結果
| 問題 |
No.2854 -1 Subsequence
|
| ユーザー |
 ecottea
|
| 提出日時 | 2025-09-25 14:20:56 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 32 ms / 2,000 ms |
| コード長 | 14,767 bytes |
| コンパイル時間 | 4,817 ms |
| コンパイル使用メモリ | 275,692 KB |
| 実行使用メモリ | 7,716 KB |
| 最終ジャッジ日時 | 2025-09-25 14:21:06 |
| 合計ジャッジ時間 | 8,781 ms |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| other | AC * 40 |
ソースコード
#ifndef HIDDEN_IN_VS // 折りたたみ用
// 警告の抑制
#define _CRT_SECURE_NO_WARNINGS
// ライブラリの読み込み
#include <bits/stdc++.h>
using namespace std;
// 型名の短縮
using ll = long long; using ull = unsigned long long; // -2^63 ～ 2^63 = 9e18（int は -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;
// 定数の定義
const double PI = acos(-1);
int DX[4] = { 1, 0, -1, 0 }; // 4 近傍（下，右，上，左）
int DY[4] = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004003094073385LL; // (int)INFL = INF, (int)(-INFL) = -INF;
// 入出力高速化
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
// 汎用マクロの定義
#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 から n-1 まで昇順
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s から t まで昇順
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s から t まで降順
#define repe(v, a) for(const auto& v : (a)) // a の全要素（変更不可能）
#define repea(v, a) for(auto& v : (a)) // a の全要素（変更可能）
#define repb(set, d) for(int set = 0, set##_ub = 1 << int(d); set < set##_ub; ++set) // d ビット全探索（昇順）
#define repis(i, set) for(int i = lsb(set), bset##i = set; i < 32; bset##i -= 1 << i, i = lsb(bset##i)) // set の全要素（昇順）
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a の順列全て（昇順）
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} // 重複除去
#define EXIT(a) {cout << (a) << endl; exit(0);} // 強制終了
#define inQ(x, y, u, l, d, r) ((u) <= (x) && (l) <= (y) && (x) < (d) && (y) < (r)) // 半開矩形内判定
// 汎用関数の定義
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; } // 最大値を更新（更新されたら true を返す）
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // 最小値を更新（更新されたら true を返す）
template <class T> inline int 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; } // 非負mod
// 演算子オーバーロード
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 // 折りたたみ用
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint998244353;
//using mint = static_modint<(int)1e9+7>;
//using mint = modint; // mint::set_mod(m);
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 // 手元環境（Visual Studio）
#include "local.hpp"
#else // 提出用（gcc）
int mute_dump = 0;
int frac_print = 0;
#if __has_include(<atcoder/all>)
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; }
}
#endif
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; }
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(v)
#define dump_math(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) { vc MLE(1<<30); EXIT(MLE.back()); } } // RE の代わりに MLE を出す
#endif
// 愚直
int S;
ll naive(const string& s) {
int n = sz(s);
vi a(n);
rep(i, n) a[i] = s[i] - '0' - S;
ll res = -INFL;
repb(set, n) {
if (set == 0) continue;
ll sc = 0; int t = 0;
repis(i, set) {
if (t) sc += a[i];
else sc -= a[i];
t ^= 1;
}
chmax(res, sc);
}
return res;
}
// 遷移行列の係数を計算し，埋め込み用のコードを出力する．
// 待てない場合は len_max とか LB_max とかを指定する．
pair<vvvl, vl> embed_coefs(int COL, int len_min = -INF, int len_max = INF, int LB_max = INF,
vector<string> ssT = { "" }) {
vector<string> ssB{ "" };
int idx = 0;
int PDIM = -1;
repi(len, 0, INF) {
dump("----------- len:", len, "--------------");
//dump("ss:", ss);
int LT = sz(ssT); int LB = min(sz(ssB), LB_max);
dump("LT:", LT, "LB:", LB);
// (i,j) 成分が naive(ss[i] + ss[j]) であるような行列 mat を得る．
vvl mat(LT, vl(LB));
rep(i, LT) rep(j, LB) mat[i][j] = naive(ssT[i] + ssB[j]);
//dump("mat:"); dumpel(mat);
// mat から max-plus 線形独立な行を抜き出す．
vi is; int DIM = 0;
rep(i, LT) {
vl coef(DIM, INFL);
rep(i2, DIM) rep(j, LB) {
if (mat[is[i2]][j] == -INFL) continue;
chmin(coef[i2], mat[i][j] - mat[is[i2]][j]);
}
//dump("i:", i, "coef:", coef);
bool ok = true;
rep(j, LB) {
ll val = -INFL;
rep(i2, DIM) {
ll nval = mat[is[i2]][j] + coef[i2];
if (nval < -INFL / 2) continue;
chmax(val, nval);
}
//dump("j:", j, "val:", val, "mat[i][j]:", mat[i][j]);
if (val != mat[i][j]) {
ok = false;
break;
}
}
if (!ok) {
is.push_back(i);
DIM++;
}
}
dump("is[0.." + to_string(DIM) + "):"); dump(is);
repe(i, is) cerr << "\"" << ssT[i] << "\",";
cerr << endl;
//repe(i, is) dump(mat[i]);
// rank の更新がなかったら必要な情報は揃ったとみなして打ち切る．
if (len == len_max || (len >= len_min && DIM == PDIM)) { // たまに失敗する．
// 各文字に対応する表現行列を得る．
vvvl matAs(COL, vvl(DIM, vl(DIM, INFL)));
rep(c, COL) {
char ch = '0' + c;
rep(i, DIM) {
vl vec(LB);
rep(j, LB) vec[j] = naive(ssT[is[i]] + ch + ssB[j]);
rep(i2, DIM) rep(j, LB) {
if (mat[is[i2]][j] == -INFL) continue;
chmin(matAs[c][i][i2], vec[j] - mat[is[i2]][j]);
}
vl vec2(LB);
rep(j, LB) {
vec2[j] = -INFL;
rep(i2, DIM) {
ll nval = mat[is[i2]][j] + matAs[c][i][i2];
if (nval < -INFL / 2) continue;
chmax(vec2[j], nval);
}
}
if (vec2 != vec) {
dump("ERROR!");
dump("c:", c, "i:", i, "ssT[is[i]]:", ssT[is[i]]);
dump("vec:"); dump(vec);
dump("vec2:"); dump(vec2);
exit(-1);
}
rep(i2_el, DIM) {
vl vec_el(LB, -INFL);
rep(i2, DIM) {
if (i2 == i2_el) continue;
rep(j, LB) {
auto nval = mat[is[i2]][j] + matAs[c][i][i2];
if (nval < -INFL / 2) continue;
chmax(vec_el[j], nval);
}
}
if (vec_el == vec) matAs[c][i][i2_el] = -INFL;
}
}
}
// 右端を閉じるためのベクトルを得る．
vl vecP(DIM);
rep(i, DIM) vecP[i] = mat[is[i]][0];
// 埋め込み用の文字列を出力する．
string eb = "constexpr int DIM = ";
eb += to_string(DIM);
eb += ";\n";
eb += "constexpr int COL = ";
eb += to_string(COL);
eb += ";\n";
eb += "VTYPE matAs[COL][DIM][DIM] = {\n";
rep(c, COL) {
eb += "{";
rep(i, DIM) {
eb += "{";
rep(j, DIM) eb += to_string(matAs[c][i][j]) + ",";
eb.pop_back();
eb += "},";
}
eb.pop_back();
eb += "},\n";
}
eb.pop_back();
eb.pop_back();
eb += "};\n";
eb += "VTYPE vecP[DIM] = {";
rep(i, DIM) eb += to_string(vecP[i]) + ",";
eb.pop_back();
eb += "};\n";
cout << eb;
exit(0);
return { matAs, vecP };
}
// 基底ガチャ
//mt19937_64 mt((int)time(NULL)); shuffle(ssB.begin() + idx, ssB.end(), mt);
// 次に長い文字列たちを ss に追加する．
int nidx = sz(ssB);
repi(i, idx, nidx - 1) rep(c, COL) {
ssB.push_back(ssB[i]);
ssB.back().push_back('0' + c);
ssT.push_back(ssB.back());
}
idx = nidx;
PDIM = DIM;
}
return pair<vvvl, vl>();
}
template <class VTYPE>
VTYPE solve(const vector<VTYPE>& a) {
// --------------- embed_coefs() からの出力を貼る ----------------
constexpr int DIM = 3;
constexpr int COL = 9;
VTYPE matAs[COL][DIM][DIM] = {
{{-4004004004,0,-4004004004},{-4004004004,0,-4004004004},{-4004004004,8,-4004004004}},
{{-4004004004,-1,-8},{-4004004004,0,-7},{-4004004004,7,0}},
{{-4004004004,-2,-8},{-4004004004,0,-6},{-4004004004,6,0}},
{{-4004004004,-3,-8},{-4004004004,0,-5},{-4004004004,5,0}},
{{-4004004004,-4,-8},{-4004004004,0,-4},{-4004004004,4,0}},
{{0,-5,-4004004004},{-4004004004,0,-3},{-4004004004,3,0}},
{{0,-6,-4004004004},{-4004004004,0,-2},{-4004004004,2,0}},
{{0,-7,-4004004004},{-4004004004,0,-1},{-4004004004,1,0}},
{{0,-8,-4004004004},{-4004004004,-4004004004,0},{-4004004004,-4004004004,0}} };
VTYPE vecP[DIM] = { -4004004004,4,8 };
// --------------------------------------------------------------
int n = sz(a);
array<VTYPE, DIM> dp;
dp.fill((VTYPE)(-INFL));
dp[0] = 0;
auto apply = [&](const array<VTYPE, DIM>& x, VTYPE w) {
array<VTYPE, DIM> z;
z.fill((VTYPE)(-INFL));
if (w <= 0) {
rep(j, DIM) rep(i, DIM) {
VTYPE add = (1 + w) * matAs[S][i][j] + (-w) * matAs[S - 1][i][j];
chmax(z[j], x[i] + add);
}
}
else {
rep(j, DIM) rep(i, DIM) {
VTYPE add = (2 - w) * matAs[S + 1][i][j] + (w - 1) * matAs[S + 2][i][j];
chmax(z[j], x[i] + add);
}
}
return z;
};
rep(i, n) {
dp = apply(dp, a[i]);
}
VTYPE res = (VTYPE)(-INFL);
rep(i, DIM) chmax(res, dp[i] + vecP[i]);
return res;
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// INFL = 999;
// bug_find();
//【方法】
// 愚直を書いて集めたデータをもとに遷移行列を復元する．
//【使い方】
// 1. mint naive(文字列) を実装する．
// 2. embed_coefs(文字の種類数); を実行する．
// 3. 出力を solve() 内に貼る．
// 4. auto dp = solve<答えの型>(文字列) で勝手に DP してくれる．
dump(naive("36")); dump("=======");
dump(naive("91")); dump("=======");
S = 4;
// embed_coefs(2 * S + 1, 0, INF, INF);
vector<string> ssT = { "", "0", "08"};
// embed_coefs(2 * S + 1, 0, INF, INF, ssT);
int n;
cin >> n;
vl a(n);
cin >> a;
cout << solve<ll>(a) << "\n";
}
/*
----------- len: 0 --------------
LT: 1 LB: 1
is[0..0):
----------- len: 1 --------------
LT: 10 LB: 10
is[0..2):
0 1
"","0",
----------- len: 2 --------------
LT: 91 LB: 91
is[0..6):
0 1 15 16 17 18
"","0","05","06","07","08",
----------- len: 3 --------------
LT: 820 LB: 820
is[0..6):
0 1 15 16 17 18
"","0","05","06","07","08",
constexpr int DIM = 6;
constexpr int COL = 9;
VTYPE matAs[COL][DIM][DIM] = {
{{-999,0,-999,-999,-999,-999},{-999,0,-999,-999,-999,-999},{-999,5,-999,-999,-999,-999},{-999,6,-999,-999,-999,-999},{-999,7,-999,-999,-999,-999},{-999,8,-999,-999,-999,-999}},
{{-999,-1,-999,-999,-999,-8},{-999,0,-999,-999,-999,-7},{-999,4,-999,-999,-999,-3},{-999,5,-999,-999,-999,-2},{-999,6,-999,-999,-999,-1},{-999,7,-999,-999,-999,0}},
{{-999,-2,-999,-999,-999,-8},{-999,0,-999,-999,-999,-6},{-999,3,-999,-999,-999,-3},{-999,4,-999,-999,-999,-2},{-999,5,-999,-999,-999,-1},{-999,6,-999,-999,-999,0}},
{{-999,-3,-999,-999,-999,-8},{-999,0,-999,-999,-999,-5},{-999,2,-999,-999,-999,-3},{-999,3,-999,-999,-999,-2},{-999,4,-999,-999,-999,-1},{-999,5,-999,-999,-999,0}},
{{-999,-4,-999,-999,-999,-8},{-999,0,-999,-999,-999,-4},{-999,1,-999,-999,-999,-3},{-999,2,-999,-999,-999,-2},{-999,3,-999,-999,-999,-1},{-999,4,-999,-999,-999,0}},
{{0,-5,-999,-999,-999,-999},{-999,-999,0,-999,-999,-999},{-999,-999,0,-999,-999,-999},{-999,-999,1,-999,-999,-999},{-999,-999,2,-999,-999,-999},{-999,-999,3,-999,-999,-999}},
{{0,-6,-999,-999,-999,-999},{-999,-999,-999,0,-999,-999},{-999,-999,-999,0,-999,-999},{-999,-999,-999,0,-999,-999},{-999,-999,-999,1,-999,-999},{-999,-999,-999,2,-999,-999}},
{{0,-7,-999,-999,-999,-999},{-999,-999,-999,-999,0,-999},{-999,-999,-999,-999,0,-999},{-999,-999,-999,-999,0,-999},{-999,-999,-999,-999,0,-999},{-999,-999,-999,-999,1,-999}},
{{0,-8,-999,-999,-999,-999},{-999,-999,-999,-999,-999,0},{-999,-999,-999,-999,-999,0},{-999,-999,-999,-999,-999,0},{-999,-999,-999,-999,-999,0},{-999,-999,-999,-999,-999,0}}};
VTYPE vecP[DIM] = {-999,4,5,6,7,8};
斜めに 0 が並んでしまうので S→∞ とはできない．
そこで状態を {"", "0", "08"} にしてみるとこうなる：
----------- len: 0 --------------
LT: 3 LB: 1
is[0..1):
1
"0",
----------- len: 1 --------------
LT: 12 LB: 10
is[0..3):
0 1 2
"","0","08",
----------- len: 2 --------------
LT: 93 LB: 91
is[0..3):
0 1 2
"","0","08",
constexpr int DIM = 3;
constexpr int COL = 9;
VTYPE matAs[COL][DIM][DIM] = {
{{-999,0,-999},{-999,0,-999},{-999,8,-999}},
{{-999,-1,-8},{-999,0,-7},{-999,7,0}},
{{-999,-2,-8},{-999,0,-6},{-999,6,0}},
{{-999,-3,-8},{-999,0,-5},{-999,5,0}},
{{-999,-4,-8},{-999,0,-4},{-999,4,0}},
{{0,-5,-999},{-999,0,-3},{-999,3,0}},
{{0,-6,-999},{-999,0,-2},{-999,2,0}},
{{0,-7,-999},{-999,0,-1},{-999,1,0}},
{{0,-8,-999},{-999,-999,0},{-999,-999,0}}};
VTYPE vecP[DIM] = {-999,4,8};
これなら正負に分けての線形補間が効く．
*/