結果
問題 | No.1907 DETERMINATION |
ユーザー | Benjamin Qi |
提出日時 | 2024-12-29 11:56:10 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 1,112 ms / 4,000 ms |
コード長 | 16,766 bytes |
コンパイル時間 | 3,061 ms |
コンパイル使用メモリ | 161,240 KB |
実行使用メモリ | 7,168 KB |
最終ジャッジ日時 | 2024-12-29 11:56:51 |
合計ジャッジ時間 | 40,712 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge2 |
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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
6,820 KB |
testcase_02 | AC | 2 ms
6,816 KB |
testcase_03 | AC | 2 ms
6,816 KB |
testcase_04 | AC | 3 ms
6,816 KB |
testcase_05 | AC | 2 ms
6,816 KB |
testcase_06 | AC | 2 ms
6,820 KB |
testcase_07 | AC | 277 ms
6,816 KB |
testcase_08 | AC | 111 ms
6,820 KB |
testcase_09 | AC | 189 ms
6,820 KB |
testcase_10 | AC | 767 ms
7,040 KB |
testcase_11 | AC | 285 ms
6,816 KB |
testcase_12 | AC | 707 ms
6,912 KB |
testcase_13 | AC | 673 ms
6,912 KB |
testcase_14 | AC | 609 ms
6,912 KB |
testcase_15 | AC | 129 ms
6,816 KB |
testcase_16 | AC | 42 ms
6,816 KB |
testcase_17 | AC | 689 ms
6,816 KB |
testcase_18 | AC | 485 ms
6,820 KB |
testcase_19 | AC | 13 ms
6,820 KB |
testcase_20 | AC | 662 ms
6,912 KB |
testcase_21 | AC | 60 ms
6,816 KB |
testcase_22 | AC | 635 ms
6,816 KB |
testcase_23 | AC | 823 ms
6,816 KB |
testcase_24 | AC | 207 ms
6,816 KB |
testcase_25 | AC | 2 ms
6,816 KB |
testcase_26 | AC | 682 ms
7,040 KB |
testcase_27 | AC | 916 ms
6,912 KB |
testcase_28 | AC | 875 ms
7,168 KB |
testcase_29 | AC | 871 ms
7,040 KB |
testcase_30 | AC | 3 ms
6,816 KB |
testcase_31 | AC | 725 ms
7,040 KB |
testcase_32 | AC | 677 ms
7,168 KB |
testcase_33 | AC | 710 ms
7,168 KB |
testcase_34 | AC | 682 ms
6,912 KB |
testcase_35 | AC | 2 ms
6,820 KB |
testcase_36 | AC | 2 ms
6,816 KB |
testcase_37 | AC | 3 ms
6,816 KB |
testcase_38 | AC | 681 ms
7,040 KB |
testcase_39 | AC | 672 ms
6,912 KB |
testcase_40 | AC | 1,092 ms
7,040 KB |
testcase_41 | AC | 694 ms
7,040 KB |
testcase_42 | AC | 1,083 ms
7,040 KB |
testcase_43 | AC | 1,112 ms
6,912 KB |
testcase_44 | AC | 795 ms
7,168 KB |
testcase_45 | AC | 908 ms
7,040 KB |
testcase_46 | AC | 674 ms
7,168 KB |
testcase_47 | AC | 679 ms
6,912 KB |
testcase_48 | AC | 676 ms
7,168 KB |
testcase_49 | AC | 767 ms
6,912 KB |
testcase_50 | AC | 681 ms
6,912 KB |
testcase_51 | AC | 682 ms
6,912 KB |
testcase_52 | AC | 2 ms
6,816 KB |
testcase_53 | AC | 806 ms
6,816 KB |
testcase_54 | AC | 810 ms
6,816 KB |
testcase_55 | AC | 2 ms
6,816 KB |
testcase_56 | AC | 836 ms
6,820 KB |
testcase_57 | AC | 837 ms
6,816 KB |
testcase_58 | AC | 664 ms
6,912 KB |
testcase_59 | AC | 474 ms
6,912 KB |
testcase_60 | AC | 475 ms
7,040 KB |
testcase_61 | AC | 603 ms
6,912 KB |
testcase_62 | AC | 473 ms
7,040 KB |
testcase_63 | AC | 678 ms
7,040 KB |
testcase_64 | AC | 2 ms
6,820 KB |
testcase_65 | AC | 3 ms
6,816 KB |
testcase_66 | AC | 2 ms
6,816 KB |
ソースコード
#include <algorithm> #include <array> #include <bitset> #include <cassert> #include <chrono> #include <climits> #include <cmath> #include <complex> #include <cstring> #include <functional> #include <iomanip> #include <iostream> #include <map> #include <numeric> #include <queue> #include <random> #include <set> #include <vector> using namespace std; using ll = long long; using db = long double; // or double, if TL is tight using str = string; // yay python! // pairs using pi = pair<int, int>; using pl = pair<ll, ll>; using pd = pair<db, db>; #define mp make_pair #define f first #define s second #define tcT template <class T #define tcTU tcT, class U // ^ lol this makes everything look weird but I'll try it tcT > using V = vector<T>; tcT, size_t SZ > using AR = array<T, SZ>; using vi = V<int>; using vb = V<bool>; using vl = V<ll>; using vd = V<db>; using vs = V<str>; using vpi = V<pi>; using vpl = V<pl>; using vpd = V<pd>; // vectors #define sz(x) int(size(x)) #define bg(x) begin(x) #define all(x) bg(x), end(x) #define rall(x) rbegin(x), rend(x) #define sor(x) sort(all(x)) #define rsz resize #define ins insert #define pb push_back #define eb emplace_back #define ft front() #define bk back() #define lb lower_bound #define ub upper_bound tcT > int lwb(const V<T> &a, const T &b) { return int(lb(all(a), b) - bg(a)); } tcT > int upb(const V<T> &a, const T &b) { return int(ub(all(a), b) - bg(a)); } // loops #define FOR(i, a, b) for (int i = (a); i < (b); ++i) #define F0R(i, a) FOR(i, 0, a) #define ROF(i, a, b) for (int i = (b)-1; i >= (a); --i) #define R0F(i, a) ROF(i, 0, a) #define rep(a) F0R(_, a) #define each(a, x) for (auto &a : x) const int MOD = 998244353; // 1e9+7; const int MX = (int)2e5 + 5; const ll BIG = 1e18; // not too close to LLONG_MAX const db PI = acos((db)-1); const int dx[4]{1, 0, -1, 0}, dy[4]{0, 1, 0, -1}; // for every grid problem!! mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); template <class T> using pqg = priority_queue<T, vector<T>, greater<T>>; // bitwise ops // also see https://gcc.gnu.org/onlinedocs/gcc/Other-Builtins.html constexpr int pct(int x) { return __builtin_popcount(x); } // # of bits set constexpr int bits(int x) { // assert(x >= 0); // make C++11 compatible until // USACO updates ... return x == 0 ? 0 : 31 - __builtin_clz(x); } // floor(log2(x)) constexpr int p2(int x) { return 1 << x; } constexpr int msk2(int x) { return p2(x) - 1; } ll cdiv(ll a, ll b) { return a / b + ((a ^ b) > 0 && a % b); } // divide a by b rounded up ll fdiv(ll a, ll b) { return a / b - ((a ^ b) < 0 && a % b); } // divide a by b rounded down tcT > bool ckmin(T &a, const T &b) { return b < a ? a = b, 1 : 0; } // set a = min(a,b) tcT > bool ckmax(T &a, const T &b) { return a < b ? a = b, 1 : 0; } // set a = max(a,b) tcTU > T fstTrue(T lo, T hi, U f) { ++hi; assert(lo <= hi); // assuming f is increasing while (lo < hi) { // find first index such that f is true T mid = lo + (hi - lo) / 2; f(mid) ? hi = mid : lo = mid + 1; } return lo; } tcTU > T lstTrue(T lo, T hi, U f) { --lo; assert(lo <= hi); // assuming f is decreasing while (lo < hi) { // find first index such that f is true T mid = lo + (hi - lo + 1) / 2; f(mid) ? lo = mid : hi = mid - 1; } return lo; } tcT > void remDup(vector<T> &v) { // sort and remove duplicates sort(all(v)); v.erase(unique(all(v)), end(v)); } tcTU > void safeErase(T &t, const U &u) { auto it = t.find(u); assert(it != end(t)); t.erase(it); } inline namespace IO { #define SFINAE(x, ...) \ template <class, class = void> struct x : std::false_type {}; \ template <class T> struct x<T, std::void_t<__VA_ARGS__>> : std::true_type {} SFINAE(DefaultI, decltype(std::cin >> std::declval<T &>())); SFINAE(DefaultO, decltype(std::cout << std::declval<T &>())); SFINAE(IsTuple, typename std::tuple_size<T>::type); SFINAE(Iterable, decltype(std::begin(std::declval<T>()))); template <auto &is> struct Reader { template <class T> void Impl(T &t) { if constexpr (DefaultI<T>::value) is >> t; else if constexpr (Iterable<T>::value) { for (auto &x : t) Impl(x); } else if constexpr (IsTuple<T>::value) { std::apply([this](auto &...args) { (Impl(args), ...); }, t); } else static_assert(IsTuple<T>::value, "No matching type for read"); } template <class... Ts> void read(Ts &...ts) { ((Impl(ts)), ...); } }; template <class... Ts> void re(Ts &...ts) { Reader<cin>{}.read(ts...); } #define def(t, args...) \ t args; \ re(args); template <auto &os, bool debug, bool print_nd> struct Writer { string comma() const { return debug ? "," : ""; } template <class T> constexpr char Space(const T &) const { return print_nd && (Iterable<T>::value or IsTuple<T>::value) ? '\n' : ' '; } template <class T> void Impl(T const &t) const { if constexpr (DefaultO<T>::value) os << t; else if constexpr (Iterable<T>::value) { if (debug) os << '{'; int i = 0; for (auto &&x : t) ((i++) ? (os << comma() << Space(x), Impl(x)) : Impl(x)); if (debug) os << '}'; } else if constexpr (IsTuple<T>::value) { if (debug) os << '('; std::apply( [this](auto const &...args) { int i = 0; (((i++) ? (os << comma() << " ", Impl(args)) : Impl(args)), ...); }, t); if (debug) os << ')'; } else static_assert(IsTuple<T>::value, "No matching type for print"); } template <class T> void ImplWrapper(T const &t) const { if (debug) os << "\033[0;31m"; Impl(t); if (debug) os << "\033[0m"; } template <class... Ts> void print(Ts const &...ts) const { ((Impl(ts)), ...); } template <class F, class... Ts> void print_with_sep(const std::string &sep, F const &f, Ts const &...ts) const { ImplWrapper(f), ((os << sep, ImplWrapper(ts)), ...), os << '\n'; } void print_with_sep(const std::string &) const { os << '\n'; } }; template <class... Ts> void pr(Ts const &...ts) { Writer<cout, false, true>{}.print(ts...); } template <class... Ts> void ps(Ts const &...ts) { Writer<cout, false, true>{}.print_with_sep(" ", ts...); } } // namespace IO inline namespace Debug { template <typename... Args> void err(Args... args) { Writer<cerr, true, false>{}.print_with_sep(" | ", args...); } template <typename... Args> void errn(Args... args) { Writer<cerr, true, true>{}.print_with_sep(" | ", args...); } void err_prefix(str func, int line, string args) { cerr << "\033[0;31m\u001b[1mDEBUG\033[0m" << " | " << "\u001b[34m" << func << "\033[0m" << ":" << "\u001b[34m" << line << "\033[0m" << " - " << "[" << args << "] = "; } #ifdef LOCAL #define dbg(args...) err_prefix(__FUNCTION__, __LINE__, #args), err(args) #define dbgn(args...) err_prefix(__FUNCTION__, __LINE__, #args), errn(args) #else #define dbg(...) #define dbgn(args...) #endif const auto beg_time = std::chrono::high_resolution_clock::now(); // https://stackoverflow.com/questions/47980498/accurate-c-c-clock-on-a-multi-core-processor-with-auto-overclock?noredirect=1&lq=1 double time_elapsed() { return chrono::duration<double>(std::chrono::high_resolution_clock::now() - beg_time) .count(); } } // namespace Debug inline namespace FileIO { void setIn(str s) { freopen(s.c_str(), "r", stdin); } void setOut(str s) { freopen(s.c_str(), "w", stdout); } void setIO(str s = "") { cin.tie(0)->sync_with_stdio(0); // unsync C / C++ I/O streams cout << fixed << setprecision(12); // cin.exceptions(cin.failbit); // throws exception when do smth illegal // ex. try to read letter into int if (sz(s)) setIn(s + ".in"), setOut(s + ".out"); // for old USACO } } // namespace FileIO /** * Description: modular arithmetic operations * Source: * KACTL * https://codeforces.com/blog/entry/63903 * https://codeforces.com/contest/1261/submission/65632855 (tourist) * https://codeforces.com/contest/1264/submission/66344993 (ksun) * also see https://github.com/ecnerwala/cp-book/blob/master/src/modnum.hpp * (ecnerwal) Verification: https://open.kattis.com/problems/modulararithmetic */ template <int MOD, int RT> struct mint { static const int mod = MOD; static constexpr mint rt() { return RT; } // primitive root for FFT int v; explicit operator int() const { return v; } // explicit -> don't silently convert to int mint() : v(0) {} mint(ll _v) { v = int((-MOD < _v && _v < MOD) ? _v : _v % MOD); if (v < 0) v += MOD; } bool operator==(const mint &o) const { return v == o.v; } friend bool operator!=(const mint &a, const mint &b) { return !(a == b); } friend bool operator<(const mint &a, const mint &b) { return a.v < b.v; } friend istream &operator>>(istream &is, mint &a) { ll x; is >> x; a = mint(x); return is; } friend ostream &operator<<(ostream &os, mint a) { os << int(a); return os; } mint &operator+=(const mint &o) { if ((v += o.v) >= MOD) v -= MOD; return *this; } mint &operator-=(const mint &o) { if ((v -= o.v) < 0) v += MOD; return *this; } mint &operator*=(const mint &o) { v = int((ll)v * o.v % MOD); return *this; } mint &operator/=(const mint &o) { return (*this) *= inv(o); } friend mint pow(mint a, ll p) { mint ans = 1; assert(p >= 0); for (; p; p /= 2, a *= a) if (p & 1) ans *= a; return ans; } friend mint inv(const mint &a) { assert(a.v != 0); return pow(a, MOD - 2); } mint operator-() const { return mint(-v); } mint &operator++() { return *this += 1; } mint &operator--() { return *this -= 1; } friend mint operator+(mint a, const mint &b) { return a += b; } friend mint operator-(mint a, const mint &b) { return a -= b; } friend mint operator*(mint a, const mint &b) { return a *= b; } friend mint operator/(mint a, const mint &b) { return a /= b; } }; using mi = mint<MOD, 5>; // 5 is primitive root for both common mods using vmi = V<mi>; using pmi = pair<mi, mi>; using vpmi = V<pmi>; V<vmi> scmb; // small combinations void genComb(int SZ) { scmb.assign(SZ, vmi(SZ)); scmb[0][0] = 1; FOR(i, 1, SZ) F0R(j, i + 1) scmb[i][j] = scmb[i - 1][j] + (j ? scmb[i - 1][j - 1] : 0); } void hessenberg(V<vmi> &v) { // https://www.phys.uri.edu/nigh/NumRec/bookfpdf/f11-5.pdf#page=3 int N = sz(v); F0R(c, N) { bool found = 0; FOR(r, c + 1, N) if (v.at(r).at(c) != 0) { swap(v.at(c + 1), v.at(r)); F0R(k, N) swap(v.at(k).at(c + 1), v.at(k).at(r)); found = true; break; } if (!found) continue; mi iv = 1 / v.at(c + 1).at(c); FOR(r, c + 2, N) { mi quo = v.at(r).at(c) * iv; FOR(co, c, N) v.at(r).at(co) -= quo * v.at(c + 1).at(co); F0R(ro, N) v.at(ro).at(c + 1) += quo * v.at(ro).at(r); assert(v.at(r).at(c) == 0); } } } /** * Description: Basic poly ops including division. Can replace \texttt{T} with * double, complex. Source: Own. Also see * https://github.com/kth-competitive-programming/kactl/blob/master/content/numerical/PolyInterpolate.h * https://github.com/ecnerwala/icpc-book/blob/master/content/numerical/fft.cpp * Verification: see FFT */ // #include "../../number-theory (11.1)/Modular Arithmetic/ModInt.h" using T = mi; using poly = V<T>; void remz(poly &p) { while (sz(p) && p.bk == T(0)) p.pop_back(); } poly REMZ(poly p) { remz(p); return p; } poly rev(poly p) { reverse(all(p)); return p; } poly shift(poly p, int x) { if (x >= 0) p.insert(begin(p), x, 0); else assert(sz(p) + x >= 0), p.erase(begin(p), begin(p) - x); return p; } poly RSZ(const poly &p, int x) { if (x <= sz(p)) return poly(begin(p), begin(p) + x); poly q = p; q.rsz(x); return q; } T eval(const poly &p, T x) { // evaluate at point x T res = 0; R0F(i, sz(p)) res = x * res + p[i]; return res; } poly dif(const poly &p) { // differentiate poly res; FOR(i, 1, sz(p)) res.pb(T(i) * p[i]); return res; } poly integ(const poly &p) { // integrate static poly invs{0, 1}; for (int i = sz(invs); i <= sz(p); ++i) invs.pb(-MOD / i * invs[MOD % i]); poly res(sz(p) + 1); F0R(i, sz(p)) res[i + 1] = p[i] * invs[i + 1]; return res; } poly &operator+=(poly &l, const poly &r) { l.rsz(max(sz(l), sz(r))); F0R(i, sz(r)) l[i] += r[i]; return l; } poly &operator-=(poly &l, const poly &r) { l.rsz(max(sz(l), sz(r))); F0R(i, sz(r)) l[i] -= r[i]; return l; } poly &operator*=(poly &l, const T &r) { each(t, l) t *= r; return l; } poly &operator/=(poly &l, const T &r) { each(t, l) t /= r; return l; } poly operator+(poly l, const poly &r) { return l += r; } poly operator-(poly l, const poly &r) { return l -= r; } poly operator-(poly l) { each(t, l) t *= -1; return l; } poly operator*(poly l, const T &r) { return l *= r; } poly operator*(const T &r, const poly &l) { return l * r; } poly operator/(poly l, const T &r) { return l /= r; } poly operator*(const poly &l, const poly &r) { if (!min(sz(l), sz(r))) return {}; poly x(sz(l) + sz(r) - 1); F0R(i, sz(l)) F0R(j, sz(r)) x[i + j] += l[i] * r[j]; return x; } poly &operator*=(poly &l, const poly &r) { return l = l * r; } pair<poly, poly> quoRemSlow(poly a, poly b) { remz(a); remz(b); assert(sz(b)); T lst = b.bk, B = T(1) / lst; each(t, a) t *= B; each(t, b) t *= B; poly q(max(sz(a) - sz(b) + 1, 0)); for (int dif; (dif = sz(a) - sz(b)) >= 0; remz(a)) { q[dif] = a.bk; F0R(i, sz(b)) a[i + dif] -= q[dif] * b[i]; } each(t, a) t *= lst; return {q, a}; // quotient, remainder } poly operator%(const poly &a, const poly &b) { return quoRemSlow(a, b).s; } /**poly operator/(const poly& a, const poly& b) { return quoRemSlow(a,b).f; } poly a = {1,3,5,8,6,0,0,0,0}, b = {1,5,1}; ps(quoRemSlow(a,b)); a = 2*a, b = 2*b; ps(quoRemSlow(a,b)); poly gcd(poly a, poly b) { return b == poly{} ? a : gcd(b,a%b); }*/ T resultant(poly a, poly b) { // R(A,B) // =b_m^n*prod_{j=1}^mA(mu_j) // =b_m^na_n^m*prod_{i=1}^nprod_{j=1}^m(mu_j-lambda_i) // =(-1)^{mn}a_n^m*prod_{i=1}^nB(lambda_i) // =(-1)^{nm}R(B,A) // Also, R(A,B)=b_m^{deg(A)-deg(A-CB)}R(A-CB,B) int ad = sz(a) - 1, bd = sz(b) - 1; if (bd <= 0) return bd < 0 ? 0 : pow(b.bk, ad); int pw = ad; a = a % b; pw -= (ad = sz(a) - 1); return resultant(b, a) * pow(b.bk, pw) * T((bd & ad & 1) ? -1 : 1); } vmi charpoly(V<vmi> A) { // det(xI - A) int N = sz(A); hessenberg(A); V<vmi> charpoly; charpoly.pb({1}); F0R(i, N) { charpoly.pb(charpoly.bk * vmi{-A.at(i).at(i), 1}); F0R(j, i) { charpoly.bk += ((i - j) & 1 ? -1 : 1) * charpoly.at(j) * -A.at(j).at(i); } if (i + 1 < N) F0R(j, i + 1) charpoly.at(j) *= -A.at(i + 1).at(i); } return charpoly.bk; } vmi det(V<vmi> A, V<vmi> B) { // det(A + Bx) int N = sz(A); int off = 0; mi prod = 1; auto swap_cols = [&](int c1, int c2) { assert(c1 != c2); F0R(r, N) { swap(A.at(r).at(c1), A.at(r).at(c2)); swap(B.at(r).at(c1), B.at(r).at(c2)); } prod *= -1; }; auto sub_rows = [&](int r1, int r2, mi coef) { assert(r1 != r2); F0R(c, N) { A.at(r1).at(c) -= coef * A.at(r2).at(c); B.at(r1).at(c) -= coef * B.at(r2).at(c); } }; auto mul_row = [&](int r, mi coef) { F0R(c, N) { A.at(r).at(c) *= coef; B.at(r).at(c) *= coef; } }; F0R(r, N) { while (B[r][r] == 0) { FOR(c, r + 1, N) if (B.at(r).at(c) != 0) { swap_cols(r, c); break; } if (B[r][r] != 0) break; swap(A.at(r), B.at(r)); ++off; // assert(false); if (off > N) return vmi(N + 1); F0R(ro, r) sub_rows(r, ro, B.at(r).at(ro)); } prod *= B[r][r]; mul_row(r, 1 / B[r][r]); F0R(ro, N) if (r != ro) sub_rows(ro, r, B.at(ro).at(r)); } F0R(i, N) assert(B[i][i] == 1); each(a, A) each(b, a) b *= -1; auto cA = charpoly(A); vmi ret(N + 1); F0R(i, N + 1 - off) ret.at(i) = cA.at(i + off) * prod; return ret; } int main() { // read read read setIO(); def(int, N); V<vmi> A(N, vmi(N)), B(N, vmi(N)); re(A, B); auto ret = det(A, B); each(t, ret) ps(t); // vi P(N); // re(P); // V<vmi> A(N - 1, vmi(N - 1)), B(N - 1, vmi(N - 1)); // auto edge = [&](V<vmi> &v, int x, int y) { // if (x < N - 1) ++v.at(x).at(x); // if (x < N - 1 && y < N - 1) --v.at(x).at(y); // }; // F0R(i, N) FOR(j, i + 1, N) { // if (P[i] > P[j]) { // edge(B, i, j); // edge(B, j, i); // } else { // edge(A, i, j); // edge(A, j, i); // } // } // dbg(A); // dbg(B); // auto ret = det(A, B); // ps(ret); // you should actually read the stuff at the bottom } /* stuff you should look for * int overflow, array bounds * special cases (n=1?) * do smth instead of nothing and stay organized * WRITE STUFF DOWN * DON'T GET STUCK ON ONE APPROACH */