結果
問題 | No.1460 Max of Min |
ユーザー | hitonanode |
提出日時 | 2021-05-13 16:43:02 |
言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 156 ms / 2,000 ms |
コード長 | 17,065 bytes |
コンパイル時間 | 2,995 ms |
コンパイル使用メモリ | 185,216 KB |
実行使用メモリ | 6,948 KB |
最終ジャッジ日時 | 2024-09-25 05:27:22 |
合計ジャッジ時間 | 9,769 ms |
ジャッジサーバーID (参考情報) |
judge5 / judge1 |
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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
6,816 KB |
testcase_01 | AC | 2 ms
6,944 KB |
testcase_02 | AC | 2 ms
6,940 KB |
testcase_03 | AC | 2 ms
6,940 KB |
testcase_04 | AC | 2 ms
6,944 KB |
testcase_05 | AC | 2 ms
6,944 KB |
testcase_06 | AC | 155 ms
6,940 KB |
testcase_07 | AC | 147 ms
6,944 KB |
testcase_08 | AC | 2 ms
6,940 KB |
testcase_09 | AC | 2 ms
6,944 KB |
testcase_10 | AC | 141 ms
6,944 KB |
testcase_11 | AC | 150 ms
6,944 KB |
testcase_12 | AC | 32 ms
6,940 KB |
testcase_13 | AC | 60 ms
6,944 KB |
testcase_14 | AC | 70 ms
6,940 KB |
testcase_15 | AC | 27 ms
6,944 KB |
testcase_16 | AC | 61 ms
6,940 KB |
testcase_17 | AC | 63 ms
6,940 KB |
testcase_18 | AC | 7 ms
6,944 KB |
testcase_19 | AC | 56 ms
6,940 KB |
testcase_20 | AC | 9 ms
6,940 KB |
testcase_21 | AC | 14 ms
6,944 KB |
testcase_22 | AC | 54 ms
6,944 KB |
testcase_23 | AC | 7 ms
6,944 KB |
testcase_24 | AC | 61 ms
6,940 KB |
testcase_25 | AC | 5 ms
6,944 KB |
testcase_26 | AC | 80 ms
6,944 KB |
testcase_27 | AC | 33 ms
6,944 KB |
testcase_28 | AC | 15 ms
6,944 KB |
testcase_29 | AC | 75 ms
6,940 KB |
testcase_30 | AC | 69 ms
6,940 KB |
testcase_31 | AC | 48 ms
6,940 KB |
testcase_32 | AC | 35 ms
6,940 KB |
testcase_33 | AC | 26 ms
6,944 KB |
testcase_34 | AC | 27 ms
6,944 KB |
testcase_35 | AC | 16 ms
6,944 KB |
testcase_36 | AC | 2 ms
6,944 KB |
testcase_37 | AC | 33 ms
6,940 KB |
testcase_38 | AC | 32 ms
6,944 KB |
testcase_39 | AC | 25 ms
6,944 KB |
testcase_40 | AC | 18 ms
6,940 KB |
testcase_41 | AC | 16 ms
6,940 KB |
testcase_42 | AC | 14 ms
6,940 KB |
testcase_43 | AC | 40 ms
6,940 KB |
testcase_44 | AC | 46 ms
6,944 KB |
testcase_45 | AC | 8 ms
6,940 KB |
testcase_46 | AC | 31 ms
6,940 KB |
testcase_47 | AC | 39 ms
6,940 KB |
testcase_48 | AC | 49 ms
6,944 KB |
testcase_49 | AC | 46 ms
6,944 KB |
testcase_50 | AC | 7 ms
6,940 KB |
testcase_51 | AC | 45 ms
6,940 KB |
testcase_52 | AC | 17 ms
6,944 KB |
testcase_53 | AC | 33 ms
6,940 KB |
testcase_54 | AC | 35 ms
6,940 KB |
testcase_55 | AC | 55 ms
6,944 KB |
testcase_56 | AC | 31 ms
6,940 KB |
testcase_57 | AC | 44 ms
6,940 KB |
testcase_58 | AC | 149 ms
6,944 KB |
testcase_59 | AC | 39 ms
6,940 KB |
testcase_60 | AC | 44 ms
6,940 KB |
testcase_61 | AC | 34 ms
6,940 KB |
testcase_62 | AC | 33 ms
6,948 KB |
testcase_63 | AC | 2 ms
6,944 KB |
testcase_64 | AC | 3 ms
6,940 KB |
testcase_65 | AC | 53 ms
6,944 KB |
testcase_66 | AC | 34 ms
6,940 KB |
testcase_67 | AC | 32 ms
6,944 KB |
testcase_68 | AC | 43 ms
6,940 KB |
testcase_69 | AC | 38 ms
6,940 KB |
testcase_70 | AC | 37 ms
6,944 KB |
testcase_71 | AC | 48 ms
6,944 KB |
testcase_72 | AC | 32 ms
6,940 KB |
testcase_73 | AC | 34 ms
6,944 KB |
testcase_74 | AC | 31 ms
6,940 KB |
testcase_75 | AC | 32 ms
6,940 KB |
testcase_76 | AC | 32 ms
6,944 KB |
testcase_77 | AC | 28 ms
6,940 KB |
testcase_78 | AC | 31 ms
6,940 KB |
testcase_79 | AC | 28 ms
6,940 KB |
testcase_80 | AC | 31 ms
6,940 KB |
testcase_81 | AC | 29 ms
6,944 KB |
testcase_82 | AC | 31 ms
6,940 KB |
testcase_83 | AC | 31 ms
6,944 KB |
testcase_84 | AC | 155 ms
6,940 KB |
testcase_85 | AC | 151 ms
6,940 KB |
testcase_86 | AC | 149 ms
6,944 KB |
testcase_87 | AC | 156 ms
6,940 KB |
testcase_88 | AC | 148 ms
6,940 KB |
testcase_89 | AC | 154 ms
6,944 KB |
testcase_90 | AC | 154 ms
6,940 KB |
testcase_91 | AC | 153 ms
6,940 KB |
testcase_92 | AC | 148 ms
6,940 KB |
testcase_93 | AC | 153 ms
6,940 KB |
ソースコード
#include <algorithm> #include <array> #include <bitset> #include <cassert> #include <chrono> #include <cmath> #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 <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) { if (m < q) {m = q; return true;} else return false; } template <typename T> bool chmin(T &m, const T q) { if (m > q) {m = q; return true;} else return false; } int floor_lg(long long x) { return x <= 0 ? -1 : 63 - __builtin_clzll(x); } template <typename T1, typename T2> pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); } template <typename T1, typename T2> pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); } template <typename T> vector<T> sort_unique(vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template <typename 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 <typename T> int argub(const std::vector<T> &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (auto &v : vec) is >> v; return is; } template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template <typename T, size_t sz> ostream &operator<<(ostream &os, const array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } #if __cplusplus >= 201703L template <typename... T> istream &operator>>(istream &is, tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template <typename... T> ostream &operator<<(ostream &os, const tuple<T...> &tpl) { std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os; } #endif template <typename T> ostream &operator<<(ostream &os, const deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template <typename T> ostream &operator<<(ostream &os, const set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template <typename T, typename TH> ostream &operator<<(ostream &os, const unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template <typename T> ostream &operator<<(ostream &os, const multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa) { os << '(' << pa.first << ',' << pa.second << ')'; return os; } template <typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template <typename TK, typename TV, typename TH> ostream &operator<<(ostream &os, const 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) cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl #else #define dbg(x) (x) #endif template <int mod> struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int get_mod() { return mod; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set<int> fac; int v = mod - 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 (int g = 1; g < mod; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((mod - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val; MDCONST ModInt() : val(0) {} MDCONST ModInt &_setval(lint v) { return val = (v >= mod ? v - mod : v), *this; } MDCONST ModInt(lint v) { _setval(v % mod + mod); } MDCONST explicit operator bool() const { return val != 0; } MDCONST ModInt operator+(const ModInt &x) const { return ModInt()._setval((lint)val + x.val); } MDCONST ModInt operator-(const ModInt &x) const { return ModInt()._setval((lint)val - x.val + mod); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val * x.val % mod); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val * x.inv() % mod); } MDCONST ModInt operator-() const { return ModInt()._setval(mod - val); } MDCONST ModInt &operator+=(const ModInt &x) { return *this = *this + x; } MDCONST ModInt &operator-=(const ModInt &x) { return *this = *this - x; } MDCONST ModInt &operator*=(const ModInt &x) { return *this = *this * x; } MDCONST ModInt &operator/=(const ModInt &x) { return *this = *this / x; } friend MDCONST ModInt operator+(lint a, const ModInt &x) { return ModInt()._setval(a % mod + x.val); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % mod - x.val + mod); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.val % mod); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % mod * x.inv() % mod); } MDCONST bool operator==(const ModInt &x) const { return val == x.val; } MDCONST bool operator!=(const ModInt &x) const { return val != x.val; } MDCONST bool operator<(const ModInt &x) const { return val < x.val; } // To use std::map<ModInt, T> friend std::istream &operator>>(std::istream &is, ModInt &x) { lint t; return is >> t, x = ModInt(t), is; } MDCONST friend std::ostream &operator<<(std::ostream &os, const ModInt &x) { return os << x.val; } MDCONST ModInt pow(lint n) const { lint ans = 1, tmp = this->val; while (n) { if (n & 1) ans = ans * tmp % mod; tmp = tmp * tmp % mod, n /= 2; } return ans; } static std::vector<long long> facs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N <= l0) return; facs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i % mod; long long facinv = ModInt(facs.back()).pow(mod - 2).val; for (int i = N - 1; i >= l0; i--) { invs[i] = facinv * facs[i - 1] % mod; facinv = facinv * i % mod; } } MDCONST lint inv() const { if (this->val < std::min(mod >> 1, 1 << 21)) { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val]; } else { return this->pow(mod - 2).val; } } MDCONST ModInt fac() const { while (this->val >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val]; } MDCONST ModInt doublefac() const { lint k = (this->val + 1) / 2; return (this->val & 1) ? ModInt(k * 2).fac() / (ModInt(2).pow(k) * ModInt(k).fac()) : ModInt(k).fac() * ModInt(2).pow(k); } MDCONST ModInt nCr(const ModInt &r) const { return (this->val < r.val) ? 0 : this->fac() / ((*this - r).fac() * r.fac()); } ModInt sqrt() const { if (val == 0) return 0; if (mod == 2) return val; if (pow((mod - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((mod - 1) / 2) == 1) b += 1; int e = 0, m = mod - 1; while (m % 2 == 0) m >>= 1, e++; ModInt x = pow((m - 1) / 2), y = (*this) * x * x; x *= (*this); ModInt z = b.pow(m); while (y != 1) { int j = 0; ModInt t = y; while (t != 1) j++, t *= t; z = z.pow(1LL << (e - j - 1)); x *= z, z *= z, y *= z; e = j; } return ModInt(std::min(x.val, mod - x.val)); } }; template <int mod> std::vector<long long> ModInt<mod>::facs = {1}; template <int mod> std::vector<long long> ModInt<mod>::invs = {0}; using mint = ModInt<998244353>; // Integer convolution for arbitrary mod // with NTT (and Garner's algorithm) for ModInt / ModIntRuntime class. // We skip Garner's algorithm if `skip_garner` is true or mod is in `nttprimes`. // input: a (size: n), b (size: m) // return: vector (size: n + m - 1) template <typename MODINT> std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner = false); constexpr int nttprimes[3] = {998244353, 167772161, 469762049}; // Integer FFT (Fast Fourier Transform) for ModInt class // (Also known as Number Theoretic Transform, NTT) // is_inverse: inverse transform // ** Input size must be 2^n ** template <typename MODINT> void ntt(std::vector<MODINT> &a, bool is_inverse = false) { int n = a.size(); if (n == 1) return; static const int mod = MODINT::get_mod(); static const MODINT root = MODINT::get_primitive_root(); assert(__builtin_popcount(n) == 1 and (mod - 1) % n == 0); static std::vector<MODINT> w{1}, iw{1}; for (int m = w.size(); m < n / 2; m *= 2) { MODINT dw = root.pow((mod - 1) / (4 * m)), dwinv = 1 / dw; w.resize(m * 2), iw.resize(m * 2); for (int i = 0; i < m; i++) w[m + i] = w[i] * dw, iw[m + i] = iw[i] * dwinv; } if (!is_inverse) { for (int m = n; m >>= 1;) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { MODINT x = a[i], y = a[i + m] * w[k]; a[i] = x + y, a[i + m] = x - y; } } } } else { for (int m = 1; m < n; m *= 2) { for (int s = 0, k = 0; s < n; s += 2 * m, k++) { for (int i = s; i < s + m; i++) { MODINT x = a[i], y = a[i + m]; a[i] = x + y, a[i + m] = (x - y) * iw[k]; } } } int n_inv = MODINT(n).inv(); for (auto &v : a) v *= n_inv; } } template <int MOD> std::vector<ModInt<MOD>> nttconv_(const std::vector<int> &a, const std::vector<int> &b) { int sz = a.size(); assert(a.size() == b.size() and __builtin_popcount(sz) == 1); std::vector<ModInt<MOD>> ap(sz), bp(sz); for (int i = 0; i < sz; i++) ap[i] = a[i], bp[i] = b[i]; ntt(ap, false); if (a == b) bp = ap; else ntt(bp, false); for (int i = 0; i < sz; i++) ap[i] *= bp[i]; ntt(ap, true); return ap; } long long garner_ntt_(int r0, int r1, int r2, int mod) { using mint2 = ModInt<nttprimes[2]>; static const long long m01 = 1LL * nttprimes[0] * nttprimes[1]; static const long long m0_inv_m1 = ModInt<nttprimes[1]>(nttprimes[0]).inv(); static const long long m01_inv_m2 = mint2(m01).inv(); int v1 = (m0_inv_m1 * (r1 + nttprimes[1] - r0)) % nttprimes[1]; auto v2 = (mint2(r2) - r0 - mint2(nttprimes[0]) * v1) * m01_inv_m2; return (r0 + 1LL * nttprimes[0] * v1 + m01 % mod * v2.val) % mod; } template <typename MODINT> std::vector<MODINT> nttconv(std::vector<MODINT> a, std::vector<MODINT> b, bool skip_garner) { int sz = 1, n = a.size(), m = b.size(); while (sz < n + m) sz <<= 1; if (sz <= 16) { std::vector<MODINT> ret(n + m - 1); for (int i = 0; i < n; i++) { for (int j = 0; j < m; j++) ret[i + j] += a[i] * b[j]; } return ret; } int mod = MODINT::get_mod(); if (skip_garner or std::find(std::begin(nttprimes), std::end(nttprimes), mod) != std::end(nttprimes)) { a.resize(sz), b.resize(sz); if (a == b) { ntt(a, false); b = a; } else ntt(a, false), ntt(b, false); for (int i = 0; i < sz; i++) a[i] *= b[i]; ntt(a, true); a.resize(n + m - 1); } else { std::vector<int> ai(sz), bi(sz); for (int i = 0; i < n; i++) ai[i] = a[i].val; for (int i = 0; i < m; i++) bi[i] = b[i].val; auto ntt0 = nttconv_<nttprimes[0]>(ai, bi); auto ntt1 = nttconv_<nttprimes[1]>(ai, bi); auto ntt2 = nttconv_<nttprimes[2]>(ai, bi); a.resize(n + m - 1); for (int i = 0; i < n + m - 1; i++) { a[i] = garner_ntt_(ntt0[i].val, ntt1[i].val, ntt2[i].val, mod); } } return a; } // Calculate [x^N](num(x) / den(x)) // - Coplexity: O(LlgLlgN) ( L = size(num) + size(den) ) // - Reference: `Bostan–Mori algorithm` <https://qiita.com/ryuhe1/items/da5acbcce4ac1911f47a> template <typename Tp> Tp coefficient_of_rational_function(long long N, std::vector<Tp> num, std::vector<Tp> den) { assert(N >= 0); while (den.size() and den.back() == 0) den.pop_back(); assert(den.size()); int h = 0; while (den[h] == 0) h++; N += h; den.erase(den.begin(), den.begin() + h); if (den.size() == 1) { return N < int(num.size()) ? num[N] / den[0] : 0; } while (N) { std::vector<Tp> g = den; for (size_t i = 1; i < g.size(); i += 2) { g[i] = -g[i]; } auto conv_num_g = nttconv(num, g); num.resize((conv_num_g.size() + 1 - (N & 1)) / 2); for (size_t i = 0; i < num.size(); i++) { num[i] = conv_num_g[i * 2 + (N & 1)]; } auto conv_den_g = nttconv(den, g); for (size_t i = 0; i < den.size(); i++) { den[i] = conv_den_g[i * 2]; } N >>= 1; } return num[0] / den[0]; } // Find the n-th term of the sequence (0-ORIGIN) // Complexity: O(K lg K \log N) // ainit = [a_0, a_1,..., ] // c[0] = 1, \sum_j a_{i - j} * c_j = 0 template <typename Tp> Tp find_kth_term(std::vector<Tp> ainit, const std::vector<Tp> c, long long n) { assert(ainit.size() + 1 == c.size()); auto a = nttconv(ainit, c); a.resize(ainit.size()); return coefficient_of_rational_function(n, a, c); } struct rand_int_ { using lint = long long; mt19937 mt; rand_int_() : mt(chrono::steady_clock::now().time_since_epoch().count()) {} lint operator()(lint x) { return this->operator()(0, x); } // [0, x) lint operator()(lint l, lint r) { uniform_int_distribution<lint> d(l, r - 1); return d(mt); } } rnd; int main() { int K; lint N; cin >> K >> N; vector<lint> A(K), B(K); cin >> A >> B; if (N < K) { cout << A[N] << '\n'; return 0; } vector<lint> zs = A; zs.insert(zs.end(), B.begin(), B.end()); zs = sort_unique(zs); int lo = 0, hi = zs.size(); while (hi - lo > 1) { const int c = (lo + hi) / 2; vector<mint> ainit(K), C(K + 1); C[0] = 1; REP(i, K) if (A[i] >= zs[c]) ainit[i] = rnd(1, 1 << 28); REP(i, K) if (B[i] >= zs[c]) C[K - i] = rnd(1, 1 << 28); auto f = find_kth_term(ainit, C, N); (f ? lo : hi) = c; } cout << zs[lo] << '\n'; }