#810919 (C++17) No.569 3 x N グリッドのパスの数

提出ソース

結果

問題	No.569 3 x N グリッドのパスの数
ユーザー	heno239
提出日時	2022-10-25 18:32:23
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	7,968 bytes
コンパイル時間	2,951 ms
コンパイル使用メモリ	187,016 KB
実行使用メモリ	20,168 KB
最終ジャッジ日時	2024-07-03 16:19:07
合計ジャッジ時間	5,303 ms
ジャッジサーバーID （参考情報）	judge3 / judge1

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	12 ms 20,036 KB
testcase_01	AC	12 ms 20,036 KB
testcase_02	AC	12 ms 20,040 KB
testcase_03	AC	12 ms 20,040 KB
testcase_04	AC	13 ms 20,040 KB
testcase_05	AC	12 ms 20,040 KB
testcase_06	AC	12 ms 20,040 KB
testcase_07	AC	12 ms 20,036 KB
testcase_08	AC	11 ms 19,916 KB
testcase_09	AC	12 ms 20,040 KB
testcase_10	AC	13 ms 20,036 KB
testcase_11	AC	12 ms 20,036 KB
testcase_12	AC	12 ms 20,040 KB
testcase_13	AC	12 ms 20,036 KB
testcase_14	AC	11 ms 20,040 KB
testcase_15	AC	11 ms 19,912 KB
testcase_16	AC	12 ms 20,040 KB
testcase_17	AC	12 ms 20,040 KB
testcase_18	AC	12 ms 20,036 KB
testcase_19	AC	12 ms 20,040 KB
testcase_20	AC	12 ms 20,040 KB
testcase_21	AC	11 ms 20,044 KB
testcase_22	AC	13 ms 20,036 KB
testcase_23	AC	12 ms 20,040 KB
testcase_24	AC	13 ms 19,912 KB
testcase_25	AC	12 ms 20,040 KB
testcase_26	AC	12 ms 20,036 KB
testcase_27	AC	12 ms 20,044 KB
testcase_28	AC	13 ms 20,036 KB
testcase_29	AC	12 ms 20,044 KB
testcase_30	AC	13 ms 20,044 KB
testcase_31	AC	12 ms 19,912 KB
testcase_32	AC	12 ms 20,168 KB
testcase_33	AC	12 ms 20,040 KB
testcase_34	AC	13 ms 20,036 KB
testcase_35	AC	12 ms 20,036 KB
testcase_36	AC	12 ms 20,036 KB
testcase_37	AC	12 ms 20,168 KB
testcase_38	AC	12 ms 20,040 KB
testcase_39	AC	12 ms 19,912 KB
testcase_40	AC	13 ms 20,036 KB
testcase_41	AC	12 ms 20,040 KB
testcase_42	AC	13 ms 20,040 KB
testcase_43	AC	12 ms 20,040 KB
testcase_44	AC	13 ms 20,164 KB
testcase_45	AC	12 ms 19,916 KB
testcase_46	AC	12 ms 20,040 KB
testcase_47	AC	12 ms 20,044 KB
testcase_48	AC	11 ms 20,036 KB
testcase_49	AC	12 ms 19,912 KB
testcase_50	AC	13 ms 20,040 KB
testcase_51	AC	12 ms 20,036 KB
testcase_52	AC	13 ms 20,040 KB
testcase_53	AC	14 ms 19,912 KB
testcase_54	AC	13 ms 20,036 KB
testcase_55	AC	13 ms 20,168 KB
testcase_56	AC	13 ms 19,916 KB
testcase_57	AC	12 ms 19,912 KB
testcase_58	AC	13 ms 20,044 KB
testcase_59	AC	12 ms 20,040 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() {
	/*mat A(10, vector<modint>(10));
	A[0][0] = 1; A[1][0] = 1; A[2][0] = 1; A[3][0] = 1; A[4][0] = 1; A[5][0] = 1; A[6][0] = 1;
	A[0][1] = 1; A[5][1] = 1; A[1][1] = 1; A[6][1] = 1; A[2][1] = 1; A[3][1] = 1;
	A[0][2] = 1; A[1][2] = 1; A[2][2] = 1; A[7][2] = 1; A[3][2] = 1; A[8][2] = 1;
	A[3][3] = 1; A[8][3] = 1; A[9][3] = 1; A[2][3] = 1; A[7][3] = 1; A[1][3] = 1; A[0][3] = 1;
	A[2][4] = 1; A[3][4] = 1; A[4][4] = 1;*/
	vector<vector<int>> v;
	rep(i, 4)v.push_back({ {1<<i} });
	rep(i, 4)Rep(j, i + 1, 4)Rep(k, j + 1, 4) {
		vector<int> cur = { (1 << i),(1 << j) | (1 << k) };
		v.push_back(cur);
		cur = { (1 << i) | (1 << j),1 << k };
		v.push_back(cur);
	}
	mat A(v.size(), vector<modint>(v.size()));
	rep(i, v.size()) {
		rep(j, 8) {
			int id[4]; rep(k, 4)id[k] = -1;
			rep(k, v[i].size()) {
				rep(l, 4)if (v[i][k] & (1 << l))id[l] = k;
			}
			int tmp = v[i].size();
			rep(k, 4)if (id[k] < 0) {
				id[k] = tmp; tmp++;
			}
			uf u(tmp);
			bool valid = true;
			rep(l, 3)if (j & (1 << l)) {
				if (u.same(id[l], id[l + 1])) {
					valid = false; break;
				}
				u.unite(id[l], id[l + 1]);
			}
			if (!valid)continue;
			bool nex[4] = {};
			rep(k, 4) {
				int c = 0;
				if (k > 0) {
					if (j & (1 << (k - 1)))c++;
				}
				if (k < 3) {
					if (j & (1 << k))c++;
				}
				if (id[k] < v[i].size())c++;
				if (c == 1)nex[k] = true;
				else if (c == 3)valid = false;
			}
			if (!valid)continue;
			rep(k, 4)id[k] = u.find(id[k]);
			vector<int> cur;
			rep(k, tmp) {
				int s = 0;
				rep(l, 4)if (nex[l])if(id[l]==k) {
					s |= (1 << l);
				}
				if(s>0)cur.push_back(s);
			}
			sort(all(cur));
			//cout << "?? " << i << " " << j << "\n";
			//coutarray(cur);
			int to = -1;
			rep(l, v.size())if (v[l] == cur)to = l;
			assert(to >= 0);
			A[to][i] = 1;
		}
	}
	ll n; cin >> n;
	A = mtpow(A, n + 1);
	cout << A[3][0] << "\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;
}

yukicoder

結果

テストケース

ソースコード