結果
問題 | No.2039 Copy and Avoid |
ユーザー | hitonanode |
提出日時 | 2022-08-12 23:03:27 |
言語 | C++23 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 37 ms / 2,000 ms |
コード長 | 21,500 bytes |
コンパイル時間 | 2,226 ms |
コンパイル使用メモリ | 188,808 KB |
実行使用メモリ | 7,928 KB |
最終ジャッジ日時 | 2024-09-23 03:42:50 |
合計ジャッジ時間 | 3,391 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 | 37 ms
7,912 KB |
testcase_01 | AC | 10 ms
7,788 KB |
testcase_02 | AC | 10 ms
7,848 KB |
testcase_03 | AC | 10 ms
7,904 KB |
testcase_04 | AC | 10 ms
7,816 KB |
testcase_05 | AC | 10 ms
7,836 KB |
testcase_06 | AC | 10 ms
7,928 KB |
testcase_07 | AC | 9 ms
7,856 KB |
testcase_08 | AC | 10 ms
7,920 KB |
testcase_09 | AC | 9 ms
7,788 KB |
testcase_10 | AC | 10 ms
7,832 KB |
testcase_11 | AC | 9 ms
7,812 KB |
testcase_12 | AC | 10 ms
7,852 KB |
testcase_13 | AC | 37 ms
7,828 KB |
testcase_14 | AC | 37 ms
7,904 KB |
testcase_15 | AC | 37 ms
7,876 KB |
testcase_16 | AC | 35 ms
7,908 KB |
testcase_17 | AC | 11 ms
7,908 KB |
testcase_18 | AC | 10 ms
7,812 KB |
testcase_19 | AC | 10 ms
7,908 KB |
testcase_20 | AC | 12 ms
7,792 KB |
testcase_21 | AC | 10 ms
7,792 KB |
testcase_22 | AC | 9 ms
7,824 KB |
testcase_23 | AC | 10 ms
7,908 KB |
testcase_24 | AC | 10 ms
7,788 KB |
testcase_25 | AC | 9 ms
7,880 KB |
testcase_26 | AC | 9 ms
7,848 KB |
testcase_27 | AC | 9 ms
7,808 KB |
testcase_28 | AC | 10 ms
7,852 KB |
testcase_29 | AC | 9 ms
7,780 KB |
testcase_30 | AC | 9 ms
7,908 KB |
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 // 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((1 << 20)); template <typename T, T INF = std::numeric_limits<T>::max() / 2, int INVALID = -1> struct shortest_path { int V, E; bool single_positive_weight; T wmin, wmax; std::vector<std::pair<int, T>> tos; std::vector<int> head; std::vector<std::tuple<int, int, T>> edges; void build_() { if (int(tos.size()) == E and int(head.size()) == V + 1) return; tos.resize(E); head.assign(V + 1, 0); for (const auto &e : edges) ++head[std::get<0>(e) + 1]; for (int i = 0; i < V; ++i) head[i + 1] += head[i]; auto cur = head; for (const auto &e : edges) { tos[cur[std::get<0>(e)]++] = std::make_pair(std::get<1>(e), std::get<2>(e)); } } shortest_path(int V = 0) : V(V), E(0), single_positive_weight(true), wmin(0), wmax(0) {} void add_edge(int s, int t, T w) { assert(0 <= s and s < V); assert(0 <= t and t < V); edges.emplace_back(s, t, w); ++E; if (w > 0 and wmax > 0 and wmax != w) single_positive_weight = false; wmin = std::min(wmin, w); wmax = std::max(wmax, w); } void add_bi_edge(int u, int v, T w) { add_edge(u, v, w); add_edge(v, u, w); } std::vector<T> dist; std::vector<int> prev; // Dijkstra algorithm // - Requirement: wmin >= 0 // - Complexity: O(E log E) using Pque = std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>, std::greater<std::pair<T, int>>>; template <class Heap = Pque> void dijkstra(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF); prev.assign(V, INVALID); dist[s] = 0; Heap pq; pq.emplace(0, s); while (!pq.empty()) { T d; int v; std::tie(d, v) = pq.top(); pq.pop(); if (t == v) return; if (dist[v] < d) continue; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = d + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; pq.emplace(dnx, nx.first); } } } } // Dijkstra algorithm // - Requirement: wmin >= 0 // - Complexity: O(V^2 + E) void dijkstra_vquad(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF); prev.assign(V, INVALID); dist[s] = 0; std::vector<char> fixed(V, false); while (true) { int r = INVALID; T dr = INF; for (int i = 0; i < V; i++) { if (!fixed[i] and dist[i] < dr) r = i, dr = dist[i]; } if (r == INVALID or r == t) break; fixed[r] = true; int nxt; T dx; for (int e = head[r]; e < head[r + 1]; ++e) { std::tie(nxt, dx) = tos[e]; if (dist[nxt] > dist[r] + dx) dist[nxt] = dist[r] + dx, prev[nxt] = r; } } } // Bellman-Ford algorithm // - Requirement: no negative loop // - Complexity: O(VE) bool bellman_ford(int s, int nb_loop) { assert(0 <= s and s < V); build_(); dist.assign(V, INF), prev.assign(V, INVALID); dist[s] = 0; for (int l = 0; l < nb_loop; l++) { bool upd = false; for (int v = 0; v < V; v++) { if (dist[v] == INF) continue; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = dist[v] + nx.second; if (dist[nx.first] > dnx) dist[nx.first] = dnx, prev[nx.first] = v, upd = true; } } if (!upd) return true; } return false; } // Bellman-ford algorithm using deque // - Requirement: no negative loop // - Complexity: O(VE) void spfa(int s) { assert(0 <= s and s < V); build_(); dist.assign(V, INF); prev.assign(V, INVALID); dist[s] = 0; std::deque<int> q; std::vector<char> in_queue(V); q.push_back(s), in_queue[s] = 1; while (!q.empty()) { int now = q.front(); q.pop_front(), in_queue[now] = 0; for (int e = head[now]; e < head[now + 1]; ++e) { const auto &nx = tos[e]; T dnx = dist[now] + nx.second; int nxt = nx.first; if (dist[nxt] > dnx) { dist[nxt] = dnx; if (!in_queue[nxt]) { if (q.size() and dnx < dist[q.front()]) { // Small label first optimization q.push_front(nxt); } else { q.push_back(nxt); } prev[nxt] = now, in_queue[nxt] = 1; } } } } } // 01-BFS // - Requirement: all weights must be 0 or w (positive constant). // - Complexity: O(V + E) void zero_one_bfs(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF), prev.assign(V, INVALID); dist[s] = 0; std::vector<int> q(V * 4); int ql = V * 2, qr = V * 2; q[qr++] = s; while (ql < qr) { int v = q[ql++]; if (v == t) return; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = dist[v] + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; if (nx.second) { q[qr++] = nx.first; } else { q[--ql] = nx.first; } } } } } // Dial's algorithm // - Requirement: wmin >= 0 // - Complexity: O(wmax * V + E) void dial(int s, int t = INVALID) { assert(0 <= s and s < V); build_(); dist.assign(V, INF), prev.assign(V, INVALID); dist[s] = 0; std::vector<std::vector<std::pair<int, T>>> q(wmax + 1); q[0].emplace_back(s, dist[s]); int ninq = 1; int cur = 0; T dcur = 0; for (; ninq; ++cur, ++dcur) { if (cur == wmax + 1) cur = 0; while (!q[cur].empty()) { int v = q[cur].back().first; T dnow = q[cur].back().second; q[cur].pop_back(), --ninq; if (v == t) return; if (dist[v] < dnow) continue; for (int e = head[v]; e < head[v + 1]; ++e) { const auto &nx = tos[e]; T dnx = dist[v] + nx.second; if (dist[nx.first] > dnx) { dist[nx.first] = dnx, prev[nx.first] = v; int nxtcur = cur + int(nx.second); if (nxtcur >= int(q.size())) nxtcur -= q.size(); q[nxtcur].emplace_back(nx.first, dnx), ++ninq; } } } } } // Solver for DAG // - Requirement: graph is DAG // - Complexity: O(V + E) bool dag_solver(int s) { assert(0 <= s and s < V); build_(); dist.assign(V, INF), prev.assign(V, INVALID); dist[s] = 0; std::vector<int> indeg(V, 0); std::vector<int> q(V * 2); int ql = 0, qr = 0; q[qr++] = s; while (ql < qr) { int now = q[ql++]; for (int e = head[now]; e < head[now + 1]; ++e) { const auto &nx = tos[e]; ++indeg[nx.first]; if (indeg[nx.first] == 1) q[qr++] = nx.first; } } ql = qr = 0; q[qr++] = s; while (ql < qr) { int now = q[ql++]; for (int e = head[now]; e < head[now + 1]; ++e) { const auto &nx = tos[e]; --indeg[nx.first]; if (dist[nx.first] > dist[now] + nx.second) dist[nx.first] = dist[now] + nx.second, prev[nx.first] = now; if (indeg[nx.first] == 0) q[qr++] = nx.first; } } return *max_element(indeg.begin(), indeg.end()) == 0; } // Retrieve a sequence of vertex ids that represents shortest path [s, ..., goal] // If not reachable to goal, return {} std::vector<int> retrieve_path(int goal) const { assert(int(prev.size()) == V); assert(0 <= goal and goal < V); if (dist[goal] == INF) return {}; std::vector<int> ret{goal}; while (prev[goal] != INVALID) { goal = prev[goal]; ret.push_back(goal); } std::reverse(ret.begin(), ret.end()); return ret; } void solve(int s, int t = INVALID) { if (wmin >= 0) { if (single_positive_weight) { zero_one_bfs(s, t); } else if (wmax <= 10) { dial(s, t); } else { if ((long long)V * V < (E << 4)) { dijkstra_vquad(s, t); } else { dijkstra(s, t); } } } else { bellman_ford(s, V); } } // Warshall-Floyd algorithm // - Requirement: no negative loop // - Complexity: O(E + V^3) std::vector<std::vector<T>> floyd_warshall() { build_(); std::vector<std::vector<T>> dist2d(V, std::vector<T>(V, INF)); for (int i = 0; i < V; i++) { dist2d[i][i] = 0; for (const auto &e : edges) { int s = std::get<0>(e), t = std::get<1>(e); dist2d[s][t] = std::min(dist2d[s][t], std::get<2>(e)); } } for (int k = 0; k < V; k++) { for (int i = 0; i < V; i++) { if (dist2d[i][k] == INF) continue; for (int j = 0; j < V; j++) { if (dist2d[k][j] == INF) continue; dist2d[i][j] = std::min(dist2d[i][j], dist2d[i][k] + dist2d[k][j]); } } } return dist2d; } void to_dot(std::string filename = "shortest_path") const { std::ofstream ss(filename + ".DOT"); ss << "digraph{\n"; build_(); for (int i = 0; i < V; i++) { for (int e = head[i]; e < head[i + 1]; ++e) { ss << i << "->" << tos[e].first << "[label=" << tos[e].second << "];\n"; } } ss << "}\n"; ss.close(); return; } }; int main() { int N, M, A, B; cin >> N >> M >> A >> B; auto ds = sieve.divisors(N); sort(ds.begin(), ds.end()); dbg(ds); vector<int> C(M); cin >> C; vector<lint> dp(ds.size(), 1LL << 60); dp[0] = 0; // shortest_path<lint> graph(ds.size()); REP(s, ds.size()) { if (ds[s] >= ds.back()) continue; int v0 = ds.at(s); int hi = N; for (auto c : C) { if (c % v0 == 0) { chmin(hi, c - 1); } } if (hi < v0) continue; FOR(t, s + 1, ds.size()) { int v1 = ds.at(t); if (v1 > hi or v1 % v0) continue; chmin(dp[t], dp[s] + (v1 / v0 - 1) * lint(A) + B); } } // graph.solve(0); // auto ret = graph.dist.back(); auto ret = dp.back(); if (ret > 1LL << 58) { puts("-1"); } else { cout << ret - B << endl; } }