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 |
|
提出日時 | 2022-08-28 19:19:00 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 9 ms / 2,000 ms |
コード長 | 9,842 bytes |
コンパイル時間 | 3,851 ms |
コンパイル使用メモリ | 241,116 KB |
最終ジャッジ日時 | 2025-02-06 22:59:41 |
ジャッジサーバーID (参考情報) |
judge5 / judge2 |
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ファイルパターン | 結果 |
---|---|
other | AC * 80 |
ソースコード
#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 modmint 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;}