結果
| 問題 | No.578 3 x N グリッド上のサイクルのサイズ(easy) |
| ユーザー |
 はむこ
|
| 提出日時 | 2017-06-07 11:05:57 |
| 言語 | C++11 (gcc 13.3.0) |
| 結果 |
AC
|
| 実行時間 | 29 ms / 2,000 ms |
| コード長 | 14,057 bytes |
| コンパイル時間 | 2,502 ms |
| コンパイル使用メモリ | 188,644 KB |
| 実行使用メモリ | 6,944 KB |
| 最終ジャッジ日時 | 2024-09-22 12:42:18 |
| 合計ジャッジ時間 | 4,314 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge5 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 50 |
ソースコード
#include <bits/stdc++.h>
#include <sys/time.h>
using namespace std;
#define rep(i,n) for(long long i = 0; i < (long long)(n); i++)
#define repi(i,a,b) for(long long i = (long long)(a); i < (long long)(b); i++)
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define fi first
#define se second
#define mt make_tuple
#define mp make_pair
template<class T1, class T2> bool chmin(T1 &a, T2 b) { return b < a && (a = b, true); }
template<class T1, class T2> bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
#define exists find_if
#define forall all_of
using ll = long long; using vll = vector<ll>; using vvll = vector<vll>; using P = pair<ll, ll>;
using ld = long double; using vld = vector<ld>;
using vi = vector<int>; using vvi = vector<vi>; vll conv(vi& v) { vll r(v.size()); rep(i, v.size()) r[i] = v[i]; return r; }
using Pos = complex<double>;
template <typename T, typename U> ostream &operator<<(ostream &o, const pair<T, U> &v) { o << "(" << v.first << ", " << v.second << ")"; return o; }
template<size_t...> struct seq{}; template<size_t N, size_t... Is> struct gen_seq : gen_seq<N-1, N-1, Is...>{}; template<size_t... Is> struct gen_seq<0, Is...> : seq<Is...>{};
template<class Ch, class Tr, class Tuple, size_t... Is>
void print_tuple(basic_ostream<Ch,Tr>& os, Tuple const& t, seq<Is...>){ using s = int[]; (void)s{0, (void(os << (Is == 0? "" : ", ") << get<Is>(t)), 0)...}; }
template<class Ch, class Tr, class... Args>
auto operator<<(basic_ostream<Ch, Tr>& os, tuple<Args...> const& t) -> basic_ostream<Ch, Tr>& { os << "("; print_tuple(os, t, gen_seq<sizeof...(Args)>()); return os << ")"; }
ostream &operator<<(ostream &o, const vvll &v) { rep(i, v.size()) { rep(j, v[i].size()) o << v[i][j] << " "; o << endl; } return o; }
template <typename T> ostream &operator<<(ostream &o, const vector<T> &v) { o << '['; rep(i, v.size()) o << v[i] << (i != v.size()-1 ? ", " : ""); o << "]"; return o; }
template <typename T> ostream &operator<<(ostream &o, const set<T> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; }
template <typename T, typename U> ostream &operator<<(ostream &o, const map<T, U> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it << (next(it) != m.end() ? ", " : ""); o << "]"; return o; }
template <typename T, typename U, typename V> ostream &operator<<(ostream &o, const unordered_map<T, U, V> &m) { o << '['; for (auto it = m.begin(); it != m.end(); it++) o << *it; o << "]"; return o; }
vector<int> range(const int x, const int y) { vector<int> v(y - x + 1); iota(v.begin(), v.end(), x); return v; }
template <typename T> istream& operator>>(istream& i, vector<T>& o) { rep(j, o.size()) i >> o[j]; return i;}
string bits_to_string(ll input, ll n=64) { string s; rep(i, n) s += '0' + !!(input & (1ll << i)); reverse(all(s)); return s; }
template <typename T> unordered_map<T, ll> counter(vector<T> vec){unordered_map<T, ll> ret; for (auto&& x : vec) ret[x]++; return ret;};
string substr(string s, P x) {return s.substr(x.fi, x.se - x.fi); }
struct ci : public iterator<forward_iterator_tag, ll> { ll n; ci(const ll n) : n(n) { } bool operator==(const ci& x) { return n == x.n; } bool operator!=(const ci& x) { return !(*this == x); } ci &operator++() { n++; return *this; } ll operator*() const { return n; } };
size_t random_seed; namespace std { using argument_type = P; template<> struct hash<argument_type> { size_t operator()(argument_type const& x) const { size_t seed = random_seed; seed ^= hash<ll>{}(x.fi); seed ^= (hash<ll>{}(x.se) << 1); return seed; } }; }; // hash for various class
namespace myhash{ const int Bsizes[]={3,9,13,17,21,25,29,33,37,41,45,49,53,57,61,65,69,73,77,81}; const int xor_nums[]={0x100007d1,0x5ff049c9,0x14560859,0x07087fef,0x3e277d49,0x4dba1f17,0x709c5988,0x05904258,0x1aa71872,0x238819b3,0x7b002bb7,0x1cf91302,0x0012290a,0x1083576b,0x76473e49,0x3d86295b,0x20536814,0x08634f4d,0x115405e8,0x0e6359f2}; const int hash_key=xor_nums[rand()%20]; const int mod_key=xor_nums[rand()%20]; template <typename T> struct myhash{ std::size_t operator()(const T& val) const { return (hash<T>{}(val)%mod_key)^hash_key; } }; };
template <typename T> class uset:public std::unordered_set<T,myhash::myhash<T>> { using SET=std::unordered_set<T,myhash::myhash<T>>; public: uset():SET(){SET::rehash(myhash::Bsizes[rand()%20]);} };
template <typename T,typename U> class umap:public std::unordered_map<T,U,myhash::myhash<T>> { public: using MAP=std::unordered_map<T,U,myhash::myhash<T>>; umap():MAP(){MAP::rehash(myhash::Bsizes[rand()%20]);} };
struct timeval start; double sec() { struct timeval tv; gettimeofday(&tv, NULL); return (tv.tv_sec - start.tv_sec) + (tv.tv_usec - start.tv_usec) * 1e-6; }
struct init_{init_(){ gettimeofday(&start, NULL); ios::sync_with_stdio(false); cin.tie(0); srand((unsigned int)time(NULL)); random_seed = RAND_MAX / 2 + rand() / 2; }} init__;
static const double EPS = 1e-14;
static const long long INF = 1e18;
static const long long mo = 1e9+7;
#define ldout fixed << setprecision(40)
template<int MOD>
struct ModInt {
static const int Mod = MOD;
unsigned x;
ModInt() : x(0) {}
ModInt(signed sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; }
ModInt(signed long long sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; }
int get() const { return (int)x; }
ModInt &operator+=(ModInt that) { if((x += that.x) >= MOD) x -= MOD; return *this; }
ModInt &operator-=(ModInt that) { if((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
ModInt &operator/=(ModInt that) { return *this *= that.inverse(); }
ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
ModInt inverse() const {
signed a = x, b = MOD, u = 1, v = 0;
while(b) {
signed t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
if(u < 0) u += Mod;
ModInt res; res.x = (unsigned)u;
return res;
}
bool operator==(ModInt that) const { return x == that.x; }
bool operator!=(ModInt that) const { return x != that.x; }
ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; }
};
template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) {
ModInt<MOD> r = 1;
while(k) {
if(k & 1) r *= a;
a *= a;
k >>= 1;
}
return r;
}
typedef ModInt<1000000007> mint;
typedef vector<mint> vmint;
ostream &operator<<(ostream &o, const mint v) { o << v.x; return o; }
// 行列xベクトル
vector<mint> mul(vector<vector<mint>> A, vector<mint> x) {
assert(A.size() >= 0); assert(A[0].size() == x.size());
vector<mint> b(A.size());
rep(i, A.size()) {
rep(j, A[0].size()) {
b[i] += A[i][j] * x[j];
}
}
return b;
}
// 行列x行列
vector<vector<mint>> mul(vector<vector<mint>> A, vector<vector<mint>> B) {
assert(A[0].size() == B.size());
vector<vector<mint>> C(A.size(), vector<mint>(B[0].size()));
rep(i, A.size()) rep(j, B[0].size()) {
rep(h, A[0].size()) {
C[i][j] += A[i][h] * B[h][j];
}
}
return C;
}
// ベクトル+ベクトル
vector<mint> plu(vector<mint> x, vector<mint> y) {
assert(x.size() == y.size());
rep(i, x.size()) {
y[i] += x[i];
}
return y;
}
// 行列+行列
vector<vector<mint>> plu(vector<vector<mint>> A, vector<vector<mint>> B) {
assert(A.size() == B.size());
assert(A[0].size() == B[0].size());
rep(i, A.size()) rep(j, A[0].size()) {
B[i][j] += A[i][j];
}
return B;
}
vector<vector<mint>> transpose(vector<vector<mint>> A) {
rep(i, A.size()) repi(j, i+1, A.size()) swap(A[i][j], A[j][i]);
return A;
}
mint dot(vector<mint> x, vector<mint> y) {
mint ret = 0;
rep(i, x.size())
ret += x[i] * y[i];
return ret;
}
vector<mint> pow(vector<vector<mint>> A, vector<mint> x, long long k) {
if (k == 0) return x;
vector<vector<vector<mint>>> Ak; // Ak[i] = A^{2^i}
Ak.pb(A);
rep(i, 70)
Ak.pb(mul(Ak[i], Ak[i]));
ll cyc = 0;
while (k) {
if (k & 1)
x = mul(Ak[cyc], x);
k /= 2;
cyc++;
}
return x;
}
// GF(mo)列sから、それを生成する最小線形漸化式Cを復元する
//
// 入力: 漸化式が生成したGF(mo)列s
// 出力: d項間漸化式の係数C (size = d+1)
// 漸化式
// C_0 s_{n} + C_1 s_{n-1} + ... + C_{L} s{n-L} = 0
// がsを生成した時、Cを求める。
//
// O(n^2)
//
// 例:
// s = [1, 2, 4, 8] -> C = [1, 1000000005(-2)] (s[1] - 2 * s[0] = 0)
// s = [1, 1, 1, 1] -> C = [1, 1000000006(-1)] (s[1] - s[0] = 0)
int berlekampMassey(const vector<mint> &s, vector<mint> &C) {
int N = (int)s.size();
C.assign(N + 1, mint());
vector<mint> B(N + 1, mint());
C[0] = B[0] = 1;
int degB = 0;
vector<mint> T;
int L = 0, m = 1;
mint b = 1;
for(int n = 0; n < N; ++ n) {
mint d = s[n];
for(int i = 1; i <= L; ++ i)
d += C[i] * s[n - i];
if(d == mint()) {
++ m;
} else {
if(2 * L <= n)
T.assign(C.begin(), C.begin() + (L + 1));
mint coeff = -d * b.inverse();
for(int i = -1; i <= degB; ++ i)
C[m + i] += coeff * B[i];
if(2 * L <= n) {
L = n + 1 - L;
B.swap(T);
degB = (int)B.size() - 1;
b = d;
m = 1;
} else {
++ m;
}
}
}
C.resize(L + 1);
return L;
}
// GF(mo)列aから、それを生成する最小線形漸化式\phiを復元する
// berlekampMasseyとの違いは、係数の順序が違うのと安全用のassertチェックがあること。
//
// 入力: 漸化式が生成したGF(mo)列a
// 出力: d項間漸化式の係数\phi (size = d+1)
// 漸化式
// \phi_0 a_{i} + \phi_1 a_{1} + ... + \phi_L a_L = 0
// がaを生成した時、\phiを求める。
//
// O(n^2)
//
// 例:
// s = [1, 2, 4, 8] -> C = [1000000005(-2), 1] (s[1] - 2 * s[0] = 0)
// s = [1, 1, 1, 1] -> C = [1000000006(-1), 1] (s[1] - s[0] = 0)
void computeMinimumPolynomialForLinearlyRecurrentSequence(const vector<mint> &a, vector<mint> &phi) {
assert(a.size() % 2 == 0);
int L = berlekampMassey(a, phi);
reverse(phi.begin(), phi.begin() + (L + 1));
}
// 漸化式
// \phi_0 a_0 + \phi_1 a_1 + ... + \phi_L a_L = 0
// と、initValues = a[0:phi.size()-1]が与えられる。
// この時、a[k]をinitValues(=a[0:phi.size()-1])の線形結合の係数を返す。
// a[k] = coeff[0] * initValues[0] + coeff[1] * initValues[1] + ... + coeff[d-1] * initValues[d-1]
//
// O(n^2 log k)
void linearlyRecurrentSequenceCoeffs(long long k, const vector<mint> &phi_in, vector<mint> &coeffs) {
int d = (int)phi_in.size() - 1;
assert(d >= 0);
assert(phi_in[d].get() == 1);
coeffs = vector<mint>(d);
vector<mint> square;
coeffs[0] = 1;
int l = 0;
while ((k >> l) > 1) ++l;
for (; l >= 0; --l) {
square.assign(d * 2 - 1, mint());
rep(i, d) rep(j, d) square[i + j] += coeffs[i] * coeffs[j];
for (int i = d * 2 - 2; i >= d; -- i) {
mint c = square[i];
if (c.x == 0) continue;
rep(j, d) square[i - d + j] -= c * phi_in[j];
}
rep(i, d)
coeffs[i] = square[i];
if (k >> l & 1) {
mint lc = coeffs[d - 1];
for(int i = d - 1; i >= 1; -- i)
coeffs[i] = coeffs[i - 1] - lc * phi_in[i];
coeffs[0] = mint() - lc * phi_in[0];
}
}
}
// 漸化式
// \phi_0 a_{i} + \phi_1 a_{1} + ... + \phi_L a_L = 0
// と、initValues = a[0:phi.size()-1]が与えられる。
// この時、
// a_{k}を求める
//
// O(n^2 log k)
//
// また、副産物として、a[k]をinitVectorの線形結合として表す係数coeffが得られる
// a[k] = coeff[0] * initValues[0] + coeff[1] * initValues[1] + ... + coeff[d-1] * initValues[d-1]
//
mint linearlyRecurrentSequenceValue(long long k, const vector<mint> &initValues, const vector<mint> &phi) {
int d = phi.size() - 1;
if(d == 0) return mint();
assert(d <= (int)initValues.size());
assert(k >= 0);
if(k < (int)initValues.size())
return initValues[(int)k];
vector<mint> coeffs;
linearlyRecurrentSequenceCoeffs(k, phi, coeffs);
mint res; rep(i, d) res += coeffs[i] * initValues[i];
return res;
}
// 線形漸化的数列aのk番目は？
// O(n^2 log k)
mint reconstruct(long long k, vector<mint> a) {
if (a.size() % 2) a.pop_back();
vector<mint> a_first_half;
rep(i, a.size() / 2)
a_first_half.push_back(a[i]);
vector<mint> phi;
computeMinimumPolynomialForLinearlyRecurrentSequence(a, phi);
return linearlyRecurrentSequenceValue(k, a_first_half, phi);
}
int main(void) {
ll n; cin >> n;
ll m = 10;
using mat = vector<vector<mint>>;
using vec = vector<mint>;
mat Adot = {
{ 2,-1,-1, 4,-1, 6,-1, 6,-1, 0},
{-1, 2,-1, 4, 4,-1,-1, 6,-1, 0},
{-1,-1, 2,-1, 4, 6,-1, 6,-1, 0},
{ 2, 2,-1, 2, 4,-1,-1, 4,-1, 0},
{-1, 2, 2, 4, 2,-1,-1, 4,-1, 0},
{-1,-1,-1,-1,-1, 4,-1, 4,-1,-1},
{ 2,-1, 2,-1,-1,-1, 4,-1,-1, 0},
{ 2, 2, 2, 2, 2,-1, 4, 2,-1, 0},
{ 4, 4, 4, 6, 6, 8,-1, 8, 0,-1},
{-1,-1,-1,-1,-1,-1,-1,-1,-1, 0},
};
Adot = transpose(Adot);
mat A = Adot;
rep(i, m) rep(j, m) A[i][j] = A[i][j] != -1;
rep(i, m) rep(j, m) if (Adot[i][j] == -1) Adot[i][j] = 0;
vec x = {0,0,0,0,0,0,0,0,1,0};
vec ret(10);
rep(i, n+1) {
vec tmp = x;
tmp = pow(A, tmp, n-i);
tmp = mul(Adot, tmp);
tmp = pow(A, tmp, i);
ret = plu(ret, tmp);
}
cout << ret[9] << endl;
return 0;
}