結果
| 問題 | No.1666 累乗数 |
| ユーザー |
 iiljj
|
| 提出日時 | 2021-09-03 23:10:57 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,022 ms / 2,000 ms |
| コード長 | 17,171 bytes |
| コンパイル時間 | 1,795 ms |
| コンパイル使用メモリ | 139,868 KB |
| 最終ジャッジ日時 | 2025-01-24 07:00:44 |
|
ジャッジサーバーID （参考情報） |
judge3 / judge3 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 19 |
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 + 7// constexpr 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 << "}";}// 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>(cout, a); }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;template <typename T = ll> vc<T> get_primes_eratosthenes(T n) {vc<char> iscomposite(n + 1, 0); // 合成数だとフラグが立つvc<T> res;REPM(i, 2, n) {if (iscomposite[i]) continue;res.emplace_back(i);REPMD(j, i * i, n, i) iscomposite[j] = 1;}return res;}template <class tProposition, typename T = ll> T binarySearchIntMax(T left, T right, tProposition p) {if (right < left) return -1;T mid;while (left + 1 < right) {mid = (left + right) / 2;if (p(mid))left = mid;else // fn > 0right = mid - 1;}if (p(right))return right;else if (p(left))return left;elsereturn -1;}template <class tProposition, typename T = ll> T binarySearchIntMin(T left, T right, tProposition p) {if (right < left) return -1;T mid;while (left + 1 < right) {mid = (left + right) / 2;if (p(mid))right = mid;else // fn > 0left = mid + 1;}if (p(left))return left;else if (p(right))return right;elsereturn -1;}template <typename T = ll> inline constexpr T add_overflow(T x, T y) {T result = 0;if (__builtin_add_overflow(x, y, &result)) return std::numeric_limits<T>::max();return result;}template <typename T = ll> inline constexpr T mul_overflow(T x, T y) {T result = 0;if (__builtin_mul_overflow(x, y, &result)) return std::numeric_limits<T>::max();return result;}template <typename T = ll> T powll(T n, T t) {if (!t) return 1;// if (t == 1) return n;// dump(n, t, t >> 1);// assert(t >= 0);T a = powll(n, t >> 1); // ⌊t/2⌋ 乗a = mul_overflow(a, a); // ⌊t/2⌋*2 乗if (t & 1) // ⌊t/2⌋*2 == t-1 のときa = mul_overflow(a, n); // ⌊t/2⌋*2+1 乗 => t 乗return a;}vll pn = {1, 4, 8, 9, 16, 25, 27, 32, 36, 49, 64, 81, 100, 121,125, 128, 144, 169, 196, 216, 225, 243, 256, 289, 324, 343, 361, 400,441, 484, 512, 529, 576, 625, 676, 729, 784, 841, 900, 961, 1000, 1024,1089, 1156, 1225, 1296, 1331, 1369, 1444, 1521, 1600, 1681, 1728, 1764, 1849, 1936,2025, 2048, 2116, 2187, 2197, 2209, 2304, 2401, 2500, 2601, 2704, 2744, 2809, 2916,3025, 3125, 3136, 3249, 3364, 3375, 3481, 3600, 3721, 3844, 3969, 4096, 4225, 4356,4489, 4624, 4761, 4900, 4913, 5041, 5184, 5329, 5476, 5625, 5776, 5832, 5929, 6084,6241, 6400, 6561, 6724, 6859, 6889, 7056, 7225, 7396, 7569, 7744, 7776, 7921, 8000,8100, 8192, 8281, 8464, 8649, 8836, 9025, 9216, 9261, 9409, 9604, 9801, 10000, 10201,10404, 10609, 10648, 10816, 11025, 11236, 11449, 11664, 11881, 12100, 12167, 12321, 12544, 12769,12996, 13225, 13456, 13689, 13824, 13924, 14161, 14400, 14641, 14884, 15129, 15376, 15625, 15876,16129, 16384, 16641, 16807, 16900, 17161, 17424, 17576, 17689, 17956, 18225, 18496, 18769, 19044,19321, 19600, 19683, 19881, 20164, 20449, 20736, 21025, 21316, 21609, 21904, 21952, 22201, 22500,22801, 23104, 23409, 23716, 24025, 24336, 24389, 24649, 24964, 25281, 25600, 25921, 26244, 26569,26896, 27000, 27225, 27556, 27889, 28224, 28561, 28900, 29241, 29584, 29791, 29929, 30276, 30625,30976, 31329, 31684, 32041, 32400, 32761, 32768, 33124, 33489, 33856, 34225, 34596, 34969, 35344,35721, 35937, 36100, 36481, 36864, 37249, 37636, 38025, 38416, 38809, 39204, 39304, 39601, 40000,40401, 40804, 41209, 41616, 42025, 42436, 42849, 42875, 43264, 43681, 44100, 44521, 44944, 45369,45796, 46225, 46656, 47089, 47524, 47961, 48400, 48841, 49284, 49729, 50176, 50625, 50653, 51076,51529, 51984, 52441, 52900, 53361, 53824, 54289, 54756, 54872, 55225, 55696, 56169, 56644, 57121,57600, 58081, 58564, 59049, 59319, 59536, 60025, 60516, 61009, 61504, 62001, 62500, 63001, 63504,64000, 64009, 64516, 65025, 65536, 66049, 66564, 67081, 67600, 68121, 68644, 68921, 69169, 69696,70225, 70756, 71289, 71824, 72361, 72900, 73441, 73984, 74088, 74529, 75076, 75625, 76176, 76729,77284, 77841, 78125, 78400, 78961, 79507, 79524, 80089, 80656, 81225, 81796, 82369, 82944, 83521,84100, 84681, 85184, 85264, 85849, 86436, 87025, 87616, 88209, 88804, 89401, 90000, 90601, 91125,91204, 91809, 92416, 93025, 93636, 94249, 94864, 95481, 96100, 96721, 97336, 97344, 97969, 98596,99225, 99856, 100000, 100489, 101124, 101761, 102400, 103041, 103684, 103823, 104329, 104976, 105625, 106276,106929, 107584, 108241, 108900, 109561, 110224, 110592, 110889, 111556, 112225, 112896, 113569, 114244, 114921,115600, 116281, 116964, 117649, 118336, 119025, 119716, 120409, 121104, 121801, 122500, 123201, 123904, 124609,125000, 125316, 126025, 126736, 127449, 128164, 128881, 129600, 130321, 131044, 131072, 131769, 132496, 132651,133225, 133956, 134689, 135424, 136161, 136900, 137641, 138384, 139129, 139876, 140608, 140625, 141376, 142129,142884, 143641, 144400, 145161, 145924, 146689, 147456, 148225, 148877, 148996, 149769, 150544, 151321, 152100,152881, 153664, 154449, 155236, 156025, 156816, 157464, 157609, 158404, 159201, 160000, 160801, 161051, 161604,162409, 163216, 164025, 164836, 165649, 166375, 166464, 167281, 168100, 168921, 169744, 170569, 171396, 172225,173056, 173889, 174724, 175561, 175616, 176400, 177147, 177241, 178084, 178929, 179776, 180625, 181476, 182329,183184, 184041, 184900, 185193, 185761, 186624, 187489, 188356, 189225, 190096, 190969, 191844, 192721, 193600,194481, 195112, 195364, 196249, 197136, 198025, 198916, 199809, 200704, 201601, 202500, 203401, 204304, 205209,205379, 206116, 207025, 207936, 208849, 209764, 210681, 211600, 212521, 213444, 214369, 215296, 216000, 216225,217156, 218089, 219024, 219961, 220900, 221841, 222784, 223729, 224676, 225625, 226576, 226981, 227529, 228484,229441, 230400, 231361, 232324, 233289, 234256, 235225, 236196, 237169, 238144, 238328, 239121, 240100, 241081,242064, 243049, 244036, 245025, 246016, 247009, 248004, 248832, 249001, 250000, 250047, 251001, 252004, 253009,254016, 255025, 256036, 257049, 258064, 259081, 260100, 261121, 262144, 263169, 264196, 265225, 266256, 267289,268324, 269361, 270400, 271441, 272484, 273529, 274576, 274625, 275625, 276676, 277729, 278784};ll get_kth_perfect_power(const ll k, const vll &primes) {// a^p <= n となる a がいくつあるか数える// それをすべての p について足す// 合計個数が k 個以上になるような最小の n が答えll sz = SIZE(primes);ll n = binarySearchIntMin(1LL, INF, [&](ll mid) -> bool {ll cnt = 1;auto dfs = [&](auto &&dfs, ll val = 1, ll cnt_p = 0, ll ptr = 0) -> void {if (val > 64) return;if (ptr == sz) {if (val == 1) return;ll bmax = binarySearchIntMax(1LL, INF, [&](ll mid2) -> bool { return powll(mid2, val) <= mid; });if (bmax == -1) return;ll dif = bmax - 1; // 1 を除くcnt += (cnt_p % 2 == 0 ? -dif : dif);return;} else {dfs(dfs, val, cnt_p, ptr + 1);dfs(dfs, val * primes[ptr], cnt_p + 1, ptr + 1);}};dfs(dfs);return cnt >= k;});assert(n != -1);return n;}void check(const vll &primes) {dump(SIZE(pn), primes);REPM(i, 1, 600) {ll target = pn[i - 1];ll ans = get_kth_perfect_power(i, primes);pprint(i, target, ans);std::flush(std::cout);assert(ans == target);}}// ★ 指数部を素数に限定しても，複数通りの表し方がある// 包除で適切に取り除く必要がある// Problemvoid solve() {vll primes = get_primes_eratosthenes(64LL);// check(primes);// return;VAR(ll, t);REP(_case, 0, t) {VAR(ll, k); //ll n = get_kth_perfect_power(k, primes);pprint(n);}}// entry pointint main() {solve();return 0;}