結果
問題 | No.2004 Incremental Coins |
ユーザー | hitonanode |
提出日時 | 2022-07-10 21:06:08 |
言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
結果 |
WA
|
実行時間 | - |
コード長 | 22,631 bytes |
コンパイル時間 | 3,307 ms |
コンパイル使用メモリ | 220,288 KB |
実行使用メモリ | 52,592 KB |
最終ジャッジ日時 | 2024-06-11 11:47:36 |
合計ジャッジ時間 | 6,565 ms |
ジャッジサーバーID (参考情報) |
judge4 / judge5 |
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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 | 1 ms
5,248 KB |
testcase_01 | AC | 1 ms
5,376 KB |
testcase_02 | AC | 1 ms
5,376 KB |
testcase_03 | WA | - |
testcase_04 | WA | - |
testcase_05 | WA | - |
testcase_06 | WA | - |
testcase_07 | WA | - |
testcase_08 | WA | - |
testcase_09 | WA | - |
testcase_10 | AC | 155 ms
52,592 KB |
testcase_11 | WA | - |
testcase_12 | WA | - |
testcase_13 | WA | - |
testcase_14 | WA | - |
testcase_15 | AC | 130 ms
32,672 KB |
testcase_16 | WA | - |
testcase_17 | AC | 119 ms
32,176 KB |
testcase_18 | WA | - |
testcase_19 | WA | - |
testcase_20 | WA | - |
testcase_21 | WA | - |
ソースコード
#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 <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::upper_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) { os << '('; 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 #define dbgif(cond, x) ((cond) ? cerr << BRIGHT_CYAN << #x << COLOR_RESET << " = " << (x) << NORMAL_FAINT << " (L" << __LINE__ << ") " << __FILE__ << COLOR_RESET << endl : cerr) #else #define dbg(x) 0 #define dbgif(cond, x) 0 #endif template <int md> struct ModInt { #if __cplusplus >= 201402L #define MDCONST constexpr #else #define MDCONST #endif using lint = long long; MDCONST static int mod() { return md; } static int get_primitive_root() { static int primitive_root = 0; if (!primitive_root) { primitive_root = [&]() { std::set<int> fac; int 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 (int g = 1; g < md; g++) { bool ok = true; for (auto i : fac) if (ModInt(g).pow((md - 1) / i) == 1) { ok = false; break; } if (ok) return g; } return -1; }(); } return primitive_root; } int val_; int val() const noexcept { return val_; } MDCONST ModInt() : val_(0) {} MDCONST ModInt &_setval(lint v) { return val_ = (v >= md ? v - md : v), *this; } MDCONST ModInt(lint v) { _setval(v % md + md); } 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_ + md); } MDCONST ModInt operator*(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.val_ % md); } MDCONST ModInt operator/(const ModInt &x) const { return ModInt()._setval((lint)val_ * x.inv().val() % md); } MDCONST ModInt operator-() const { return ModInt()._setval(md - 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 % md + x.val_); } friend MDCONST ModInt operator-(lint a, const ModInt &x) { return ModInt()._setval(a % md - x.val_ + md); } friend MDCONST ModInt operator*(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.val_ % md); } friend MDCONST ModInt operator/(lint a, const ModInt &x) { return ModInt()._setval(a % md * x.inv().val() % md); } 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 { ModInt ans = 1, tmp = *this; while (n) { if (n & 1) ans *= tmp; tmp *= tmp, n >>= 1; } return ans; } static std::vector<ModInt> facs, facinvs, invs; MDCONST static void _precalculation(int N) { int l0 = facs.size(); if (N > md) N = md; if (N <= l0) return; facs.resize(N), facinvs.resize(N), invs.resize(N); for (int i = l0; i < N; i++) facs[i] = facs[i - 1] * i; facinvs[N - 1] = facs.back().pow(md - 2); for (int i = N - 2; i >= l0; i--) facinvs[i] = facinvs[i + 1] * (i + 1); for (int i = N - 1; i >= l0; i--) invs[i] = facinvs[i] * facs[i - 1]; } MDCONST ModInt inv() const { if (this->val_ < std::min(md >> 1, 1 << 21)) { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return invs[this->val_]; } else { return this->pow(md - 2); } } MDCONST ModInt fac() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facs[this->val_]; } MDCONST ModInt facinv() const { while (this->val_ >= int(facs.size())) _precalculation(facs.size() * 2); return facinvs[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).facinv() * r.facinv(); } MDCONST ModInt nPr(const ModInt &r) const { return (this->val_ < r.val_) ? 0 : this->fac() * (*this - r).facinv(); } ModInt sqrt() const { if (val_ == 0) return 0; if (md == 2) return val_; if (pow((md - 1) / 2) != 1) return 0; ModInt b = 1; while (b.pow((md - 1) / 2) == 1) b += 1; int e = 0, m = md - 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_, md - x.val_)); } }; template <int md> std::vector<ModInt<md>> ModInt<md>::facs = {1}; template <int md> std::vector<ModInt<md>> ModInt<md>::facinvs = {1}; template <int md> std::vector<ModInt<md>> ModInt<md>::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); 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::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().val(); 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().val(); static const long long m01_inv_m2 = mint2(m01).inv().val(); 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) { if (a.empty() or b.empty()) return {}; 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::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; } template <typename MODINT> std::vector<MODINT> nttconv(const std::vector<MODINT> &a, const std::vector<MODINT> &b) { return nttconv<MODINT>(a, b, false); } // Preorder Euler Tour // (行きがけ順,部分木の頂点クエリ等に有用) struct PreorderEulerTour { int V; // # of vertices of tree int root; std::vector<std::vector<int>> edges; std::vector<int> subtree_begin, subtree_end; std::vector<int> vis_order; void _build_dfs(int now, int prv) { subtree_begin[now] = vis_order.size(); vis_order.push_back(now); for (auto nxt : edges[now]) if (nxt != prv) _build_dfs(nxt, now); subtree_end[now] = vis_order.size(); } PreorderEulerTour() = default; PreorderEulerTour(const std::vector<std::vector<int>> &to, int root) : V(to.size()), root(root), edges(to) { assert(root >= 0 and root < V); subtree_begin.resize(V); subtree_end.resize(V); _build_dfs(root, -1); } }; #include <atcoder/segtree> using S = pair<int, int>; S op(S l, S r) { return max(l, r); } S e() { return {-1, -1}; } struct ConvolutionOnTree { int N; int root; std::vector<int> par; std::vector<std::vector<int>> children; std::vector<int> depth; std::vector<int> farthest_leaf; void _rec_build_hld(int now) { farthest_leaf[now] = now; for (int nxt : children[now]) { depth[nxt] = depth[now] + 1; _rec_build_hld(nxt); if (depth[farthest_leaf[now]] < depth[farthest_leaf[nxt]]) { farthest_leaf[now] = farthest_leaf[nxt]; } } } void _build_hld() { depth.assign(N, 0); farthest_leaf.assign(N, -1); _rec_build_hld(root); } ConvolutionOnTree(std::vector<int> par_) : N(par_.size()), par(par_), children(par.size()) { root = -1; for (int i = 0; i < N; ++i) { if (par[i] >= 0 and par[i] < N) { children[par[i]].push_back(i); } else { assert(root == -1); par[i] = -1; root = i; } } assert(root != -1); _build_hld(); dbg(children); } std::vector<mint> _run_rec(const int r, int h, std::vector<mint> &ret, const std::vector<mint> &f, const std::vector<mint> &trans) { dbg(make_pair(r, h)); const int leaf = farthest_leaf[r], d = depth[leaf] - depth[r] + 1; std::vector<mint> g; std::vector<int> ids; g.reserve(d), ids.reserve(d); for (int cur = leaf, prv = -1;; prv = cur, cur = par[cur]) { ids.push_back(cur); g.push_back(f[cur]); for (int nxt : children[cur]) { if (nxt == prv) continue; int nxtlen = depth[farthest_leaf[nxt]] - depth[cur]; std::vector<mint> gchild = _run_rec(nxt, ids.at(int(ids.size()) - nxtlen - 1), ret, f, trans); for (int i = 0; i < int(gchild.size()); ++i) { g.at(int(g.size()) - int(gchild.size()) - 1 + i) += gchild[i]; } } if (cur == r) break; } std::vector<mint> trans_sub(trans.begin(), trans.begin() + min(trans.size(), g.size())); g = nttconv(g, trans_sub); g.resize(ids.size()); for (int cur = leaf, i = 0;; cur = par[cur], ++i, h = h >= 0 ? par[h] : h) { ret.at(cur) += g.at(i); if (h >= 0) ret.at(h) -= g.at(i); if (cur == r) break; } return g; } std::vector<mint> run(const std::vector<mint> &f, const std::vector<mint> &trans) { std::vector<mint> ret(N, mint()); _run_rec(root, -1, ret, f, trans); return ret; } }; int main() { int N; lint K; cin >> N >> K; vector<mint> A(N + 1); vector<int> par(N); cin >> A >> par; par.insert(par.begin(), -1); // vector<vector<int>> child(N + 1); // FOR(i, 1, N + 1) child[par[i]].push_back(i); // dbg(child); // vector<mint> ret(N + 1); vector<mint> trans(N + 1); { mint tmp = 1; REP(i, trans.size()) { trans[i] = tmp; tmp = tmp * (mint(K) - i) / (i + 1); } } ConvolutionOnTree tree(par); for (auto x : tree.run(A, trans)) cout << x << '\n'; // PreorderEulerTour et(child, 0); // using PP = pair<int, mint>; // vector<int> depth(N + 1); // auto dfs_depth = [&](auto &&self, int now) -> void { // for (auto nxt : child[now]) { // chmax(depth[nxt], depth[now] + 1); // self(self, nxt); // } // }; // dfs_depth(dfs_depth, 0); // vector<vector<pair<int, mint>>> acs(N + 1, vector<pair<int, mint>>(1, pair<int, mint>(-1, 0))); // for (auto i : et.vis_order) { // mint sum = acs[depth[i]].back().second + A[i]; // acs[depth[i]].emplace_back(et.subtree_begin[i], sum); // } // vector<S> depth_segtree; // for (auto i : et.vis_order) depth_segtree.emplace_back(depth[i], i); // atcoder::segtree<S, op, e> tree(depth_segtree); // auto subtree_getter = [&](int i) -> vector<mint> { // int farthest = tree.prod(et.subtree_begin[i], et.subtree_end[i]).second; // vector<mint> ret; // FOR(d, depth[i], depth[farthest] + 1) { // auto l = arglb(acs[d], PP(et.subtree_begin[i], 0)) - 1; // auto r = arglb(acs[d], PP(et.subtree_end[i], 0)) - 1; // ret.push_back(acs[d][r].second - acs[d][l].second); // } // return ret; // }; // auto find_farthest = [&](int i) -> int { // int farthest = tree.prod(et.subtree_begin[i], et.subtree_end[i]).second; // return farthest; // }; // auto rec = [&](auto &&self, int root, int erase_pointer) -> void { // const int c = find_farthest(root); // vector<int> path; // vector<mint> atmp = subtree_getter(root); // reverse(ALL(atmp)); // for (int i = c; i != root; i = par[i]) { // path.push_back(i); // } // path.push_back(root); // vector<mint> tt(atmp.size()); // REP(i, tt.size()) tt[i] = trans[i]; // auto conv = nttconv(atmp, tt); // int p = c, pinv = erase_pointer; // int cur = 0; // while (true) { // ret[p] += conv[cur]; // if (pinv >= 0) ret[pinv] -= conv[cur]; // if (p == root) break; // p = par[p]; // if (pinv >= 0) pinv = par[pinv]; // cur++; // } // reverse(ALL(path)); // int prv = -1; // for (auto i = c; i >= 0; i = par[i]) { // for (auto nxt : child[i]) { // if (nxt == prv) continue; // int f = find_farthest(nxt); // int dd = depth[f] - depth[root]; // self(self, nxt, path[dd]); // } // if (i == root) break; // prv = i; // } // }; // rec(rec, 0, -1); // for (auto x : ret) cout << x << '\n'; }