#182210 (C++11) No.578 3 x N グリッド上のサイクルのサイズ(easy)

提出ソース

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	2017-06-22 10:09:17
言語	C++11 (gcc 11.4.0)
結果	AC
実行時間	26 ms / 2,000 ms
コード長	9,477 bytes
コンパイル時間	2,461 ms
コンパイル使用メモリ	180,788 KB
実行使用メモリ	5,248 KB
最終ジャッジ日時	2024-10-02 10:10:01
合計ジャッジ時間	4,426 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

このコードへのチャレンジ
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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	2 ms 5,248 KB
testcase_01	AC	2 ms 5,248 KB
testcase_02	AC	3 ms 5,248 KB
testcase_03	AC	4 ms 5,248 KB
testcase_04	AC	4 ms 5,248 KB
testcase_05	AC	5 ms 5,248 KB
testcase_06	AC	5 ms 5,248 KB
testcase_07	AC	6 ms 5,248 KB
testcase_08	AC	6 ms 5,248 KB
testcase_09	AC	6 ms 5,248 KB
testcase_10	AC	6 ms 5,248 KB
testcase_11	AC	7 ms 5,248 KB
testcase_12	AC	7 ms 5,248 KB
testcase_13	AC	9 ms 5,248 KB
testcase_14	AC	10 ms 5,248 KB
testcase_15	AC	9 ms 5,248 KB
testcase_16	AC	10 ms 5,248 KB
testcase_17	AC	10 ms 5,248 KB
testcase_18	AC	11 ms 5,248 KB
testcase_19	AC	12 ms 5,248 KB
testcase_20	AC	11 ms 5,248 KB
testcase_21	AC	11 ms 5,248 KB
testcase_22	AC	12 ms 5,248 KB
testcase_23	AC	13 ms 5,248 KB
testcase_24	AC	13 ms 5,248 KB
testcase_25	AC	13 ms 5,248 KB
testcase_26	AC	14 ms 5,248 KB
testcase_27	AC	14 ms 5,248 KB
testcase_28	AC	15 ms 5,248 KB
testcase_29	AC	15 ms 5,248 KB
testcase_30	AC	15 ms 5,248 KB
testcase_31	AC	16 ms 5,248 KB
testcase_32	AC	17 ms 5,248 KB
testcase_33	AC	18 ms 5,248 KB
testcase_34	AC	19 ms 5,248 KB
testcase_35	AC	19 ms 5,248 KB
testcase_36	AC	19 ms 5,248 KB
testcase_37	AC	19 ms 5,248 KB
testcase_38	AC	20 ms 5,248 KB
testcase_39	AC	20 ms 5,248 KB
testcase_40	AC	21 ms 5,248 KB
testcase_41	AC	22 ms 5,248 KB
testcase_42	AC	21 ms 5,248 KB
testcase_43	AC	23 ms 5,248 KB
testcase_44	AC	22 ms 5,248 KB
testcase_45	AC	23 ms 5,248 KB
testcase_46	AC	24 ms 5,248 KB
testcase_47	AC	25 ms 5,248 KB
testcase_48	AC	25 ms 5,248 KB
testcase_49	AC	26 ms 5,248 KB

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ソースコード

raw source code

#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;
}

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;
}

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結果

テストケース

ソースコード