結果

問題 No.579 3 x N グリッド上のサイクルのサイズ(hard)
ユーザー fumofumofunifumofumofuni
提出日時 2022-08-28 19:19:00
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 7 ms / 2,000 ms
コード長 9,842 bytes
コンパイル時間 3,630 ms
コンパイル使用メモリ 250,932 KB
実行使用メモリ 6,528 KB
最終ジャッジ日時 2024-10-15 16:46:32
合計ジャッジ時間 6,469 ms
ジャッジサーバーID
（参考情報） 		judge3 / judge2
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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 6 ms
6,400 KB
testcase_01 AC 6 ms
6,400 KB
testcase_02 AC 6 ms
6,400 KB
testcase_03 AC 6 ms
6,528 KB
testcase_04 AC 7 ms
6,400 KB
testcase_05 AC 7 ms
6,528 KB
testcase_06 AC 7 ms
6,400 KB
testcase_07 AC 6 ms
6,528 KB
testcase_08 AC 7 ms
6,400 KB
testcase_09 AC 6 ms
6,400 KB
testcase_10 AC 6 ms
6,400 KB
testcase_11 AC 6 ms
6,528 KB
testcase_12 AC 7 ms
6,400 KB
testcase_13 AC 7 ms
6,528 KB
testcase_14 AC 7 ms
6,528 KB
testcase_15 AC 7 ms
6,528 KB
testcase_16 AC 7 ms
6,528 KB
testcase_17 AC 7 ms
6,400 KB
testcase_18 AC 6 ms
6,400 KB
testcase_19 AC 7 ms
6,528 KB
testcase_20 AC 7 ms
6,528 KB
testcase_21 AC 6 ms
6,528 KB
testcase_22 AC 7 ms
6,528 KB
testcase_23 AC 7 ms
6,400 KB
testcase_24 AC 6 ms
6,400 KB
testcase_25 AC 7 ms
6,528 KB
testcase_26 AC 7 ms
6,400 KB
testcase_27 AC 6 ms
6,400 KB
testcase_28 AC 6 ms
6,400 KB
testcase_29 AC 7 ms
6,400 KB
testcase_30 AC 7 ms
6,528 KB
testcase_31 AC 7 ms
6,400 KB
testcase_32 AC 6 ms
6,400 KB
testcase_33 AC 6 ms
6,400 KB
testcase_34 AC 7 ms
6,528 KB
testcase_35 AC 6 ms
6,528 KB
testcase_36 AC 7 ms
6,528 KB
testcase_37 AC 7 ms
6,528 KB
testcase_38 AC 7 ms
6,400 KB
testcase_39 AC 6 ms
6,400 KB
testcase_40 AC 6 ms
6,528 KB
testcase_41 AC 7 ms
6,400 KB
testcase_42 AC 6 ms
6,528 KB
testcase_43 AC 7 ms
6,400 KB
testcase_44 AC 7 ms
6,528 KB
testcase_45 AC 6 ms
6,528 KB
testcase_46 AC 7 ms
6,400 KB
testcase_47 AC 7 ms
6,400 KB
testcase_48 AC 7 ms
6,528 KB
testcase_49 AC 6 ms
6,528 KB
testcase_50 AC 7 ms
6,400 KB
testcase_51 AC 6 ms
6,528 KB
testcase_52 AC 7 ms
6,528 KB
testcase_53 AC 6 ms
6,528 KB
testcase_54 AC 6 ms
6,528 KB
testcase_55 AC 7 ms
6,400 KB
testcase_56 AC 7 ms
6,400 KB
testcase_57 AC 7 ms
6,528 KB
testcase_58 AC 7 ms
6,400 KB
testcase_59 AC 6 ms
6,528 KB
testcase_60 AC 6 ms
6,400 KB
testcase_61 AC 7 ms
6,400 KB
testcase_62 AC 7 ms
6,528 KB
testcase_63 AC 7 ms
6,400 KB
testcase_64 AC 6 ms
6,400 KB
testcase_65 AC 7 ms
6,528 KB
testcase_66 AC 7 ms
6,400 KB
testcase_67 AC 7 ms
6,528 KB
testcase_68 AC 6 ms
6,400 KB
testcase_69 AC 7 ms
6,528 KB
testcase_70 AC 7 ms
6,400 KB
testcase_71 AC 7 ms
6,400 KB
testcase_72 AC 6 ms
6,528 KB
testcase_73 AC 7 ms
6,400 KB
testcase_74 AC 6 ms
6,528 KB
testcase_75 AC 7 ms
6,400 KB
testcase_76 AC 7 ms
6,528 KB
testcase_77 AC 7 ms
6,400 KB
testcase_78 AC 7 ms
6,400 KB
testcase_79 AC 7 ms
6,528 KB
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ソースコード

diff # 

#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)];
    }
};
ll score(ll bit){
  if(bit==7||bit==5)return 4;
  if(__builtin_popcount(bit)==2)return 3;
  return 2;
}
ll sc(vl v){
  ll bit=0;
  rep(i,3)if(v[i])bit|=1<<i;
  return score(bit);
}
mint solve(ll n){
    map<pair<vl,ll>,mint> dp;
    mint ans=0;
    rep(_,n+1){
        map<pair<vl,ll>,mint> ndp;
        for(auto [x,ret]:dp){
            auto [v,leng]=x;
            if(v.back()!=2)ans+=ret*(leng+sc(v));
        }
        for(auto [x,rrr]:dp){
            auto [v,leng]=x;
            repl(bit,1,1<<3){
                ll cir=0;
                if(bit==7&&v==(vl){1,0,1})continue;//穴あきの防止
                {//自己交差の防止
                    vl nnn;
                    nnn.push_back(bit>>0&1);
                    nnn.push_back(bit>>1&1);
                    nnn.push_back(min(1LL,v[0]));
                    nnn.push_back(min(1LL,v[1]));
                    if(nnn==(vl){1,0,0,1}||nnn==(vl){0,1,1,0})continue;
                    if(nnn!=(vl){1,1,1,1}&&nnn!=(vl){0,0,0,0})cir++;
                }
                {
                    vl nnn;
                    nnn.push_back(bit>>1&1);
                    nnn.push_back(bit>>2&1);
                    nnn.push_back(min(1LL,v[1]));
                    nnn.push_back(min(1LL,v[2]));
                    if(nnn==(vl){1,0,0,1}||nnn==(vl){0,1,1,0})continue;
                    if(nnn!=(vl){1,1,1,1}&&nnn!=(vl){0,0,0,0})cir++;
                }
                {
                  vl nnn;
                  nnn.push_back(bit>>0&1);
                  nnn.push_back(min(1LL,v[0]));
                  if(nnn!=(vl){0,0})cir++;
                }
                {
                  vl nnn;
                  nnn.push_back(bit>>2&1);
                  nnn.push_back(min(1LL,v[2]));
                  if(nnn!=(vl){0,0})cir++;
                }
                UnionFind uf(6);
                if(v[0]&&v[1])uf.merge(0,1);
                if(v[1]&&v[2])uf.merge(1,2);
                if(v[0]&&(bit>>0&1))uf.merge(0,3);
                if(v[1]&&(bit>>1&1))uf.merge(1,4);
                if(v[2]&&(bit>>2&1))uf.merge(2,5);
                if((bit>>0&1)&&(bit>>1&1))uf.merge(3,4);
                if((bit>>1&1)&&(bit>>2&1))uf.merge(4,5);
                if(v[0]==v[2]&&v[0])uf.merge(0,2);
                vl nv={0,0,0};
                rep(i,3){
                    rep(j,3){
                        if(uf.same(i,j+3))nv[i]=1;
                    }
                }
                if(v[0]&&nv[0]==0)continue;
                if(v[1]&&nv[1]==0)continue;
                if(v[2]&&nv[2]==0)continue;
                vl con(3);map<ll,ll> mp;ll now=1;
                rep(i,3){
                    if(bit>>i&1){
                        ll p=uf.root(i+3);
                        if(mp.count(p))con[i]=mp[p];
                        else{
                            mp[p]=now;now++;
                            con[i]=mp[p];
                        }
                    }
                }
                ndp[{con,leng+cir}]+=rrr;
            }
        }
        ndp[{{0,0,1},2}]+=1;
        ndp[{{0,1,1},3}]+=1;
        ndp[{{1,1,1},4}]+=1;
        ndp[{{0,1,0},2}]+=1;
        ndp[{{1,0,0},2}]+=1;
        ndp[{{1,1,0},3}]+=1;
        ndp[{{1,0,2},4}]+=1;
        swap(dp,ndp);
    }
    return ans;
}



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);
}
vm ps={
0,
32,
316,
2292,
14422,
84744,
479004,
2638328,
14258574,
75940592,
399782668,
84795558,
786749020,
442043859,
352536615,
76576421,
744912747,
420315017,
25759333,
562730793,
424899366,
153177921,
250747498,
306910436,
324829483,
572545341,
104022619,
226237183,
421453002,
754280938,
291624319,
60437277,
297658752,
677142927,
63550828,
801541292,
683008492,
650348,
519624175,
715484025,
724658778,
152363657,
280344328,
892278238,
206785631,
227202296,
788486407,
392284243,
927772200,
781378846,
881515964,
905982211,
674841192,
139044658,
711210295,
384364637,
137653614,
441363040,
812818651,
929556368,
494420762,
802527485,
700803632,
461521718,
152786116,
688977792,
48724029,
642700933,
15567410,
246397043,
859581827,
685250826,//71
};
int main(){
  ll n;cin >> n;
    auto ip=interpolation(ps);
    cout << ip[n] << endl;
}
0