#861645 (C++17) No.2279 OR Insertion

• 問題: No.2279 OR Insertion
• ユーザー: shotoyoo
• 提出日時: 2023-04-21 22:36:35
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 106 ms / 2,000 ms
• コード長: 7,091 bytes
• コンパイル時間: 2,558 ms
• コンパイル使用メモリ: 206,460 KB
• 実行使用メモリ: 5,376 KB
• 最終ジャッジ日時: 2024-04-24 08:43:16
• 合計ジャッジ時間: 5,850 ms
• ジャッジサーバーID （参考情報）: judge1 / judge3

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 5,248 KB
testcase_01	AC	2 ms; 5,376 KB
testcase_02	AC	13 ms; 5,376 KB
testcase_03	AC	6 ms; 5,376 KB
testcase_04	AC	96 ms; 5,376 KB
testcase_05	AC	3 ms; 5,376 KB
testcase_06	AC	37 ms; 5,376 KB
testcase_07	AC	41 ms; 5,376 KB
testcase_08	AC	14 ms; 5,376 KB
testcase_09	AC	54 ms; 5,376 KB
testcase_10	AC	92 ms; 5,376 KB
testcase_11	AC	11 ms; 5,376 KB
testcase_12	AC	70 ms; 5,376 KB
testcase_13	AC	6 ms; 5,376 KB
testcase_14	AC	6 ms; 5,376 KB
testcase_15	AC	48 ms; 5,376 KB
testcase_16	AC	2 ms; 5,376 KB
testcase_17	AC	36 ms; 5,376 KB
testcase_18	AC	60 ms; 5,376 KB
testcase_19	AC	81 ms; 5,376 KB
testcase_20	AC	40 ms; 5,376 KB
testcase_21	AC	29 ms; 5,376 KB
testcase_22	AC	2 ms; 5,376 KB
testcase_23	AC	2 ms; 5,376 KB
testcase_24	AC	1 ms; 5,376 KB
testcase_25	AC	2 ms; 5,376 KB
testcase_26	AC	2 ms; 5,376 KB
testcase_27	AC	2 ms; 5,376 KB
testcase_28	AC	2 ms; 5,376 KB
testcase_29	AC	2 ms; 5,376 KB
testcase_30	AC	2 ms; 5,376 KB
testcase_31	AC	1 ms; 5,376 KB
testcase_32	AC	102 ms; 5,376 KB
testcase_33	AC	104 ms; 5,376 KB
testcase_34	AC	104 ms; 5,376 KB
testcase_35	AC	101 ms; 5,376 KB
testcase_36	AC	103 ms; 5,376 KB
testcase_37	AC	104 ms; 5,376 KB
testcase_38	AC	104 ms; 5,376 KB
testcase_39	AC	104 ms; 5,376 KB
testcase_40	AC	106 ms; 5,376 KB
testcase_41	AC	104 ms; 5,376 KB
testcase_42	AC	100 ms; 5,376 KB
testcase_43	AC	104 ms; 5,376 KB
testcase_44	AC	104 ms; 5,376 KB
testcase_45	AC	96 ms; 5,376 KB
testcase_46	AC	100 ms; 5,376 KB
testcase_47	AC	96 ms; 5,376 KB
testcase_48	AC	100 ms; 5,376 KB
testcase_49	AC	95 ms; 5,376 KB

ソースコード

 bool TEST = false;

using namespace std;
#include<bits/stdc++.h>
#include<fstream>

#define rep(i,n) for(ll (i)=0;(i)<(ll)(n);i++)
#define rrep(i,n) for(ll (i)=(ll)(n)-1;(i)>=0;i--)
#define range(i,start,end,step) for(ll (i)=start;(i)<(ll)(end);(i)+=(step))
#define rrange(i,start,end,step) for(ll (i)=start;(i)>(ll)(end);(i)+=(step))

#define dump(x)  cerr << "Line " << __LINE__ << ": " <<  #x << " = " << (x) << "\n";
#define spa << " " <<
#define fi first
#define se second
#define all(a)  (a).begin(),(a).end()
#define allr(a)  (a).rbegin(),(a).rend()
template <typename T>
T SUM(vector<T> &A) {
  T sum = T(0);
  for (auto &&a: A) sum += a;
  return sum;
}
#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))

using ld = long double;
using ll = long long;
using ull = unsigned long long;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
 
template<typename T> using V = vector<T>;
template<typename T> using VV = V<V<T>>;
template<typename T, typename T2> using P = pair<T, T2>;
template<typename T, typename T2> using UM = unordered_map<T, T2>;
template<typename T> using PQ = priority_queue<T, V<T>, greater<T>>;
template<typename T> using rPQ = priority_queue<T, V<T>, less<T>>;
template<class T>vector<T> make_vec(size_t a){return vector<T>(a);}
template<class T, class... Ts>auto make_vec(size_t a, Ts... ts){return vector<decltype(make_vec<T>(ts...))>(a, make_vec<T>(ts...));}
template<class SS, class T> ostream& operator << (ostream& os, const pair<SS, T> v){os << "(" << v.first << ", " << v.second << ")"; return os;}
template<typename T> ostream& operator<<(ostream &os, const vector<T> &v) { for (auto &e : v) os << e << ' '; return os; }
template<class T> ostream& operator<<(ostream& os, const vector<vector<T>> &v){ for(auto &e : v){os << e << "\n";} return os;}
struct fast_ios { fast_ios(){ cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
 
template <class T> void UNIQUE(vector<T> &x) {sort(all(x));x.erase(unique(all(x)), x.end());}
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
void fail() { cout << -1 << '\n'; exit(0); }
inline int popcount(const int x) { return __builtin_popcount(x); }
inline int popcount(const ll x) { return __builtin_popcountll(x); }
template<typename T> void debug(vector<vector<T>>&v){for(ll i=0;i<v.size();i++)
{cerr<<v[i][0];for(ll j=1;j<v[i].size();j++)cerr spa v[i][j];cerr<<"\n";}};
template<typename T> void debug(vector<T>&v){if(v.size()!=0)cerr<<v[0];
for(ll i=1;i<v.size();i++)cerr spa v[i];
cerr<<"\n";};
template<typename T> void debug(priority_queue<T>&v){V<T> vals; while(!v.empty()) {cerr << v.top() << " "; vals.push_back(v.top()); v.pop();} cerr<<"\n"; for(auto val: vals) v.push(val);}
template<typename T, typename T2> void debug(map<T,T2>&v){for(auto [k,v]: v) cerr << k spa v << "\n"; cerr<<"\n";}
template<typename T, typename T2> void debug(unordered_map<T,T2>&v){for(auto [k,v]: v) cerr << k spa v << "\n";cerr<<"\n";}
V<int> listrange(int n) {V<int> res(n); rep(i,n) res[i]=i; return res;}
string YES = "Yes";
string NO = "No";
void pans(bool v){if (v) cout << YES << "\n"; else cout << NO << "\n";}

template<typename T> P<T,T> divmod(T a, T b) {return make_pair(a/b, a%b);}

const ll INF = (1ll<<62);
// const ld EPS   = 1e-10;
// const ld PI    = acos(-1.0);

template< int mod >
struct ModInt {
  int x;

  ModInt() : x(0) {}

  ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

  ModInt &operator+=(const ModInt &p) {
    if((x += p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator-=(const ModInt &p) {
    if((x += mod - p.x) >= mod) x -= mod;
    return *this;
  }

  ModInt &operator*=(const ModInt &p) {
    x = (int) (1LL * x * p.x % mod);
    return *this;
  }

  ModInt &operator/=(const ModInt &p) {
    *this *= p.inverse();
    return *this;
  }

  ModInt operator-() const { return ModInt(-x); }

  ModInt operator+(const ModInt &p) const { return ModInt(*this) += p; }

  ModInt operator-(const ModInt &p) const { return ModInt(*this) -= p; }

  ModInt operator*(const ModInt &p) const { return ModInt(*this) *= p; }

  ModInt operator/(const ModInt &p) const { return ModInt(*this) /= p; }

  bool operator==(const ModInt &p) const { return x == p.x; }

  bool operator!=(const ModInt &p) const { return x != p.x; }

  ModInt inverse() const {
    int a = x, b = mod, u = 1, v = 0, t;
    while(b > 0) {
      t = a / b;
      swap(a -= t * b, b);
      swap(u -= t * v, v);
    }
    return ModInt(u);
  }

  ModInt pow(int64_t n) const {
    ModInt ret(1), mul(x);
    while(n > 0) {
      if(n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  friend ostream &operator<<(ostream &os, const ModInt &p) {
    return os << p.x;
  }

  friend istream &operator>>(istream &is, ModInt &a) {
    int64_t t;
    is >> t;
    a = ModInt< mod >(t);
    return (is);
  }

  static int get_mod() { return mod; }
};

using m17 = ModInt<1'000'000'007>;
using m98 = ModInt<998'244'353>;
using MOD = m98;
ll mod = 998'244'353;
// using MOD = m17;
// ll mod = 1'000'000'007;


V<MOD> g1;
V<MOD> g2;
V<MOD> inverse;
void prepare(int n) {
  chmax(n,10);
  int s = max(2, (int)g1.size());
  g1.resize(n+1);
  g2.resize(n+1);
  inverse.resize(n+1);
  g1[0] = g1[1] = g2[0] = g2[1] = 1;
  inverse[0] = 0;
  inverse[1] = 1;
  range(i,s,n+1,1) {
    g1[i] = g1[i-1]*i;
    inverse[i] = -inverse[mod%i]*(mod/i);
    g2[i] = g2[i-1]*inverse[i];
  }
}
template<typename T>
MOD cmb(T n, T r) {
  if (r<0 || r>n) return 0;
  if (g1.size()<=n) prepare(n);
  r = min(r, n-r);
  return g1[n]*g2[r]*g2[n-r];
}
template<typename T>
MOD perm(T n, T r) {
  if (r<0 || r>n) return 0;
  if (g1.size()<=n) prepare(n);
  return g1[n]*g2[n-r];
}

void Main(){
    ll n;
    cin >> n;
    string s;
    V<ll> vs(n);
    cin >> s;
    rep(i,n) vs[i] = (s[i]=='1');
    MOD ans = 0;
    range(k,1,n+1,1) {
        VV<MOD> dp = make_vec<MOD>(2,n+1);
        VV<MOD> cum = make_vec<MOD>(2,n+1);
        dp[0][0] = cum[0][0] = 1;
        range(i, 1, n+1, 1) {
            MOD v0 = 0, v1 = 0;
            v1 = cum[1][i-1];
            v0 = cum[0][i-1];
            if (i>=k && vs[i-k]) {
                v1 += cum[0][i-k];
                v0 -= cum[0][i-k];
            }
            dp[0][i] = v0;
            dp[1][i] = v1;
            cum[0][i] += v0 + cum[0][i-1];
            cum[1][i] += v1 + cum[1][i-1];
        }
        ans += dp[1][n] * MOD(2).pow(k-1);
        // cout << k spa dp[1][n] << endl;
        // debug(dp[0]);
        // debug(dp[1]);
        // cout << endl;
    }
    cout << ans << "\n";
}

int main(void){
    std::ifstream in("tmp_in");
    if (TEST) {
        std::cin.rdbuf(in.rdbuf());
        std::cout << std::fixed << std::setprecision(15);
    } else {
        std::cin.tie(nullptr);
        std::ios_base::sync_with_stdio(false);
        std::cout << std::fixed << std::setprecision(15);
    }
    Main();
}