結果

問題 No.621 3 x N グリッド上のドミノの置き方の数
ユーザー fumofumofuni
提出日時 2022-08-28 21:30:08
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 22 ms / 3,000 ms
コード長 10,131 bytes
コンパイル時間 3,582 ms
コンパイル使用メモリ 240,488 KB
最終ジャッジ日時 2025-02-06 23:06:09
ジャッジサーバーID
（参考情報） 		judge2 / judge2
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 2
other AC * 66
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ソースコード

diff #
プレゼンテーションモードにする

#include<bits/stdc++.h>
using namespace std;
#define rep(i,n) for(ll i=0;i<n;i++)
#define repl(i,l,r) for(ll i=(l);i<(r);i++)
#define per(i,n) for(ll i=(n)-1;i>=0;i--)
#define perl(i,r,l) for(ll i=r-1;i>=l;i--)
#define fi first
#define se second
#define pb push_back
#define ins insert
#define pqueue(x) priority_queue<x,vector<x>,greater<x>>
#define all(x) (x).begin(),(x).end()
#define CST(x) cout<<fixed<<setprecision(x)
#define vtpl(x,y,z) vector<tuple<x,y,z>>
#define rev(x) reverse(x);
using ll=long long;
using vl=vector<ll>;
using vvl=vector<vector<ll>>;
using pl=pair<ll,ll>;
using vpl=vector<pl>;
using vvpl=vector<vpl>;
const ll MOD=1000000007;
const ll MOD9=998244353;
const int inf=1e9+10;
const ll INF=4e18;
const ll dy[9]={0,1,0,-1,1,1,-1,-1,0};
const ll dx[9]={1,0,-1,0,1,-1,1,-1,0};
template<class T> inline bool chmin(T& a, T b) {
    if (a > b) {
        a = b;
        return true;
    }
    return false;
}
template<class T> inline bool chmax(T& a, T b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}
const int mod = MOD;
const int max_n = 200005;
struct mint {
  ll x; // typedef long long ll;
  mint(ll x=0):x((x%mod+mod)%mod){}
  mint operator-() const { return mint(-x);}
  mint& operator+=(const mint a) {
    if ((x += a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator-=(const mint a) {
    if ((x += mod-a.x) >= mod) x -= mod;
    return *this;
  }
  mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;}
  mint operator+(const mint a) const { return mint(*this) += a;}
  mint operator-(const mint a) const { return mint(*this) -= a;}
  mint operator*(const mint a) const { return mint(*this) *= a;}
  mint pow(ll t) const {
    if (!t) return 1;
    mint a = pow(t>>1);
    a *= a;
    if (t&1) a *= *this;
    return a;
  }
  bool operator==(const mint &p) const { return x == p.x; }
  bool operator!=(const mint &p) const { return x != p.x; }
  // for prime mod
  mint inv() const { return pow(mod-2);}
  mint& operator/=(const mint a) { return *this *= a.inv();}
  mint operator/(const mint a) const { return mint(*this) /= a;}
};
istream& operator>>(istream& is, mint& a) { return is >> a.x;}
ostream& operator<<(ostream& os, const mint& a) { return os << a.x;}
using vm=vector<mint>;
using vvm=vector<vm>;
struct combination {
  vector<mint> fact, ifact;
  combination(int n):fact(n+1),ifact(n+1) {
    assert(n < mod);
    fact[0] = 1;
    for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i;
    ifact[n] = fact[n].inv();
    for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i;
  }
  mint operator()(int n, int k) {
    if (k < 0 || k > n) return 0;
    return fact[n]*ifact[k]*ifact[n-k];
  }
}comb(max_n);
struct UnionFind {
    vector<int> par;
    vector<int> edge;
    
    UnionFind(int n) : par(n, -1),edge(n, 0) {}
    int root(int x) {
        if (par[x] < 0) return x;
        else return par[x] = root(par[x]);
    }
    
    bool same(int x, int y) {
        return root(x) == root(y);
    }
    
    bool merge(int x, int y) {
        x = root(x); y = root(y);
        if (x == y) {
            edge[x]++;
            return false;
        }
        if (par[x] > par[y]) swap(x, y);
        par[x] += par[y];
        par[y] = x;
        edge[x] += edge[y]+1;
        return true;
    }
    
    int size(int x) {
        return -par[root(x)];
    }
};
vector<mint> BerlekampMassey(const vector<mint> &s) {
  const int N = (int)s.size();
  vector<mint> b, c;
  b.reserve(N + 1);
  c.reserve(N + 1);
  b.push_back(mint(1));
  c.push_back(mint(1));
  mint y = mint(1);
  for (int ed = 1; ed <= N; ed++) {
    int l = int(c.size()), m = int(b.size());
    mint x = 0;
    for (int i = 0; i < l; i++) x += c[i] * s[ed - l + i];
    b.emplace_back(mint(0));
    m++;
    if (x == mint(0)) continue;
    mint freq = x / y;
    if (l < m) {
      auto tmp = c;
      c.insert(begin(c), m - l, mint(0));
      for (int i = 0; i < m; i++) c[m - 1 - i] -= freq * b[m - 1 - i];
      b = tmp;
      y = x;
    } else {
      for (int i = 0; i < m; i++) c[l - 1 - i] -= freq * b[m - 1 - i];
    }
  }
  reverse(begin(c), end(c));
  return c;
}
template <typename mint>
vector<mint> kitamasa(vector<mint> Q,vector<mint> a) {
  assert(!Q.empty() && Q[0] != 0);
  assert((int)a.size() >= int(Q.size()) - 1);
  vector<mint> P(Q.size()*2-2);
  for(ll i=0;i<Q.size()-1;i++){
    for(ll j=0;j<Q.size();j++){
     P[i+j]+=a[i]*Q[j];
    }
  } 
  P.resize(Q.size() - 1);
  return P;
}
template<class T>
struct bostan_mori {
  vector<T> p, q;
  bostan_mori(vector<T> &_p, vector<T> &_q) : p(_p), q(_q) {}
  void rever(vector<T> &f) const {
    int d = f.size();
    rep(i, d) if (i&1) f[i] = -f[i];
  }
  void even(vector<T> &f) const {
    int d = (f.size() + 1) >> 1;
    rep(i, d) f[i] = f[i<<1];
    f.resize(d);
  }
  void odd(vector<T> &f) const {
    int d = f.size() >> 1;
    rep(i, d) f[i] = f[i<<1|1];
    f.resize(d);
  }
  vector<T> convolution(vector<T> a,vector<T> b) const{
    int n=a.size(),m=b.size();
    vector<T> c(n+m-1);
    rep(i,n)rep(j,m)c[i+j]+=a[i]*b[j];
    return c;
  }
  T operator[] (ll n) const {
    vector<T> _p(p), _q(q), _q_rev(q);
    rever(_q_rev);
    for (; n; n >>= 1) {
      _p = convolution(move(_p), _q_rev);
      if (n&1) odd(_p);
      else     even(_p);
      _q = convolution(move(_q), move(_q_rev));
      even(_q);
      _q_rev = _q; rever(_q_rev);
    }
    return _p[0] / _q[0];
  }
};
//https://nyaannyaan.github.io/library/fps/kitamasa.hpp
//https://atcoder.jp/contests/tdpc/submissions/34362182
//線形漸化式のprefixからn項目を復元できる。
bostan_mori<mint> interpolation(vm a){
  auto q=BerlekampMassey(a);
  auto p=kitamasa(q,a);
  return bostan_mori<mint>(p,q);
}
mint solve(ll n){
  map<vl,mint> dp;
  dp[{2,2,2}]=1;
  rep(_,n){
    map<vl,mint> ndp;
    for(auto [v,val]:dp){
      set<vl> st;
      st.insert(vl({-1,-1,-1}));
      {
        set<vl> nst=st;
        for(auto p:st){
          if(p[0]==-1&&p[1]==-1&&v[0]!=0&&v[1]!=0){
            p[0]=2;p[1]=2;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(p[1]==-1&&p[2]==-1&&v[1]!=0&&v[2]!=0){
            p[1]=2;p[2]=2;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[0]==0&&p[0]==-1){
            p[0]=2;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[1]==0&&p[1]==-1){
            p[1]=2;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[2]==0&&p[2]==-1){
            p[2]=2;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[0]!=0&&p[0]==-1){
            p[0]=0;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[1]!=0&&p[1]==-1){
            p[1]=0;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[2]!=0&&p[2]==-1){
            p[2]=0;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[0]!=0&&p[0]==-1&&v[0]!=1&&p[1]!=1){
            p[0]=1;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[1]!=0&&p[1]==-1&&v[1]!=1&&p[0]!=1&&p[2]!=1){
            p[1]=1;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      {
        set<vl> nst=st;
        for(auto p:st){
          if(v[2]!=0&&p[2]==-1&&v[2]!=1&&p[1]!=1){
            p[2]=1;
            nst.insert(p);
          }
        }
        swap(st,nst);
      }
      for(auto to:st){
        bool ok=true;
        rep(i,3)if(to[i]==-1)ok=false;
        if(ok)ndp[to]+=val;
      }
    }
    swap(dp,ndp);
  }
  mint ans=0;
  for(auto p:dp){
    bool ok=true;
    rep(i,3)if(p.first[i]==0)ok=false;
    if(ok)ans+=p.second;
  }
  return ans;
}
vm dp={
1,
2,
5,
22,
75,
264,
941,
3286,
11623,
40960,
144267,
508812,
1792981,
6319994,
22277291,
78518760,
276763545,
975517878,
438444562,
119670782,
718700373,
572582090,
730060385,
688016070,
699386708,
110529611,
995262545,
597995343,
640606626,
241830833,
272804340,
283380443,
545790282,
699375508,
859877759,
656285179,
175970508,
314324844,
545142464,
835141447,
795582614,
192966456,
219968013,
455478810,
545912024,
375190023,
626023603,
293536141,
560368619,
515677853,
858117007,
300028037,
323658700,
884276037,
615126475,
820479119,
409463537,
519011336,
207995574,
676075945,
573865793,
859615676,
937178370,
254676667,
361664011,
247757645,
807832664,
823378986,
553804392,
846880559,
787975932,
653917694,
636527187,
952330033,
103503637,
561719530,
68932534,
83040414,
231438915,
389821013,
925377561,
942722655,
395984742,
581085945,
336440498,
145041049,
95458618,
909033807,
307451509,
297905891,
519194781,
15254485,
80527014,
867190435,
565648478,
116363033,
22522660,
23400456,
66368402,
85236134,
217561183,
35604679,
960146403,
31549076,
894013996,
13564442,
791506429,
932281824,
471367224,
76874437,
675671298,
561189725,
270253654,
685195151,
303935889,
277050023,
619882550,
658318681,
876159999,
982371168,
710953743,
103955127,
175947231,
87173702,
606258895,
533286899,
275053460,
56133425,
985751894,
54859081,
260694339,
445176464,
471996759,
832484215,
127132888,
790868694,
903376452,
791292432,
873258058,
402781172,
933259293,
732236683,
651088116,
469228293,
258009983,
917049638,
564753087,
187008063,
591180573,
382553735,
737338319,
570739188,
726174728,
305294669,
359583017
};
int main(){
  /*rep(i,200){
    cout << solve(i) <<","<< endl;
  }*/
  ll n;cin >> n;
  auto ip=interpolation(dp);
  cout << ip[n] << endl;
}
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