,493 bytes
コンパイル時間	2,173 ms
コンパイル使用メモリ	192,784 KB
実行使用メモリ	46,988 KB
最終ジャッジ日時	2024-06-07 00:05:51
合計ジャッジ時間	6,846 ms
ジャッジサーバーID （参考情報）	judge1 / judge3

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	78 ms 46,860 KB
testcase_01	AC	80 ms 46,772 KB
testcase_02	AC	81 ms 46,856 KB
testcase_03	AC	114 ms 46,856 KB
testcase_04	AC	86 ms 46,988 KB
testcase_05	AC	82 ms 46,860 KB
testcase_06	AC	84 ms 46,860 KB
testcase_07	AC	86 ms 46,852 KB
testcase_08	AC	84 ms 46,984 KB
testcase_09	AC	84 ms 46,988 KB
testcase_10	AC	89 ms 46,860 KB
testcase_11	AC	89 ms 46,860 KB
testcase_12	AC	91 ms 46,984 KB
testcase_13	AC	87 ms 46,856 KB
testcase_14	AC	87 ms 46,840 KB
testcase_15	AC	87 ms 46,984 KB
testcase_16	AC	83 ms 46,736 KB
testcase_17	AC	83 ms 46,856 KB
testcase_18	AC	77 ms 46,984 KB
testcase_19	AC	80 ms 46,988 KB
testcase_20	AC	96 ms 46,860 KB
testcase_21	AC	99 ms 46,772 KB
testcase_22	AC	88 ms 46,852 KB
testcase_23	AC	86 ms 46,984 KB
testcase_24	AC	84 ms 46,856 KB
testcase_25	AC	82 ms 46,764 KB
testcase_26	AC	86 ms 46,860 KB
testcase_27	AC	81 ms 46,856 KB
testcase_28	AC	78 ms 46,980 KB
testcase_29	AC	78 ms 46,988 KB
testcase_30	AC	80 ms 46,984 KB
testcase_31	AC	78 ms 46,732 KB
testcase_32	AC	84 ms 46,980 KB
testcase_33	AC	79 ms 46,852 KB
testcase_34	AC	81 ms 46,856 KB
testcase_35	AC	78 ms 46,856 KB
testcase_36	AC	77 ms 46,728 KB
testcase_37	AC	77 ms 46,856 KB
testcase_38	AC	78 ms 46,860 KB
testcase_39	AC	82 ms 46,984 KB
testcase_40	AC	90 ms 46,988 KB
testcase_41	AC	88 ms 46,860 KB
testcase_42	AC	85 ms 46,856 KB
testcase_43	AC	85 ms 46,856 KB

権限があれば一括ダウンロードができます

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; }
const std::vector<std::pair<int, int>> grid_dxs{{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); }
template <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
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; }
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 << ')'; }
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

#include <iostream>
#include <set>
#include <vector>

using lint = __int128;

struct ModIntRuntime {
private:
    static lint md;

public:
    // using lint = long long;
    static lint mod() { return md; }
    lint val_;
    static std::vector<ModIntRuntime> &facs() {
        static std::vector<ModIntRuntime> facs_;
        return facs_;
    }
    static lint &get_primitive_root() {
        static lint primitive_root_ = 0;
        if (!primitive_root_) {
            primitive_root_ = [&]() {
                std::set<lint> fac;
                lint v = md - 1;
                for (lint i = 2; i * i <= v; i++)
                    while (v % i == 0) fac.insert(i), v /= i;
                if (v > 1) fac.insert(v);
                for (lint g = 1; g < md; g++) {
                    bool ok = true;
                    for (auto i : fac)
                        if (ModIntRuntime(g).power((md - 1) / i) == 1) {
                            ok = false;
                            break;
                        }
                    if (ok) return g;
                }
                return (lint)-1;
            }();
        }
        return primitive_root_;
    }
    static void set_mod(const lint &m) {
        if (md != m) facs().clear();
        md = m;
        get_primitive_root() = 0;
    }
    ModIntRuntime &_setval(lint v) {
        val_ = (v >= md ? v - md : v);
        return *this;
    }
    lint val() const noexcept { return val_; }
    ModIntRuntime() : val_(0) {}
    ModIntRuntime(lint v) { _setval(v % md + md); }
    explicit operator bool() const { return val_ != 0; }
    ModIntRuntime operator+(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ + x.val_);
    }
    ModIntRuntime operator-(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ - x.val_ + md);
    }
    ModIntRuntime operator*(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ * x.val_ % md);
    }
    ModIntRuntime operator/(const ModIntRuntime &x) const {
        return ModIntRuntime()._setval((lint)val_ * x.inv().val() % md);
    }
    ModIntRuntime operator-() const { return ModIntRuntime()._setval(md - val_); }
    ModIntRuntime &operator+=(const ModIntRuntime &x) { return *this = *this + x; }
    ModIntRuntime &operator-=(const ModIntRuntime &x) { return *this = *this - x; }
    ModIntRuntime &operator*=(const ModIntRuntime &x) { return *this = *this * x; }
    ModIntRuntime &operator/=(const ModIntRuntime &x) { return *this = *this / x; }
    friend ModIntRuntime operator+(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md + x.val_);
    }
    friend ModIntRuntime operator-(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md - x.val_ + md);
    }
    friend ModIntRuntime operator*(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md * x.val_ % md);
    }
    friend ModIntRuntime operator/(lint a, const ModIntRuntime &x) {
        return ModIntRuntime()._setval(a % md * x.inv().val() % md);
    }
    bool operator==(const ModIntRuntime &x) const { return val_ == x.val_; }
    bool operator!=(const ModIntRuntime &x) const { return val_ != x.val_; }
    bool operator<(const ModIntRuntime &x) const {
        return val_ < x.val_;
    } // To use std::map<ModIntRuntime, T>

    lint power(lint n) const {
        lint ans = 1, tmp = this->val_;
        while (n) {
            if (n & 1) ans = ans * tmp % md;
            tmp = tmp * tmp % md;
            n /= 2;
        }
        return ans;
    }
    ModIntRuntime pow(lint n) const { return power(n); }
    ModIntRuntime inv() const { return this->pow(md - 2); }

    ModIntRuntime fac() const {
        int l0 = facs().size();
        if (l0 > this->val_) return facs()[this->val_];

        facs().resize(this->val_ + 1);
        for (int i = l0; i <= this->val_; i++)
            facs()[i] = (i == 0 ? ModIntRuntime(1) : facs()[i - 1] * ModIntRuntime(i));
        return facs()[this->val_];
    }

    ModIntRuntime doublefac() const {
        lint k = (this->val_ + 1) / 2;
        return (this->val_ & 1)
                   ? ModIntRuntime(k * 2).fac() / (ModIntRuntime(2).pow(k) * ModIntRuntime(k).fac())
                   : ModIntRuntime(k).fac() * ModIntRuntime(2).pow(k);
    }

    ModIntRuntime nCr(const ModIntRuntime &r) const {
        return (this->val_ < r.val_) ? ModIntRuntime(0)
                                     : this->fac() / ((*this - r).fac() * r.fac());
    }

    ModIntRuntime sqrt() const {
        if (val_ == 0) return 0;
        if (md == 2) return val_;
        if (power((md - 1) / 2) != 1) return 0;
        ModIntRuntime b = 1;
        while (b.power((md - 1) / 2) == 1) b += 1;
        lint e = 0, m = md - 1;
        while (m % 2 == 0) m >>= 1, e++;
        ModIntRuntime x = power((m - 1) / 2), y = (*this) * x * x;
        x *= (*this);
        ModIntRuntime z = b.power(m);
        while (y != 1) {
            lint j = 0;
            ModIntRuntime t = y;
            while (t != 1) j++, t *= t;
            z = z.power(lint(1) << (e - j - 1));
            x *= z, z *= z, y *= z;
            e = j;
        }
        return ModIntRuntime(std::min(x.val_, md - x.val_));
    }
};
lint ModIntRuntime::md = 1;

// Linear sieve algorithm for fast prime factorization
// Complexity: O(N) time, O(N) space:
// - MAXN = 10^7:  ~44 MB,  80~100 ms (Codeforces / AtCoder GCC, C++17)
// - MAXN = 10^8: ~435 MB, 810~980 ms (Codeforces / AtCoder GCC, C++17)
// Reference:
// [1] D. Gries, J. Misra, "A Linear Sieve Algorithm for Finding Prime Numbers,"
//     Communications of the ACM, 21(12), 999-1003, 1978.
// - https://cp-algorithms.com/algebra/prime-sieve-linear.html
// - https://37zigen.com/linear-sieve/
struct Sieve {
    std::vector<int> min_factor;
    std::vector<int> primes;
    Sieve(int MAXN) : min_factor(MAXN + 1) {
        for (int d = 2; d <= MAXN; d++) {
            if (!min_factor[d]) {
                min_factor[d] = d;
                primes.emplace_back(d);
            }
            for (const auto &p : primes) {
                if (p > min_factor[d] or d * p > MAXN) break;
                min_factor[d * p] = p;
            }
        }
    }
    // Prime factorization for 1 <= x <= MAXN^2
    // Complexity: O(log x)           (x <= MAXN)
    //             O(MAXN / log MAXN) (MAXN < x <= MAXN^2)
    template <class T> std::map<T, int> factorize(T x) const {
        std::map<T, int> ret;
        assert(x > 0 and
               x <= ((long long)min_factor.size() - 1) * ((long long)min_factor.size() - 1));
        for (const auto &p : primes) {
            if (x < T(min_factor.size())) break;
            while (!(x % p)) x /= p, ret[p]++;
        }
        if (x >= T(min_factor.size())) ret[x]++, x = 1;
        while (x > 1) ret[min_factor[x]]++, x /= min_factor[x];
        return ret;
    }
    // Enumerate divisors of 1 <= x <= MAXN^2
    // Be careful of highly composite numbers https://oeis.org/A002182/list
    // https://gist.github.com/dario2994/fb4713f252ca86c1254d#file-list-txt (n, (# of div. of n)):
    // 45360->100, 735134400(<1e9)->1344, 963761198400(<1e12)->6720
    template <class T> std::vector<T> divisors(T x) const {
        std::vector<T> ret{1};
        for (const auto p : factorize(x)) {
            int n = ret.size();
            for (int i = 0; i < n; i++) {
                for (T a = 1, d = 1; d <= p.second; d++) {
                    a *= p.first;
                    ret.push_back(ret[i] * a);
                }
            }
        }
        return ret; // NOT sorted
    }
    // Euler phi functions of divisors of given x
    // Verified: ABC212 G https://atcoder.jp/contests/abc212/tasks/abc212_g
    // Complexity: O(sqrt(x) + d(x))
    template <class T> std::map<T, T> euler_of_divisors(T x) const {
        assert(x >= 1);
        std::map<T, T> ret;
        ret[1] = 1;
        std::vector<T> divs{1};
        for (auto p : factorize(x)) {
            int n = ret.size();
            for (int i = 0; i < n; i++) {
                ret[divs[i] * p.first] = ret[divs[i]] * (p.first - 1);
                divs.push_back(divs[i] * p.first);
                for (T a = divs[i] * p.first, d = 1; d < p.second; a *= p.first, d++) {
                    ret[a * p.first] = ret[a] * p.first;
                    divs.push_back(a * p.first);
                }
            }
        }
        return ret;
    }
    // Moebius function Table, (-1)^{# of different prime factors} for square-free x
    // return: [0=>0, 1=>1, 2=>-1, 3=>-1, 4=>0, 5=>-1, 6=>1, 7=>-1, 8=>0, ...] https://oeis.org/A008683
    std::vector<int> GenerateMoebiusFunctionTable() const {
        std::vector<int> ret(min_factor.size());
        for (unsigned i = 1; i < min_factor.size(); i++) {
            if (i == 1) {
                ret[i] = 1;
            } else if ((i / min_factor[i]) % min_factor[i] == 0) {
                ret[i] = 0;
            } else {
                ret[i] = -ret[i / min_factor[i]];
            }
        }
        return ret;
    }
    // Calculate [0^K, 1^K, ..., nmax^K] in O(nmax)
    // Note: **0^0 == 1**
    template <class MODINT> std::vector<MODINT> enumerate_kth_pows(long long K, int nmax) const {
        assert(nmax < int(min_factor.size()));
        assert(K >= 0);
        if (K == 0) return std::vector<MODINT>(nmax + 1, 1);
        std::vector<MODINT> ret(nmax + 1);
        ret[0] = 0, ret[1] = 1;
        for (int n = 2; n <= nmax; n++) {
            if (min_factor[n] == n) {
                ret[n] = MODINT(n).pow(K);
            } else {
                ret[n] = ret[n / min_factor[n]] * ret[min_factor[n]];
            }
        }
        return ret;
    }
};
Sieve sieve(10101010);


bool check(lint p, int deg, lint val) {
    if (p == 2) {
        // dbg(make_tuple(p, deg, val));
        if (deg == 1) return true;
        if (deg == 2) return val % 4 <= 1;
        while (val and val % 4 == 0) val /= 4;
        return val % 8 == 1 or val == 0;
    }
    using mint = ModIntRuntime;
    mint::set_mod(p);
    mint x = ModIntRuntime(val);
    mint sq = x.sqrt();
    // dbg(make_tuple(p, val, x, sq, sq * sq - x));
    dbg(make_tuple((long long)p, (long long)val, (long long)(sq * sq - x).val()));
    return sq * sq - x == 0;
}

int main() {
    long long B, N;
    cin >> B >> N;
    dbg(make_tuple(B, N));

    auto fac = sieve.factorize(B);
    dbg(fac);
    for (auto [p, deg] : fac) {
        if (!check(p, deg, N)) {
            puts("NO");
            return 0;
        }
    }
    puts("YES");
}

yukicoder

結果

テストケース

ソースコード