結果

問題 No.1867 Partitions and Inversions
ユーザー ecotteaecottea
提出日時 2024-09-24 15:05:41
言語 C++17(gcc12)
(gcc 12.3.0 + boost 1.87.0)
結果
AC  
実行時間 3,170 ms / 5,000 ms
コード長 11,779 bytes
コンパイル時間 7,499 ms
コンパイル使用メモリ 320,696 KB
実行使用メモリ 91,776 KB
最終ジャッジ日時 2024-09-24 15:07:52
合計ジャッジ時間 126,986 ms
ジャッジサーバーID
(参考情報)
judge3 / judge5
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 65
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

// QCFium
#pragma GCC target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; using ull = unsigned long long; // -2^63 2^63 = 9e18int -2^31 2^31 = 2e9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>; using vvvvi = vector<vvvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>; using vvvvl = vector<vvvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), (x)))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), (x)))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) //
//
template <class T> inline ll powi(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T getb(T set, int i) { return (set >> i) & T(1); }
template <class T> inline T smod(T n, T m) { n %= m; if (n < 0) n += m; return n; } // mod
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
//using mint = modint1000000007;
using mint = modint998244353;
//using mint = static_modint<1000000000>;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>; using vvvvm = vector<vvvm>; using pim = pair<int, mint>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : 32; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : 64; }
template <size_t N> inline int lsb(const bitset<N>& b) { return b._Find_first(); }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define dump(...)
#define dumpel(...)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE MLE
#endif
//O(n log n)
/*
* a[0..n) a_cp[0..n)
* xs[j] j
*
* a a_cp[i] a[i]
* xs[j] j
*/
template <class T>
int coordinate_compression(const vector<T>& a, vi& a_cp, vector<T>* xs = nullptr) {
// verify : https://atcoder.jp/contests/tessoku-book/tasks/tessoku_book_o
int n = sz(a);
if (xs == nullptr) xs = new vector<T>;
// *xs : a x
*xs = a;
uniq(*xs);
// a[i] xs
a_cp.resize(n);
rep(i, n) a_cp[i] = lbpos(*xs, a[i]);
return sz(*xs);
}
//O(n log n)
/*
* a[0..n)
*
*
*/
template <class T>
vl inversion_number_cc(const vector<T>& a) {
// verify : https://onlinejudge.u-aizu.ac.jp/courses/lesson/1/ALDS1/all/ALDS1_5_D
int n = sz(a);
// b : a
vi b;
int m = coordinate_compression(a, b);
// fw[i] : i
fenwick_tree<int> fw(m);
vl res(n);
//
rep(i, n) {
fw.add(b[i], 1);
// 調
res[i] = fw.sum(b[i] + 1, m) + (i > 0 ? res[i - 1] : 0);
}
return res;
}
//monotone minimaO(w log h + h)
/*
* monotone a[0..h)[0..w)
*/
template <class FUNC>
vi monotone_minima(int h, int w, const FUNC& a) {
// : https://speakerdeck.com/tatyam_prime/monge-noshou-yin-shu
// verify : https://judge.yosupo.jp/problem/min_plus_convolution_convex_arbitrary
//
// lsb 調
// 1 lsb 調 O(w)
vi j_min(h);
// di : 調 / 2 2
for (int di = 1 << msb(h); di > 0; di >>= 1) {
// i : 調1-indexed
// 2 di lsb
for (int i = di; i <= h; i += di << 1) {
int jL = (i - di > 0 ? j_min[i - di - 1] : 0);
int jR = (i + di <= h ? j_min[i + di - 1] : w - 1);
ll a_min = 2 * INFL + 10;
repi(j, jL, jR) if (chmin<ll>(a_min, a(i - 1, j))) j_min[i - 1] = j;
}
}
return j_min;
/* a
auto a = [&](int i, int j) {
return 0LL;
};
*/
}
//Monge DAG O(n^2 (log n)^2)
/*
* DAG G
* [0..n]
* s→ts<t n+1 Monge sc(s,t)
* k∈[0..n], i∈[0..n]
* 0 i k
*
* monotone minima
*/
template <class T>
vector<vector<T>> monge_DAG_highest_score_path(int n, const vector<vector<T>>& sc) {
//
// dp[k][i] : 0 i k
//
// dp[k+1][t] = MAX_s∈[0..t) (dp[k][s] + sc(s,t))
// max-plus
// dp[k+1] = dp[k] * c
//
//
// k
// sc Monge t dp[k][t] Monge
// Monge
// monotone minima
// dp[k+1]
//
//
// dp[k][i] : 0 i k
vector<vector<T>> dp(n + 1, vector<T>(n + 1, -T(INFL)));
dp[0][0] = 0;
// rects_sml :
vector<pii> rects_sml;
// rects_lrg :
vector<tuple<int, int, int, int>> rects_lrg;
// {(i,j) | l≦i<j<r}
function<void(int, int)> rf = [&](int l, int r) {
//
if (r - l <= 10) {
rects_sml.emplace_back(l, r);
return;
}
int m = (l + r) / 2;
rects_lrg.emplace_back(l, m, m, r);
rf(l, m);
rf(m, r);
};
rf(0, n + 1);
rep(k, n) {
// c c[i1..i2)[j1..j2)
for (auto [l, r] : rects_sml) {
//
repi(i, l, r - 1) repi(j, i + 1, r - 1) {
chmax(dp[k + 1][j], dp[k][i] + sc[i][j]);
}
}
// c c[i1..i2)[j1..j2)
for (auto [i1, i2, j1, j2] : rects_lrg) {
int h = i2 - i1;
int w = j2 - j1;
// sc Monge & -1 & Monge
//
auto A = [&](int j, int i) {
return -(sc[i1 + i][j2 - 1 - j] + dp[k][i1 + i]);
};
auto i_min = monotone_minima(w, h, A);
//
rep(j, w) chmax(dp[k + 1][j2 - 1 - j], -A(j, i_min[j]));
}
}
return dp;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
int n;
cin >> n;
vi p(n);
cin >> p;
vvi M(n + 1, vi(n + 1));
rep(i, n) {
vi a(p.begin() + i, p.end());
auto b = inversion_number_cc(a);
repi(j, i + 1, n) M[i][j] = (int)b[j - (i + 1)];
}
vl res(n, M[0][n]);
auto sc = monge_DAG_highest_score_path(n, M);
rep(i, n) res[i] -= sc[i + 1][n];
rep(i, n) cout << res[i] << "\n";
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0