結果
| 問題 | No.1529 Constant Lcm |
| ユーザー |
 iiljj
|
| 提出日時 | 2021-06-04 20:27:33 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 686 ms / 3,000 ms |
| コード長 | 12,433 bytes |
| コンパイル時間 | 1,808 ms |
| コンパイル使用メモリ | 144,820 KB |
| 最終ジャッジ日時 | 2025-01-21 22:04:11 |
|
ジャッジサーバーID （参考情報） |
judge5 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 24 |
ソースコード
/* #region Head */// #include <bits/stdc++.h>#include <algorithm>#include <array>#include <bitset>#include <cassert> // assert.h#include <cmath> // math.h#include <cstring>#include <ctime>#include <deque>#include <fstream>#include <functional>#include <iomanip>#include <iostream>#include <list>#include <map>#include <memory>#include <numeric>#include <queue>#include <random>#include <set>#include <sstream>#include <stack>#include <string>#include <unordered_map>#include <unordered_set>#include <vector>using namespace std;using ll = long long;using ull = unsigned long long;using ld = long double;using pll = pair<ll, ll>;template <class T> using vc = vector<T>;template <class T> using vvc = vc<vc<T>>;using vll = vc<ll>;using vvll = vvc<ll>;using vld = vc<ld>;using vvld = vvc<ld>;using vs = vc<string>;using vvs = vvc<string>;template <class T, class U> using um = unordered_map<T, U>;template <class T> using pq = priority_queue<T>;template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;template <class T> using us = unordered_set<T>;#define TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)#define REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); itr++)#define ALL(x) begin(x), end(x)#define SIZE(x) ((ll)(x).size())#define PERM(c) \sort(ALL(c)); \for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))#define UNIQ(v) v.erase(unique(ALL(v)), v.end());#define CEIL(a, b) (((a) + (b)-1) / (b))#define endl '\n'constexpr ll INF = 1'010'000'000'000'000'017LL;constexpr int IINF = 1'000'000'007LL;// constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7constexpr ll MOD = 998244353;constexpr ld EPS = 1e-12;constexpr ld PI = 3.14159265358979323846;template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力for (T &x : vec) is >> x;return is;}template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec) { // vector 出力 (for dump)os << "{";REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");os << "}";return os;}template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec) { // vector 出力 (inline)REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");return os;}template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力REP(i, 0, SIZE(arr)) is >> arr[i];return is;}template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)os << "{";REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");os << "}";return os;}template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力is >> pair_var.first >> pair_var.second;return is;}template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var) { // pair 出力os << "(" << pair_var.first << ", " << pair_var.second << ")";return os;}// map, um, set, us 出力template <class T> ostream &out_iter(ostream &os, const T &map_var) {os << "{";REPI(itr, map_var) {os << *itr;auto itrcp = itr;if (++itrcp != map_var.end()) os << ", ";}return os << "}";}template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var) {return out_iter(os, map_var);}template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var) {os << "{";REPI(itr, map_var) {auto [key, value] = *itr;os << "(" << key << ", " << value << ")";auto itrcp = itr;if (++itrcp != map_var.end()) os << ", ";}os << "}";return os;}template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var) { return out_iter(os, set_var); }template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var) {pq<T> pq_cp(pq_var);os << "{";if (!pq_cp.empty()) {os << pq_cp.top(), pq_cp.pop();while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();}return os << "}";}void pprint() { cout << endl; }template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {cout << head;if (sizeof...(Tail) > 0) cout << ' ';pprint(move(tail)...);}// dump#define DUMPOUT cerrvoid dump_func() { DUMPOUT << endl; }template <class Head, class... Tail> void dump_func(Head &&head, Tail &&...tail) {DUMPOUT << head;if (sizeof...(Tail) > 0) DUMPOUT << ", ";dump_func(move(tail)...);}// chmax (更新「される」かもしれない値が前)template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {if (comp(xmax, x)) {xmax = x;return true;}return false;}// chmin (更新「される」かもしれない値が前)template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {if (comp(x, xmin)) {xmin = x;return true;}return false;}// ローカル用#ifndef ONLINE_JUDGE#define DEBUG_#endif#ifdef DEBUG_#define DEB#define dump(...) \DUMPOUT << " " << string(#__VA_ARGS__) << ": " \<< "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \<< " ", \dump_func(__VA_ARGS__)#else#define DEB if (false)#define dump(...)#endif#define VAR(type, ...) \type __VA_ARGS__; \cin >> __VA_ARGS__;template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }struct AtCoderInitialize {static constexpr int IOS_PREC = 15;static constexpr bool AUTOFLUSH = false;AtCoderInitialize() {ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);cout << fixed << setprecision(IOS_PREC);if (AUTOFLUSH) cout << unitbuf;}} ATCODER_INITIALIZE;void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }/* #endregion */// #include <atcoder/all>// using namespace atcoder;/* #region mint */// 自動で MOD を取る整数struct mint {ll x;mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}mint &operator+=(const mint a) {if ((x += a.x) >= MOD) x -= MOD;return *this;}mint &operator-=(const mint a) {if ((x += MOD - a.x) >= MOD) x -= MOD;return *this;}mint &operator*=(const mint a) {(x *= a.x) %= MOD;return *this;}mint operator+(const mint a) const {mint res(*this);return res += a;}mint operator-(const mint a) const {mint res(*this);return res -= a;}mint operator*(const mint a) const {mint res(*this);return res *= a;}// O(log(t))mint pow(ll t) const {if (!t) return 1;mint a = pow(t >> 1); // ⌊t/2⌋ 乗a *= a; // ⌊t/2⌋*2 乗if (t & 1) // ⌊t/2⌋*2 == t-1 のときa *= *this; // ⌊t/2⌋*2+1 乗 => t 乗return a;}// for prime modmint inv() const {return pow(MOD - 2); // オイラーの定理から， x^(-1) ≡ x^(p-2)}mint &operator/=(const mint a) { return (*this) *= a.inv(); }mint operator/(const mint a) const {mint res(*this);return res /= a;}bool operator==(const mint a) const { return this->x == a.x; }bool operator==(const ll a) const { return this->x == a; }// mint 入力friend istream &operator>>(istream &is, mint &x) {is >> x.x;return is;}// mint 出力friend ostream &operator<<(ostream &os, mint x) {os << x.x;return os;}};/* #endregion *//* #region BigLCM */// 10^6 程度以下の整数の集合の LCM が巨大になるときに使うclass BigLCM {ll R; // lcm() の引数の最大値vll cnt; // 素因数が最大何回使われたかカウントするテーブルpublic:BigLCM(ll R) : R(R), cnt(vll(R + 1, 0)) {}// LCM 計算対象の整数を追加するvoid append(ll n) {REPM(i, 2, ceil(sqrt(n))) { // exec PFDll c = 0; // n を i で割れる回数while (n % i == 0) n /= i, c++;chmax(cnt[i], c);}if (n > 1) chmax(cnt[n], 1); // 残り物があったらそれは素数}void append(const map<int, int> &mp) {for (auto [k, v] : mp) {chmax(cnt[k], v); //}}// mint 型で LCM を計算して返すmint lcmmint() {mint l = 1;REPM(i, 1, R) if (cnt[i] > 0) REP(j, 0, cnt[i]) l *= i;return l;}};/* #endregion */struct Sieve {int n;int sqrtn;vc<int> sieve; // sieve[i] := i の最小の素因数// コンストラクタ．前処理を行う．Sieve(int n) : n(n), sqrtn((int)sqrtl(n)), sieve(n + 1) {iota(ALL(sieve), 0); // 各要素をインデックスで初期化（0, 1, ..., n）．使用するのは 2, 3, ...REPM(i, 2, sqrtn) {if (sieve[i] < i) continue; // i は合成数// assert(i は素数)sieve[i] = i;// n 以下の任意の i の倍数 j について，j が i 未満の素数で割れなかった場合REPMD(j, i * i, n, i) if (sieve[j] == j) sieve[j] = i; // j の最小の素因数は i}}// 素因数分解クエリ，O(log n)vc<int> pfd(int n) const {vc<int> prime_factors;while (n > 1) {prime_factors.push_back(sieve[n]);n /= sieve[n];}return prime_factors;}// 素因数分解クエリ，O(log n)map<int, int> pfd_map(int n) const {map<int, int> prime_factors; //while (n > 1) {prime_factors[sieve[n]]++;n /= sieve[n];}return prime_factors;}vc<int> primes() const {vc<int> ret;REPM(i, 2, n) if (sieve[i] == i) ret.push_back(i);return ret;}};// Problemvoid solve() {VAR(ll, n); //Sieve s(n + 1);BigLCM biglcm(n + 1);REPM(i, 1, n - 1) {// i*(n-i)vc<int> a = s.pfd(i);vc<int> b = s.pfd(n - i);map<int, int> mp;for (auto aa : a) mp[aa]++;for (auto bb : b) mp[bb]++;biglcm.append(mp);}pprint(biglcm.lcmmint());}// entry pointint main() {solve();return 0;}