結果
| 問題 |
No.2829 GCD Divination
|
| コンテスト | |
| ユーザー |
 iiljj
|
| 提出日時 | 2024-08-02 22:58:37 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 13,049 bytes |
| コンパイル時間 | 2,049 ms |
| コンパイル使用メモリ | 181,668 KB |
| 実行使用メモリ | 283,452 KB |
| 最終ジャッジ日時 | 2024-08-02 22:58:43 |
| 合計ジャッジ時間 | 5,496 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 2 TLE * 1 -- * 32 |
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 ISIZE(x) ((int)(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 + 7
// constexpr ll MOD = 998244353;
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;
// 前方宣言
template <typename T> istream &operator>>(istream &is, vc<T> &vec);
template <typename T> ostream &operator<<(ostream &os, const vc<T> &vec);
template <typename T> ostream &operator>>(ostream &os, const vc<T> &vec);
template <typename T, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr);
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr);
template <typename T, size_t _Nm> ostream &operator>>(ostream &os, const array<T, _Nm> &arr);
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var);
template <typename T, typename U> ostream &operator<<(ostream &os, const pair<T, U> &pair_var);
template <class T> ostream &out_iter(ostream &os, const T &map_var);
template <typename T, typename U> ostream &operator<<(ostream &os, const map<T, U> &map_var);
template <typename T, typename U> ostream &operator<<(ostream &os, const um<T, U> &map_var);
template <typename T> ostream &operator<<(ostream &os, const set<T> &set_var);
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var);
template <typename T> ostream &operator<<(ostream &os, const pq<T> &pq_var);
template <typename T> ostream &operator<<(ostream &os, const queue<T> &queue_var);
template <typename T> ostream &operator<<(ostream &os, const stack<T> &stk_var);
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 << "}";
}
// tuple 出力
template <size_t N = 0, bool end_line = false, typename... Args> ostream &operator<<(ostream &os, tuple<Args...> &a) {
if constexpr (N < std::tuple_size_v<tuple<Args...>>) {
os << get<N>(a);
if constexpr (N + 1 < std::tuple_size_v<tuple<Args...>>) {
os << ' ';
} else if constexpr (end_line) {
os << '\n';
}
return operator<< <N + 1, end_line>(os, a);
}
return os;
}
template <typename... Args> void print_tuple(tuple<Args...> &a) { operator<< <0, true>(std::cout, a); }
void pprint() { std::cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
std::cout << head;
if (sizeof...(Tail) > 0) std::cout << ' ';
pprint(move(tail)...);
}
// dump
#define DUMPOUT cerr
void 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
#ifndef MYLOCAL
#undef 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__; \
assert((std::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), std::cin.tie(nullptr), std::cout.tie(nullptr);
std::cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) std::cout << unitbuf;
}
} ATCODER_INITIALIZE;
void Yn(bool p) { std::cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { std::cout << (p ? "YES" : "NO") << endl; }
template <typename T> constexpr void operator--(vc<T> &v, int) noexcept {
for (int i = 0; i < ISIZE(v); ++i)
v[i]--;
}
template <typename T> constexpr void operator++(vc<T> &v, int) noexcept {
for (int i = 0; i < ISIZE(v); ++i)
v[i]++;
}
/* #endregion */
// #include <atcoder/all>
// using namespace atcoder;
struct Eratosthenes {
int n;
vc<int> is_prime;
vc<int> min_factor;
vc<int> mobius; // mobius[i] := メビウス関数 μ(i)
Eratosthenes(const int n) : n(n), is_prime(n + 1, true), min_factor(n + 1, -1), mobius(n + 1, 1) {
is_prime[0] = false;
is_prime[1] = false;
min_factor[1] = 1;
TREPM(int, p, 2, n) {
if (not is_prime[p]) {
continue;
}
min_factor[p] = p;
mobius[p] = -1;
int q = p * 2;
while (q <= n) {
is_prime[q] = false;
if (min_factor[q] == -1) {
min_factor[q] = p;
}
if ((q / p) % p == 0) {
mobius[q] = 0;
} else {
mobius[q] = -mobius[q];
}
q += p;
}
}
}
// n 以下の素数一覧を返す
vc<int> primes() const {
vc<int> ret;
REPM(i, 2, n) if (is_prime[i]) ret.push_back(i);
return ret;
}
// N の素因数分解
vc<pair<int, int>> factorize(const int N) const {
vc<pair<int, int>> ret;
int n = N;
while (n > 1) {
const int p = min_factor[n];
int exp = 0;
while (min_factor[n] == p) {
n /= p;
exp += 1;
}
ret.emplace_back(p, exp);
}
return ret;
}
// N の約数
vc<int> divisors(const int N) const {
vc<int> ret = {1};
vc<pair<int, int>> pf = factorize(N);
for (const auto &[p, exp] : pf) {
const int m = ISIZE(ret);
TREP(int, i, 0, m) {
int v = 1;
TREP(int, j, 0, exp) {
v *= p;
ret.push_back(ret[i] * v);
}
}
}
sort(ALL(ret));
return ret;
}
};
// Problem
void solve() {
VAR(ll, n); //
Eratosthenes s(n + 1);
// dp[i] := iが1になるまでの回数の期待値
vc<ld> dp(n + 1, -1);
dp[1] = 0;
REP(i, 2, n + 1) {
// 1以上i未満へ遷移した場合の期待値を求める
const vc<int> divisors = s.divisors(i);
// dump(i, divisors);
ld dsum = 0.0l;
for (const int &d : divisors) {
// if (d == i) continue;
dsum += dp[d] + 1.0l;
}
// dump(dsum, i - 1, SIZE(divisors));
// dsum/SIZE(divisors) 回: SIZE(divisors) 個
// 1 回: (i-1) - SIZE(divisors) 個
dp[i] = (1.0l + dsum + i - 1 - (SIZE(divisors) - 1)) / (i - 1);
}
// dump(dp);
pprint(dp.back());
}
// entry point
int main() {
solve();
return 0;
}