#810909 (C++17) 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	heno239
提出日時	2022-10-25 17:50:34
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	14 ms / 2,000 ms
コード長	8,840 bytes
コンパイル時間	3,050 ms
コンパイル使用メモリ	179,656 KB
実行使用メモリ	20,164 KB
最終ジャッジ日時	2024-07-03 15:48:19
合計ジャッジ時間	4,569 ms
ジャッジサーバーID （参考情報）	judge1 / judge3

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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	13 ms 20,044 KB
testcase_01	AC	13 ms 19,912 KB
testcase_02	AC	13 ms 20,036 KB
testcase_03	AC	13 ms 20,036 KB
testcase_04	AC	13 ms 19,908 KB
testcase_05	AC	13 ms 20,040 KB
testcase_06	AC	13 ms 20,164 KB
testcase_07	AC	13 ms 19,908 KB
testcase_08	AC	13 ms 19,912 KB
testcase_09	AC	13 ms 19,916 KB
testcase_10	AC	12 ms 20,040 KB
testcase_11	AC	12 ms 20,036 KB
testcase_12	AC	13 ms 19,912 KB
testcase_13	AC	14 ms 20,040 KB
testcase_14	AC	13 ms 20,044 KB
testcase_15	AC	13 ms 19,912 KB
testcase_16	AC	12 ms 19,912 KB
testcase_17	AC	13 ms 20,040 KB
testcase_18	AC	12 ms 19,908 KB
testcase_19	AC	13 ms 20,044 KB
testcase_20	AC	11 ms 19,912 KB
testcase_21	AC	11 ms 19,916 KB
testcase_22	AC	11 ms 19,912 KB
testcase_23	AC	11 ms 20,036 KB
testcase_24	AC	10 ms 20,040 KB
testcase_25	AC	12 ms 19,912 KB
testcase_26	AC	12 ms 20,040 KB
testcase_27	AC	11 ms 20,040 KB
testcase_28	AC	12 ms 19,912 KB
testcase_29	AC	12 ms 20,036 KB
testcase_30	AC	13 ms 19,912 KB
testcase_31	AC	11 ms 19,916 KB
testcase_32	AC	13 ms 20,040 KB
testcase_33	AC	13 ms 20,044 KB
testcase_34	AC	12 ms 20,036 KB
testcase_35	AC	12 ms 20,036 KB
testcase_36	AC	12 ms 19,912 KB
testcase_37	AC	12 ms 20,040 KB
testcase_38	AC	11 ms 20,036 KB
testcase_39	AC	10 ms 20,040 KB
testcase_40	AC	12 ms 19,908 KB
testcase_41	AC	11 ms 20,044 KB
testcase_42	AC	11 ms 19,912 KB
testcase_43	AC	13 ms 20,040 KB
testcase_44	AC	12 ms 20,040 KB
testcase_45	AC	12 ms 20,040 KB
testcase_46	AC	12 ms 19,908 KB
testcase_47	AC	11 ms 19,912 KB
testcase_48	AC	11 ms 19,916 KB
testcase_49	AC	11 ms 19,912 KB

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ソースコード

raw source code

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;

//#define int long long
typedef long long ll;

typedef unsigned long long ul;
typedef unsigned int ui;
//constexpr ll mod = 998244353;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;

#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;

template<typename T>
void chmin(T& a, T b) {
	a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
	a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
	rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
	rep(i, v.size()) {
		if (i > 0)cout << " "; cout << v[i];
	}
	cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
	if (n < 0) {
		ll res = mod_pow(x, -n, m);
		return mod_pow(res, m - 2, m);
	}
	if (abs(x) >= m)x %= m;
	if (x < 0)x += m;
	//if (x == 0)return 0;
	ll res = 1;
	while (n) {
		if (n & 1)res = res * x % m;
		x = x * x % m; n >>= 1;
	}
	return res;
}
//mod should be <2^31
struct modint {
	int n;
	modint() :n(0) { ; }
	modint(ll m) {
		if (m < 0 || mod <= m) {
			m %= mod; if (m < 0)m += mod;
		}
		n = m;
	}
	operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
	if (n == 0)return modint(1);
	modint res = (a * a) ^ (n / 2);
	if (n % 2)res = res * a;
	return res;
}

ll inv(ll a, ll p) {
	return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 21;
modint fact[max_n], factinv[max_n];
void init_f() {
	fact[0] = modint(1);
	for (int i = 0; i < max_n - 1; i++) {
		fact[i + 1] = fact[i] * modint(i + 1);
	}
	factinv[max_n - 1] = modint(1) / fact[max_n - 1];
	for (int i = max_n - 2; i >= 0; i--) {
		factinv[i] = factinv[i + 1] * modint(i + 1);
	}
}
modint comb(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
	if (a < 0 || b < 0 || a < b)return 0;
	return fact[a] * factinv[a - b];
}

ll gcd(ll a, ll b) {
	a = abs(a); b = abs(b);
	if (a < b)swap(a, b);
	while (b) {
		ll r = a % b; a = b; b = r;
	}
	return a;
}
using ld = long double;
//typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
	if (loc >= v.size())v.resize(loc + 1, 0);
	v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
	fill(isp + 2, isp + mn, true);
	for (int i = 2; i < mn; i++) {
		if (!isp[i])continue;
		ps.push_back(i);
		for (int j = 2 * i; j < mn; j += i) {
			isp[j] = false;
		}
	}
}*/

//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	if (res == st.begin())return st.end();
	res--; return res;
}

//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
	auto res = st.lower_bound(val);
	return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
	return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
	a = a + b; return a;
}
mP operator-(mP a, mP b) {
	return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
	a = a - b; return a;
}
LP operator+(LP a, LP b) {
	return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
	a = a + b; return a;
}
LP operator-(LP a, LP b) {
	return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
	a = a - b; return a;
}

mt19937 mt(time(0));

const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------
struct uf {
private:
	vector<int> par, ran;
public:
	uf(int n) {
		par.resize(n, 0);
		ran.resize(n, 0);
		rep(i, n) {
			par[i] = i;
		}
	}
	int find(int x) {
		if (par[x] == x)return x;
		else return par[x] = find(par[x]);
	}
	void unite(int x, int y) {
		x = find(x), y = find(y);
		if (x == y)return;
		if (ran[x] < ran[y]) {
			par[x] = y;
		}
		else {
			par[y] = x;
			if (ran[x] == ran[y])ran[x]++;
		}
	}
	bool same(int x, int y) {
		return find(x) == find(y);
	}
};
typedef vector<vector<modint>> mat;
typedef vector<modint> vec;
mat mtmul(mat& A, mat& B) {
	mat C(A.size(), vec(B[0].size()));
	rep(i, (int)A.size()) {
		rep(k, (int)B.size()) {
			rep(j, (int)B[0].size()) {
				C[i][j] += A[i][k] * B[k][j];
			}
		}
	}
	return C;
}
mat mtpow(mat A, ll n) {
	mat B(A.size(), vec(A.size()));
	rep(i, (int)A.size()) {
		B[i][i] = 1;
	}
	while (n > 0) {
		if (n & (ll)1)B = mtmul(B, A);
		A = mtmul(A, A);
		n >>= 1;
	}
	return B;
}
void solve() {
	vector<vector<int>> v;
	rep(i, 8)if (i > 0) {
		v.push_back({ i });
	}
	v.push_back({ 1,4 });
	const int ad = v.size() + 2;
	mat A(2*ad, vector<modint>(2*ad));
	rep(i, v.size()) {
		rep1(j, 7) {
			if (v[i] == vector<int>{5}&& j == 7)continue;
			int id[3][2];
			rep(x, 3)rep(y, 2)id[x][y] = -1;
			rep(k, v[i].size()) {
				rep(l, 3) {
					if (v[i][k] & (1 << l)) {
						id[l][0] = k;
					}
				}
			}
			int tmp = v[i].size();
			rep(x, 3) {
				if (j & (1 << x)) {
					id[x][1] = tmp; tmp++;
				}
				else {
					id[x][1] = -1;
				}
			}
			bool valid = true;
			rep(i, 2)rep(t, 2) {
				int c = 0;
				rep(x, 2)rep(y, 2) {
					int b = (id[i + x][y] >= 0);
					if ((x + y) % 2)b ^= 1;
					b ^= t;
					c += b;
				}
				if (c == 4)valid = false;
			}
			if (!valid)continue;
			if (id[1][0] < 0 && id[0][0] == id[2][0] && (j & 2)) {
				assert(false);
			}
			//if (id[1][0] >= 0 && (id[0][0] < 0 || id[2][0] < 0) && j == 5)assert(false);

			uf u(tmp);
			auto upd = [&](int a, int b) {
				if (a < 0 || b < 0)return;
				u.unite(a, b);
			};
			rep(x, 3)rep(y, 2) {
				if (x + 1 < 3) {
					upd(id[x][y], id[x + 1][y]);
				}
				if (y + 1 < 2) {
					upd(id[x][y], id[x][y + 1]);
				}
			}
			vector<int> ps;
			rep(x, 3)rep(y, 2) {
				if (id[x][y] >= 0) {
					id[x][y] = u.find(id[x][y]);
					ps.push_back(id[x][y]);
				}
			}
			sort(all(ps));
			ps.erase(unique(all(ps)), ps.end());
			vector<int> nex;
			for (int p : ps) {
				int s = 0;
				rep(x, 3)if (id[x][1] == p) {
					s |= (1 << x);
				}
				nex.push_back(s);
			}
			sort(all(nex));
			int z = -1;
			rep(x, v.size()) {
				if (v[x] == nex)z = x;
			}
			if (z >= 0) {
				A[z][i] += 1;
				A[z + ad][i + ad] += 1;
				for (int j = -1; j <= 2; j++) {
					int c = 0;
					rep(x, 2)rep(y, 2) {
						if (j + x >= 0 && j + x <= 2 && id[j+x][y] >= 0)c++;
					}
					if (0 < c && c < 4) {
						A[z + ad][i] += 1;
					}
				}
			}
		}
	}
	A[v.size()][v.size()] = 1;
	rep(i, v.size()) {
		if (v[i] != vector<int>{5}) {
			A[i][v.size()] += 1;
			bool exi[3] = {};
			for (int s : v[i])rep(j, 3)if (s & (1 << j))exi[j] = true;
			rep(j, 4) {
				bool e = false;
				if (j - 1 >= 0 && exi[j - 1])e = true;
				if (j < 3 && exi[j])e = true;
				if (e)A[i+ad][v.size()] += 1;
			}
		}
	}
	A[ad+v.size() + 1][ad+v.size() + 1] = 1;
	rep(i, v.size()) {
		if (v[i].size() == 1) {
			A[ad+v.size() + 1][ad+i] += 1;
			bool exi[3] = {};
			for (int s : v[i])rep(j, 3)if (s & (1 << j))exi[j] = true;
			rep(j, 4) {
				bool e = false;
				if (j - 1 >= 0 && exi[j - 1])e = true;
				if (j < 3 && exi[j])e = true;
				if (e)A[ad + v.size() + 1][i] += 1;
			}
		}
	}
	ll n; cin >> n;
	A = mtpow(A, n + 1);
	cout << A[ad+v.size() + 1][v.size()] << "\n";
}


signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	//init_f();
	//init();
	//expr();
	//while(true)
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}

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結果

テストケース

ソースコード