結果
| 問題 |
No.3271 PQ Dot Product
|
| ユーザー |
 hitonanode
|
| 提出日時 | 2025-09-12 23:38:22 |
| 言語 | C++23 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 46 ms / 1,000 ms |
| コード長 | 10,440 bytes |
| コンパイル時間 | 2,975 ms |
| コンパイル使用メモリ | 235,612 KB |
| 実行使用メモリ | 7,716 KB |
| 最終ジャッジ日時 | 2025-09-12 23:45:56 |
| 合計ジャッジ時間 | 9,258 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge10 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 46 |
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 <memory>
#include <numeric>
#include <optional>
#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> 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; }
const std::vector<std::pair<int, int>> 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 <class T1, class T2> T1 floor_div(T1 num, T2 den) { return (num > 0 ? num / den : -((-num + den - 1) / den)); }
template <class T1, class T2> std::pair<T1, T2> operator+(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first + r.first, l.second + r.second); }
template <class T1, class T2> std::pair<T1, T2> operator-(const std::pair<T1, T2> &l, const std::pair<T1, T2> &r) { return std::make_pair(l.first - r.first, l.second - r.second); }
template <class T> std::vector<T> sort_unique(std::vector<T> vec) { sort(vec.begin(), vec.end()), vec.erase(unique(vec.begin(), vec.end()), vec.end()); return vec; }
template <class 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 <class 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 <class IStream, class T> IStream &operator>>(IStream &is, std::vector<T> &vec) { for (auto &v : vec) is >> v; return is; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec);
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr);
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const pair<T, U> &pa);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec);
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa);
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp);
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::unordered_map<TK, TV, TH> &mp);
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl);
template <class OStream, class T> OStream &operator<<(OStream &os, const std::vector<T> &vec) { os << '['; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T, size_t sz> OStream &operator<<(OStream &os, const std::array<T, sz> &arr) { os << '['; for (auto v : arr) os << v << ','; os << ']'; return os; }
template <class... T> std::istream &operator>>(std::istream &is, std::tuple<T...> &tpl) { std::apply([&is](auto &&... args) { ((is >> args), ...);}, tpl); return is; }
template <class OStream, class... T> OStream &operator<<(OStream &os, const std::tuple<T...> &tpl) { os << '('; std::apply([&os](auto &&... args) { ((os << args << ','), ...);}, tpl); return os << ')'; }
template <class OStream, class T, class TH> OStream &operator<<(OStream &os, const std::unordered_set<T, TH> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::deque<T> &vec) { os << "deq["; for (auto v : vec) os << v << ','; os << ']'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::set<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T> OStream &operator<<(OStream &os, const std::unordered_multiset<T> &vec) { os << '{'; for (auto v : vec) os << v << ','; os << '}'; return os; }
template <class OStream, class T, class U> OStream &operator<<(OStream &os, const std::pair<T, U> &pa) { return os << '(' << pa.first << ',' << pa.second << ')'; }
template <class OStream, class TK, class TV> OStream &operator<<(OStream &os, const std::map<TK, TV> &mp) { os << '{'; for (auto v : mp) os << v.first << "=>" << v.second << ','; os << '}'; return os; }
template <class OStream, class TK, class TV, class TH> OStream &operator<<(OStream &os, const std::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) 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
vector<int> Experiment(int N) {
vector<int> Q(N);
REP(i, N) Q.at(i) = i + 1;
set<int> ret;
do {
int sum = 0;
REP(i, N) sum += Q.at(i) * (i + 1);
ret.insert(sum);
} while (next_permutation(ALL(Q)));
return vector<int>(ALL(ret));
}
lint Min(int N) {
// lint ret = 0;
// FOR(i, 1, N + 1) {
// int j = N + 1 - i;
// ret += lint(i) * j;
// }
// return ret;
return lint(N) * lint(N + 1) * lint(N + 2) / 6;
}
lint Max(int N) { return lint(N) * lint(N + 1) * lint(N * 2 + 1) / 6; }
vector<lint> BruteforceSolve(int N, lint K) {
assert(Min(N) <= K);
assert(K <= Max(N));
vector<lint> seq(N);
REP(i, N) seq.at(i) = i + 1;
do {
lint sum = 0;
REP(i, N) sum += seq.at(i) * (i + 1);
if (sum == K) return seq;
} while (next_permutation(ALL(seq)));
dbg(make_tuple(N, K));
assert(false);
}
vector<lint> Solve(int N, const lint &K) {
lint rem = K;
for (int i = N; i >= 1; --i) {
if (i <= 10) {
auto sol = BruteforceSolve(i, rem);
// dbg(make_tuple(i, rem, sol));
FOR(j, i + 1, N + 1) sol.push_back(j);
return sol;
}
lint nxt_min = Min(i - 1);
if (rem - lint(i) * i < nxt_min) {
vector<lint> ret;
IFOR(j, 1, i + 1) ret.push_back(j);
FOR(j, i + 1, N + 1) ret.push_back(j);
lint sum = 0;
REP(j, N) sum += ret.at(j) * (j + 1);
// dbg(make_tuple(i, K, rem, sum));
auto rec = [&](auto &&self, int l, int r) -> void {
if (l + 1 >= r) return;
for (int i = l; i + 1 < r; ++i) {
const lint diff = ret.at(i) - ret.at(i + 1);
assert(diff > 0);
if (sum + diff <= K) {
sum += diff;
swap(ret.at(i), ret.at(i + 1));
continue;
} else {
self(self, l, i);
self(self, i + 1, r);
return;
}
}
self(self, l, r - 1);
};
rec(rec, 0, i);
return ret;
} else {
rem -= lint(i) * i;
continue;
}
}
assert(false);
}
bool Validate(int N, lint K, const vector<lint> &P) {
if ((int)P.size() != N) return false;
{
auto s = P;
sort(ALL(s));
REP(i, N) if (s.at(i) != i + 1) return false;
}
lint sum = 0;
REP(i, N) sum += P.at(i) * (i + 1);
if (sum != K) return false;
return true;
}
int main() {
FOR(n, 1, 11) {
break;
// dbg(make_tuple(n, Experiment(n)));
dbg(n);
dbg(Min(n));
dbg(Max(n));
auto ex = Experiment(n);
FOR(i, Min(n), Max(n)) {
if (!binary_search(ALL(ex), i)) {
dbg(make_tuple(n, i));
}
}
}
FOR(n, 4, 15) {
break;
dbg(n);
const int mini = Min(n), maxi = Max(n);
FOR(k, mini, maxi + 1) {
auto sol = Solve(n, k);
if (!Validate(n, k, sol)) {
dbg(make_tuple(n, k, sol));
assert(false);
}
}
}
int N;
lint K;
cin >> N >> K;
dbg(make_tuple(N, K, Min(N), Max(N)));
if (K < Min(N)) {
puts("No");
return 0;
} else if (K > Max(N)) {
puts("No");
return 0;
}
if (N == 3 and K == 12) {
puts("No");
return 0;
}
auto ret = Solve(N, K);
assert(Validate(N, K, ret));
cout << "Yes\n";
REP(i, N) cout << i + 1 << ' ';
cout << '\n';
REP(i, N) cout << ret.at(i) << ' ';
cout << '\n';
}