結果
| 問題 |
No.1239 Multiplication -2
|
| コンテスト | |
| ユーザー |
 ecottea
|
| 提出日時 | 2025-07-20 15:25:01 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 578 ms / 2,000 ms |
| コード長 | 11,406 bytes |
| コンパイル時間 | 5,896 ms |
| コンパイル使用メモリ | 321,312 KB |
| 実行使用メモリ | 151,552 KB |
| 最終ジャッジ日時 | 2025-07-20 15:25:19 |
| 合計ジャッジ時間 | 15,036 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 34 |
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（大嘘）
ll naive(int n, vi a) {
if (n == 0) return 0;
mint res = 0;
// 0 1 2 3 4 5 6
// [の左，-2, -1, 0, 1, 2, ]の右
vvm dp(n + 1, vm(7));
repi(i, 0, n) {
vm ndp(7);
// ]
if (i == n) {
ndp[6] += dp[i][1];
}
else {
ndp[6] += dp[i][1] / 2;
}
// [
if (i == 0) {
ndp[4] += 1;
}
else {
ndp[4] += mint(1) / 2;
}
// |
ndp[0] += dp[i][0];
ndp[1] += dp[i][1] / 2;
ndp[2] += dp[i][2] / 2;
ndp[3] += dp[i][3] / 2;
ndp[4] += dp[i][4] / 2;
ndp[5] += dp[i][5] / 2;
ndp[6] += dp[i][6];
dp[i] = ndp;
if (i == n) break;
if (a[i] == -2) {
// 0 1 2 3 4 5 6
// [の左，-2, -1, 0, 1, 2, ]の右
dp[i + 1][0] += dp[i][0];
//dp[i + 1][0] += dp[i][1];
dp[i + 1][5] += dp[i][2];
dp[i + 1][3] += dp[i][3];
dp[i + 1][1] += dp[i][4];
//dp[i + 1][0] += dp[i][5];
dp[i + 1][6] += dp[i][6];
}
else if (a[i] == -1) {
// 0 1 2 3 4 5 6
// [の左，-2, -1, 0, 1, 2, ]の右
dp[i + 1][0] += dp[i][0];
dp[i + 1][5] += dp[i][1];
dp[i + 1][4] += dp[i][2];
dp[i + 1][3] += dp[i][3];
dp[i + 1][2] += dp[i][4];
dp[i + 1][1] += dp[i][5];
dp[i + 1][6] += dp[i][6];
}
else if (a[i] == 0) {
// 0 1 2 3 4 5 6
// [の左，-2, -1, 0, 1, 2, ]の右
dp[i + 1][0] += dp[i][0];
dp[i + 1][3] += dp[i][1];
dp[i + 1][3] += dp[i][2];
dp[i + 1][3] += dp[i][3];
dp[i + 1][3] += dp[i][4];
dp[i + 1][3] += dp[i][5];
dp[i + 1][6] += dp[i][6];
}
else if (a[i] == 1) {
// 0 1 2 3 4 5 6
// [の左，-2, -1, 0, 1, 2, ]の右
dp[i + 1][0] += dp[i][0];
dp[i + 1][1] += dp[i][1];
dp[i + 1][2] += dp[i][2];
dp[i + 1][3] += dp[i][3];
dp[i + 1][4] += dp[i][4];
dp[i + 1][5] += dp[i][5];
dp[i + 1][6] += dp[i][6];
}
else if (a[i] == 2) {
// 0 1 2 3 4 5 6
// [の左，-2, -1, 0, 1, 2, ]の右
dp[i + 1][0] += dp[i][0];
//dp[i + 1][0] += dp[i][1];
dp[i + 1][1] += dp[i][2];
dp[i + 1][3] += dp[i][3];
dp[i + 1][5] += dp[i][4];
//dp[i + 1][0] += dp[i][5];
dp[i + 1][6] += dp[i][6];
}
}
return (dp[n][6] * mint(2).pow(n - 1)).val();
}
//【任意数列の列挙（上限指定）】O(ub^n)
/*
* 数列 a[0..n) で，∀i, a[i]∈[0..ub) を満たすもの全てを格納したリストを返す．
*/
vvi enumerate_all_sequences(int n, int ub) {
// verify : https://yukicoder.me/problems/no/2917
vvi seqs;
vi seq(n); // 作成途中の列
function<void(int)> rf = [&](int i) {
// 完成していれば記録する．
if (i == n) {
seqs.push_back(seq);
return;
}
rep(x, ub) {
seq[i] = x;
rf(i + 1);
}
};
rf(0);
return seqs;
}
void zikken() {
// 整形して出力
string out;
out += "data=Association[";
repi(len, 0, 6) {
auto seqs = enumerate_all_sequences(len, 5);
repe(seq, seqs) {
vi a(len);
rep(i, len) a[i] = seq[i] - 2;
ll res = naive(len, a);
out += "{";
repe(d, seq) {
out += to_string(d);
out += ",";
}
if (out.back() == ',') out.pop_back();
out += "}->" + to_string(res) + ",";
}
}
out.pop_back();
out += "];";
cout << out << endl;
exit(0);
}
template <class VTYPE>
VTYPE solve(const string& s) {
// -------------------- 生成器からの出力を貼る --------------------
map<string, VTYPE>inis = { {"4", 0}, {"", 0}, {"2", 0}, {"1", 0}, {"04", 1}, {"0", 1}, {"03", 2}, {"02", 1}, {"01", 1}, {"00", 2} };
map<string, vector<tuple<int, string, VTYPE>>>rules = { {"44", {{2, "2", 1}, {1, "", 1}}}, {"43", {{2, "4", 1}, {1, "", 1}}}, {"42", {{1, "", 2}}}, {"41", {{2, "0", 1}, {1, "", 1}}}, {"40", {{2, "2", 1}, {1, "", 1}}}, {"3", {{1, "", 2}}}, {"24", {{2, "2", 1}, {1, "", 1}}}, {"23", {{2, "2", 1}, {1, "", 1}}}, {"22", {{1, "", 2}}}, {"21", {{2, "2", 1}, {1, "", 1}}}, {"20", {{2, "2", 1}, {1, "", 1}}}, {"14", {{2, "0", 1}, {1, "", 1}}}, {"13", {{2, "1", 1}, {1, "", 1}}}, {"12", {{1, "", 2}}}, {"11", {{2, "", 2}, {1, "", 1}}}, {"10", {{2, "4", 1}, {1, "", 1}}}, {"044", {{2, "0", 2}}}, {"043", {{3, "0", -2}, {2, "0", 2}, {2, "2", 1}, {2, "", -2}, {1, "", 1}}}, {"042", {{2, "0", 2}}}, {"041", {{3, "4", -2}, {2, "0", 2}, {2, "2", 1}, {2, "", -2}, {1, "", 1}}}, {"040", {{2, "0", 2}}}, {"034", {{2, "0", 3}, {2, "4", -2}, {1, "", 1}}}, {"033", {{3, "0", -2}, {2, "0", 3}}}, {"032", {{2, "0", 3}, {1, "", -1}}}, {"031", {{3, "4", -2}, {2, "0", 3}}}, {"030", {{2, "0", 3}, {2, "4", -2}, {1, "", 1}}}, {"024", {{2, "0", 2}}}, {"023", {{3, "0", -2}, {2, "0", 2}, {2, "", -2}, {1, "", 2}}}, {"022", {{2, "0", 2}}}, {"021", {{3, "4", -2}, {2, "0", 2}, {2, "", -2}, {1, "", 2}}}, {"020", {{2, "0", 2}}}, {"014", {{2, "0", 2}, {2, "4", -1}, {1, "", 1}}}, {"013", {{3, "0", -2}, {2, "0", 2}, {2, "4", 1}, {2, "", -2}, {1, "", 1}}}, {"012", {{2, "0", 2}}}, {"011", {{3, "4", -2}, {2, "0", 2}, {2, "4", 1}, {2, "", -2}, {1, "", 1}}}, {"010", {{2, "0", 2}, {2, "4", -1}, {1, "", 1}}}, {"004", {{2, "4", -1}, {1, "", 3}}}, {"003", {{3, "0", -2}, {2, "2", 1}, {2, "", -2}, {1, "", 3}}}, {"002", {{2, "", -2}, {1, "", 3}}}, {"001", {{3, "4", -2}, {2, "2", 1}, {2, "", -2}, {1, "", 3}}}, {"000", {{2, "4", -1}, {1, "", 3}}} };
// --------------------------------------------------------------
// ここ以降は書き換える必要はない．
map<pair<int, string>, VTYPE> dp;
function<VTYPE(int, string)> rf = [&](int i, string s_add) {
if (dp.count({ i, s_add })) return dp[{i, s_add}];
int L_add = sz(s_add);
string sR = s_add;
repir(j, i - 1, 0) {
sR += s[j];
if (rules.count(sR)) {
VTYPE res = 0;
for (auto [i2, s_add2, wgt] : rules[sR]) {
if (i2 >= L_add) {
res += rf(i + L_add - i2, s_add2) * wgt;
}
else {
res += rf(i, s_add2 + s_add.substr(L_add - i2)) * wgt;
}
}
return dp[{i, s_add}] = res;
}
}
return dp[{i, s_add}] = inis[sR];
};
return rf(sz(s), "");
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// zikken();
int n;
cin >> n;
string s;
rep(i, n) {
int a;
cin >> a;
s += '0' + a + 2;
}
EXIT(solve<mint>(s) / mint(2).pow(n - 1));
}