#933371 (C++17) No.2556 Increasing Matrix

• 問題: No.2556 Increasing Matrix
• ユーザー: i_am_noob
• 提出日時: 2023-12-02 01:51:39
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 1,543 ms / 6,000 ms
• コード長: 7,397 bytes
• コンパイル時間: 12,971 ms
• コンパイル使用メモリ: 279,488 KB
• 実行使用メモリ: 30,448 KB
• 最終ジャッジ日時: 2023-12-02 01:52:07
• 合計ジャッジ時間: 13,653 ms
• ジャッジサーバーID （参考情報）: judge13 / judge11

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	3 ms; 6,676 KB
testcase_01	AC	3 ms; 6,676 KB
testcase_02	AC	3 ms; 6,676 KB
testcase_03	AC	3 ms; 6,676 KB
testcase_04	AC	3 ms; 6,676 KB
testcase_05	AC	4 ms; 6,676 KB
testcase_06	AC	3 ms; 6,676 KB
testcase_07	AC	3 ms; 6,676 KB
testcase_08	AC	4 ms; 6,676 KB
testcase_09	AC	8 ms; 6,676 KB
testcase_10	AC	4 ms; 6,676 KB
testcase_11	AC	7 ms; 6,676 KB
testcase_12	AC	5 ms; 6,676 KB
testcase_13	AC	16 ms; 6,676 KB
testcase_14	AC	32 ms; 6,676 KB
testcase_15	AC	32 ms; 6,676 KB
testcase_16	AC	28 ms; 6,676 KB
testcase_17	AC	51 ms; 6,676 KB
testcase_18	AC	742 ms; 19,772 KB
testcase_19	AC	1,256 ms; 24,124 KB
testcase_20	AC	1,306 ms; 25,560 KB
testcase_21	AC	695 ms; 17,508 KB
testcase_22	AC	64 ms; 6,676 KB
testcase_23	AC	1,535 ms; 30,448 KB
testcase_24	AC	1,543 ms; 30,448 KB

ソースコード

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

#define all(a) a.begin(),a.end()
#define pb push_back
#define sz(a) ((int)a.size())

using ll=long long;
using u32=unsigned int;
using u64=unsigned long long;
using i128=__int128;
using u128=unsigned __int128;
using f128=__float128;

using pii=pair<int,int>;
using pll=pair<ll,ll>;

template<typename T> using vc=vector<T>;
template<typename T> using vvc=vc<vc<T>>;
template<typename T> using vvvc=vc<vvc<T>>;

using vi=vc<int>;
using vll=vc<ll>;
using vvi=vc<vi>;
using vvll=vc<vll>;

#define vv(type,name,n,...) \
    vector<vector<type>> name(n,vector<type>(__VA_ARGS__))
#define vvv(type,name,n,m,...) \
    vector<vector<vector<type>>> name(n,vector<vector<type>>(m,vector<type>(__VA_ARGS__)))

template<typename T> using min_heap=priority_queue<T,vector<T>,greater<T>>;
template<typename T> using max_heap=priority_queue<T>;

// https://trap.jp/post/1224/
#define rep1(n) for(ll i=0; i<(ll)(n); ++i)
#define rep2(i,n) for(ll i=0; i<(ll)(n); ++i)
#define rep3(i,a,b) for(ll i=(ll)(a); i<(ll)(b); ++i)
#define rep4(i,a,b,c) for(ll i=(ll)(a); i<(ll)(b); i+=(c))
#define cut4(a,b,c,d,e,...) e
#define rep(...) cut4(__VA_ARGS__,rep4,rep3,rep2,rep1)(__VA_ARGS__)
#define per1(n) for(ll i=((ll)n)-1; i>=0; --i)
#define per2(i,n) for(ll i=((ll)n)-1; i>=0; --i)
#define per3(i,a,b) for(ll i=((ll)a)-1; i>=(ll)(b); --i)
#define per4(i,a,b,c) for(ll i=((ll)a)-1; i>=(ll)(b); i-=(c))
#define per(...) cut4(__VA_ARGS__,per4,per3,per2,per1)(__VA_ARGS__)
#define rep_subset(i,s) for(ll i=(s); i>=0; i=(i==0?-1:(i-1)&(s)))

template<typename T, typename S> constexpr T ifloor(const T a, const S b){return a/b-(a%b&&(a^b)<0);}
template<typename T, typename S> constexpr T iceil(const T a, const S b){return ifloor(a+b-1,b);}

template<typename T>
void sort_unique(vector<T> &vec){
    sort(vec.begin(),vec.end());
    vec.resize(unique(vec.begin(),vec.end())-vec.begin());
}

template<typename T, typename S> constexpr bool chmin(T &a, const S b){if(a>b) return a=b,true; return false;}
template<typename T, typename S> constexpr bool chmax(T &a, const S b){if(a<b) return a=b,true; return false;}

template<typename T, typename S> istream& operator >> (istream& i, pair<T,S> &p){return i >> p.first >> p.second;}
template<typename T, typename S> ostream& operator << (ostream& o, const pair<T,S> &p){return o << p.first << ' ' << p.second;}

#ifdef i_am_noob
#define bug(...) cerr << "#" << __LINE__ << ' ' << #__VA_ARGS__ << "- ", _do(__VA_ARGS__)
template<typename T> void _do(vector<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(unordered_set<T> x){for(auto i: x) cerr << i << ' ';cerr << "\n";}
template<typename T> void _do(T && x) {cerr << x << endl;}
template<typename T, typename ...S> void _do(T && x, S&&...y) {cerr << x << ", "; _do(y...);}
#else
#define bug(...) 777771449
#endif

template<typename T> void print(vector<T> x){for(auto i: x) cout << i << ' ';cout << "\n";}
template<typename T> void print(set<T> x){for(auto i: x) cout << i << ' ';cout << "\n";}
template<typename T> void print(unordered_set<T> x){for(auto i: x) cout << i << ' ';cout << "\n";}
template<typename T> void print(T && x) {cout << x << "\n";}
template<typename T, typename... S> void print(T && x, S&&... y) {cout << x << ' ';print(y...);}

template<typename T> istream& operator >> (istream& i, vector<T> &vec){for(auto &x: vec) i >> x; return i;}

vvi read_graph(int n, int m, int base=1){
    vvi adj(n);
    for(int i=0,u,v; i<m; ++i){
        cin >> u >> v,u-=base,v-=base;
        adj[u].pb(v),adj[v].pb(u);
    }
    return adj;
}

vvi read_tree(int n, int base=1){return read_graph(n,n-1,base);}

template<typename T, typename S> pair<T,S> operator + (const pair<T,S> &a, const pair<T,S> &b){return {a.first+b.first,a.second+b.second};}

template<typename T> constexpr T inf=0;
template<> constexpr int inf<int> = 0x3f3f3f3f;
template<> constexpr ll inf<ll> = 0x3f3f3f3f3f3f3f3f;

template<typename T> vector<T> operator += (vector<T> &a, int val){for(auto &i: a) i+=val; return a;}

template<typename T> T isqrt(const T &x){T y=sqrt(x+2); while(y*y>x) y--; return y;}

#define ykh mt19937 rng(chrono::steady_clock::now().time_since_epoch().count())

#include<atcoder/all>
using namespace atcoder;

using mint=modint998244353;
//using mint=modint1000000007;

const int N=1<<17,mod=998244353;
struct NTT {
  mint w[N];
  NTT() {
    mint dw = mint(3).pow((mod-1)/N);
    w[0] = 1;
    for (int i = 1; i < N; ++i)
      w[i] = w[i-1]*dw;
  }
  void operator()(vector<mint>& a, bool inv = false) {
    int x = 0, n = a.size();
    for (int j = 1; j < n - 1; ++j) {
      for (int k = n >> 1; (x ^= k) < k; k >>= 1);
      if (j < x) swap(a[x], a[j]);
    }
    for (int L = 2; L <= n; L <<= 1) {
      int dx = N / L, dl = L >> 1;
      for (int i = 0; i < n; i += L) {
        for (int j = i, x = 0; j < i + dl; ++j, x += dx) {
          mint tmp = a[j+dl]*w[x];
          a[j + dl] = a[j]-tmp;
          a[j] = a[j]+tmp;
        }
      }
    }
    if (inv) {
      reverse(a.begin() + 1, a.end());
      mint invn = mint(n).pow(mod-2);
      for (int i = 0; i < n; ++i)
        a[i] = a[i]*invn;
    }
  }
} ntt;

vc<mint> Inverse(vc<mint> a) {
  int n = a.size();
  vc<mint> res(1, a[0].pow(mod-2));
  for (int m = 1; m < n; m <<= 1) {
    if (n < m * 2) a.resize(m * 2);
    vc<mint> v1(a.begin(), a.begin() + m * 2), v2 = res;
    v1.resize(m * 4), v2.resize(m * 4);
    ntt(v1), ntt(v2);
    for (int i = 0; i < m * 4; ++i)
      v1[i] = v1[i]*v2[i]*v2[i];
    ntt(v1, true);
    res.resize(m * 2);
    for (int i = 0; i < m; ++i)
      res[i] = res[i]+res[i];
    for (int i = 0; i < m * 2; ++i)
      res[i] = res[i]-v1[i];
  }
  res.resize(n);
  return res;
}

vc<mint> rem(vc<mint> a, vc<mint> b) {
  int n = a.size(), m = b.size(), k = n - m + 1;
  if (n < m) return a;
  vc<mint> ra = a, rb = b;
  reverse(all(ra)), ra.resize(k);
  reverse(all(rb)), rb.resize(k);
  vc<mint> Q = convolution(ra, Inverse(rb));
  Q.resize(k);
  reverse(all(Q));
  vc<mint> res = convolution(b, Q), R(m - 1);
  for (int i = 0; i < m - 1; ++i)
    R[i] = a[i] - res[i];
  return R;
}

void ahcorz(){
    int n; cin >> n;
    vc<mint> a(n);
    rep(n){
        int x; cin >> x; x+=i;
        a[i]=x;
    }
    vc<vc<mint>> vec(n*4);
    auto get=[&](auto &self, int k, int l, int r) -> void{
        if(l+1==r){
            vec[k]={-a[l],1};
            return;
        }
        int mid=l+r>>1;
        self(self,k<<1,l,mid),self(self,k<<1|1,mid,r);
        vec[k]=convolution(vec[k<<1],vec[k<<1|1]);
    };
    get(get,1,0,n);
    auto solve=[&](auto &self, int k, int l, int r, vc<mint> P) -> mint{
        if(l+1==r){
            reverse(all(P));
            mint res;
            for(auto &x: P) res=res*a[l]+x;
            return res;
        }
        int mid=l+r>>1;
        vc<mint> L=rem(convolution(P,vec[k<<1|1]),vec[k<<1]);
        vc<mint> R=rem(P,vec[k<<1|1]);
        return self(self,k<<1,l,mid,L)*self(self,k<<1|1,mid,r,R);
    };
    mint res=solve(solve,1,0,n,{1});
    mint cur=1;
    rep(i,2,n){
        cur*=i;
        res*=cur.inv();
    }
    print((res*res).val());
}

signed main(){
    ios_base::sync_with_stdio(0),cin.tie(0);
    cout << fixed << setprecision(20);
    int t=1;
    //cin >> t;
    while(t--) ahcorz();
}