#include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include using namespace std; using lint = long long; using pint = pair; using plint = pair; 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##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template void ndarray(vector& vec, const V& val, int len) { vec.assign(len, val); } template void ndarray(vector& vec, const V& val, int len, Args... args) { vec.resize(len), for_each(begin(vec), end(vec), [&](T& v) { ndarray(v, val, args...); }); } template bool chmax(T &m, const T q) { return m < q ? (m = q, true) : false; } template bool chmin(T &m, const T q) { return m > q ? (m = q, true) : false; } const std::vector> 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 T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); } template std::pair operator+(const std::pair &l, const std::pair &r) { return std::make_pair(l.first + r.first, l.second + r.second); } template std::pair operator-(const std::pair &l, const std::pair &r) { return std::make_pair(l.first - r.first, l.second - r.second); } template std::vector sort_unique(std::vector vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; } template int arglb(const std::vector &v, const T &x) { return std::distance(v.begin(), std::lower_bound(v.begin(), v.end(), x)); } template int argub(const std::vector &v, const T &x) { return std::distance(v.begin(), std::upper_bound(v.begin(), v.end(), x)); } template IStream &operator>>(IStream &is, std::vector &vec) { for (auto &v : vec) is >> v; return is; } template OStream &operator<<(OStream &os, const std::vector &vec); template OStream &operator<<(OStream &os, const std::array &arr); template OStream &operator<<(OStream &os, const std::unordered_set &vec); template OStream &operator<<(OStream &os, const pair &pa); template OStream &operator<<(OStream &os, const std::deque &vec); template OStream &operator<<(OStream &os, const std::set &vec); template OStream &operator<<(OStream &os, const std::multiset &vec); template OStream &operator<<(OStream &os, const std::unordered_multiset &vec); template OStream &operator<<(OStream &os, const std::pair &pa); template OStream &operator<<(OStream &os, const std::map &mp); template OStream &operator<<(OStream &os, const std::unordered_map &mp); template OStream &operator<<(OStream &os, const std::tuple &tpl); template OStream &operator<<(OStream &os, const std::vector &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::array &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; } template std::istream &operator>>(std::istream &is, std::tuple &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; } template OStream &operator<<(OStream &os, const std::tuple &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; } template OStream &operator<<(OStream &os, const std::unordered_set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::deque &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; } template OStream &operator<<(OStream &os, const std::set &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_multiset &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::pair &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; } template OStream &operator<<(OStream &os, const std::map &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; } template OStream &operator<<(OStream &os, const std::unordered_map &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 // Fibonacci heap // - Complexity: // - empty(), size(), top(), push(), meld(): O(1) // - pop(), decrease(): O(lg N) amortized // - Reference: // - "Introduction to Algorithms, Third Edition", Chapter 19 // - // - template struct fibonacci_heap { struct Node { Tp val; int deg; Node *parent, *left, *right, *child; bool mark; Node() = default; Node(Node const &) = default; Node(Node &&) = default; Node &operator=(Node const &) = default; Node &operator=(Node &&) = default; Node(Tp v) : val(v), deg(0), parent(nullptr), left(nullptr), right(nullptr), child(nullptr), mark(false) {} friend std::ostream &operator<<(std::ostream &os, const Node &n) { os << '(' << n.val << ','; if (n.child != nullptr) os << *(n.child) << ','; Node *now = n.right; while (now != &n) { os << now->val << ','; if (now->child != nullptr) os << *now->child << ','; now = now->right; } os << ')'; return os; } }; int sz; std::list roots; Node *ptop; inline void _chmin(Node *cand) noexcept { if (ptop == nullptr or cand->val < ptop->val) ptop = cand; } fibonacci_heap() : sz(0), roots({}), ptop(nullptr) {} bool empty() const noexcept { return sz == 0; } int size() const noexcept { return sz; } std::array _arr; void _fmerge(Node *ptr) { int d = ptr->deg; if (_arr[d] == nullptr) _arr[d] = ptr; else { Node *cptr = _arr[d]; if (cptr->val < ptr->val) std::swap(ptr, cptr); ptr->deg++; cptr->parent = ptr; if (ptr->child == nullptr) ptr->child = cptr; else { Node *cl = ptr->child, *cr = ptr->child->right; assert(cl->right == cr and cr->left == cl); cptr->left = cl, cptr->right = cr, cl->right = cr->left = cptr; } _arr[d] = nullptr; _fmerge(ptr); } } void _consolidate() { _arr.fill(nullptr); for (auto ptr : roots) if (ptr != nullptr) { if (ptr->deg < 0) delete ptr; else _fmerge(ptr); } roots.clear(), ptop = nullptr; for (auto ptr : _arr) if (ptr != nullptr) _add_tree(ptr); } void _add_tree(Node *root) noexcept { root->parent = nullptr; root->left = root->right = root; roots.emplace_back(root); _chmin(root); } Node *push(const Tp &val) noexcept { sz++; Node *ptr = new Node(val); _add_tree(ptr); return ptr; } void meld(fibonacci_heap &&hp) { sz += hp.sz; roots.splice(roots.end(), hp.roots); if (hp.ptop != nullptr) _chmin(hp.ptop); } void pop() { assert(sz > 0); sz--; Node *ch1 = ptop->child; if (ch1 != nullptr) { Node *now = ch1; while (true) { Node *nxt = now->right; _add_tree(now); now = nxt; if (now == ch1) break; } } ptop->deg = -1; _consolidate(); } void _deldfs(Node *now) { while (now != nullptr) { if (now->child != nullptr) _deldfs(now->child); Node *nxt = now->right; delete now; now = nxt; } } void clear() { for (auto root : roots) _deldfs(root); sz = 0; roots.clear(); ptop = nullptr; } void _cut(Node *x) noexcept { Node *y = x->parent; assert(y != nullptr and y->deg > 0); Node *xr = x->right, *xl = x->left; if (x == xr) { y->child = nullptr; } else { y->child = xr; xl->right = xr, xr->left = xl; } y->deg--; _add_tree(x); x->mark = false; } void _cascading_cut(Node *now) noexcept { assert(now != nullptr); Node *par = now->parent; if (par == nullptr) return; if (!now->mark) now->mark = true; else { _cut(now); _cascading_cut(par); } } void erase(Node *r) { if (r->parent != nullptr) { Node *rpar = r->parent; _cut(r); _cascading_cut(rpar); } ptop = r; pop(); } bool decrease(Node *r, const Tp new_val) { assert(r != nullptr); if (!(new_val < r->val)) return false; r->val = new_val; if (r->parent != nullptr and new_val < r->parent->val) { Node *rpar = r->parent; _cut(r); _cascading_cut(rpar); } _chmin(r); return true; } Tp top() const { assert(ptop != nullptr); return ptop->val; } friend std::ostream &operator<<(std::ostream &os, const fibonacci_heap &hp) { os << "[(fibonacci_heap: sz=" << hp.sz << ", top=" << hp.ptop->val << ", #tree = " << hp.roots.size() << ")"; for (auto x : hp.roots) { os << *x << ", "; } os << ']'; return os; } }; template struct heap { using P = std::pair; fibonacci_heap

_heap; std::vector::Node *> vp; std::vector result; void initialize(int N, Tp initval) { _heap.clear(); vp.resize(N); result.assign(N, initval); for (int i = 0; i < N; i++) { vp[i] = _heap.push(std::make_pair(initval, i)); } } heap(int N, Tp initval) { initialize(N, initval); } bool chmin(int i, Tp val) { if (val < result[i]) { result[i] = val; if (vp[i] == nullptr) { vp[i] = _heap.push(std::make_pair(result[i], i)); } else { _heap.decrease(vp[i], std::make_pair(result[i], i)); } return true; } return false; } Tp operator[](int i) const { return result.at(i); } P top() { return _heap.top(); } P pop() { P ret = _heap.top(); _heap.pop(); return ret; } int size() { return _heap.size(); } bool empty() { return _heap.empty(); } }; vector solve(int N, lint A, lint B, lint C) { const int gs = N * 2; vector ret(N * 2, 1LL << 60); heap hp(N * 2, 1LL << 60); FOR(n, 1, N + 1) hp.chmin(n == N ? 0 : n, A * n + B); while (!hp.empty()) { auto [hi, i] = hp.pop(); ret[i] = hi; if (i < N) { int j = i * 2; if (j >= N) j -= N; hp.chmin(j, hi + C); hp.chmin(i + N, hi + B); } else { hp.chmin(i - N, hi); int j = i + 1; if (j == N * 2) j = N; hp.chmin(j, hi + A); } } ret.resize(N); return ret; } int main() { int N, A, B, C; cin >> N >> A >> B >> C; for (lint x : solve(N, A, B, C)) cout << x << '\n'; }