結果

問題 No.2105 Avoid MeX
ユーザー shotoyooshotoyoo
提出日時 2022-10-21 22:43:06
言語 C++23
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 190 ms / 2,000 ms
コード長 7,093 bytes
コンパイル時間 3,308 ms
コンパイル使用メモリ 253,332 KB
実行使用メモリ 9,088 KB
最終ジャッジ日時 2024-07-01 07:09:26
合計ジャッジ時間 5,325 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
このコードへのチャレンジ
（要ログイン）

テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 7 ms
9,088 KB
testcase_01 AC 6 ms
9,088 KB
testcase_02 AC 7 ms
9,088 KB
testcase_03 AC 7 ms
8,960 KB
testcase_04 AC 80 ms
9,088 KB
testcase_05 AC 6 ms
9,088 KB
testcase_06 AC 29 ms
8,960 KB
testcase_07 AC 37 ms
9,088 KB
testcase_08 AC 10 ms
8,960 KB
testcase_09 AC 80 ms
9,088 KB
testcase_10 AC 7 ms
9,088 KB
testcase_11 AC 6 ms
9,088 KB
testcase_12 AC 14 ms
9,088 KB
testcase_13 AC 7 ms
9,088 KB
testcase_14 AC 27 ms
9,088 KB
testcase_15 AC 44 ms
9,088 KB
testcase_16 AC 7 ms
9,088 KB
testcase_17 AC 6 ms
8,960 KB
testcase_18 AC 7 ms
8,960 KB
testcase_19 AC 190 ms
9,088 KB
testcase_20 AC 188 ms
8,960 KB
testcase_21 AC 189 ms
9,088 KB
testcase_22 AC 189 ms
9,088 KB
testcase_23 AC 7 ms
9,088 KB
testcase_24 AC 6 ms
9,088 KB
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 # 

 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 M = map<T, T2>;
template<typename T> using S = set<T>;
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;}

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;


const int _B = 500500;
V<MOD> g1(_B);
V<MOD> g2(_B);
V<MOD> inverse(_B);
void prepare() {
  g1[0] = g1[1] = g2[0] = g2[1] = 1;
  inverse[0] = 0;
  inverse[1] = 1;
  range(i,2,_B,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) {
  assert(g1[0]==1);
  if (r<0 || r>n) return 0;
  if (g1.size()<=n) {
      int s = g1.size();
      g1.resize(n+1);
      g2.resize(n+1);
      inverse.resize(n+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];
      }
  }
  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;
  return g1[n]*g2[n-r];
}

void Main(){
    ll c,x;
    cin >> c >> x;
    MOD ans = 0;
    if (x==0) {
        ans = MOD(1) / (c+1);
    } else if (x<=c) {
        ans = MOD(x) / (x+1);
    } else {
        // x>c
        V<MOD> dp(x+1);
        dp[0] = 1;
        rep(i,x-c) {
            V<MOD> ndp(x+1);
            rep(j,x+1) {
                auto val = dp[j];
                if (val==0) continue;
                MOD pr = MOD(j) / (c+i+1);
                ndp[j] += val * pr;
                ndp[j+1] += val * (MOD(1)-pr);
            }
            swap(dp, ndp);
            // debug(dp);
        }
        ans = 0;
        rep(i,x) {
            ans += dp[i] * (MOD(1) - MOD(1) / MOD(x-i+1));
        }
        
    }

    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();
}
0