#225411 (C++14) No.621 3 x N グリッド上のドミノの置き方の数

提出ソース

結果

問題	No.621 3 x N グリッド上のドミノの置き方の数
ユーザー	satanic
提出日時	2017-12-22 00:08:56
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	4 ms / 3,000 ms
コード長	8,994 bytes
コンパイル時間	1,333 ms
コンパイル使用メモリ	122,248 KB
実行使用メモリ	6,820 KB
最終ジャッジ日時	2024-12-17 22:54:42
合計ジャッジ時間	2,965 ms
ジャッジサーバーID （参考情報）	judge2 / judge5

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 6,820 KB
testcase_01	AC	2 ms 6,820 KB
testcase_02	AC	2 ms 6,820 KB
testcase_03	AC	2 ms 6,820 KB
testcase_04	AC	2 ms 6,820 KB
testcase_05	AC	2 ms 6,820 KB
testcase_06	AC	2 ms 6,820 KB
testcase_07	AC	2 ms 6,816 KB
testcase_08	AC	2 ms 6,816 KB
testcase_09	AC	2 ms 6,820 KB
testcase_10	AC	2 ms 6,820 KB
testcase_11	AC	2 ms 6,816 KB
testcase_12	AC	2 ms 6,816 KB
testcase_13	AC	2 ms 6,816 KB
testcase_14	AC	2 ms 6,820 KB
testcase_15	AC	3 ms 6,816 KB
testcase_16	AC	3 ms 6,816 KB
testcase_17	AC	2 ms 6,816 KB
testcase_18	AC	2 ms 6,816 KB
testcase_19	AC	2 ms 6,820 KB
testcase_20	AC	3 ms 6,816 KB
testcase_21	AC	3 ms 6,816 KB
testcase_22	AC	3 ms 6,816 KB
testcase_23	AC	3 ms 6,820 KB
testcase_24	AC	3 ms 6,816 KB
testcase_25	AC	3 ms 6,820 KB
testcase_26	AC	3 ms 6,816 KB
testcase_27	AC	3 ms 6,816 KB
testcase_28	AC	3 ms 6,820 KB
testcase_29	AC	4 ms 6,816 KB
testcase_30	AC	3 ms 6,820 KB
testcase_31	AC	3 ms 6,816 KB
testcase_32	AC	3 ms 6,820 KB
testcase_33	AC	3 ms 6,816 KB
testcase_34	AC	4 ms 6,816 KB
testcase_35	AC	3 ms 6,820 KB
testcase_36	AC	3 ms 6,820 KB
testcase_37	AC	3 ms 6,816 KB
testcase_38	AC	4 ms 6,816 KB
testcase_39	AC	3 ms 6,816 KB
testcase_40	AC	3 ms 6,816 KB
testcase_41	AC	3 ms 6,820 KB
testcase_42	AC	3 ms 6,816 KB
testcase_43	AC	3 ms 6,816 KB
testcase_44	AC	4 ms 6,816 KB
testcase_45	AC	4 ms 6,816 KB
testcase_46	AC	4 ms 6,816 KB
testcase_47	AC	3 ms 6,820 KB
testcase_48	AC	4 ms 6,820 KB
testcase_49	AC	3 ms 6,816 KB
testcase_50	AC	3 ms 6,820 KB
testcase_51	AC	3 ms 6,816 KB
testcase_52	AC	4 ms 6,816 KB
testcase_53	AC	3 ms 6,816 KB
testcase_54	AC	4 ms 6,820 KB
testcase_55	AC	4 ms 6,816 KB
testcase_56	AC	3 ms 6,820 KB
testcase_57	AC	3 ms 6,816 KB
testcase_58	AC	3 ms 6,820 KB
testcase_59	AC	3 ms 6,816 KB
testcase_60	AC	3 ms 6,820 KB
testcase_61	AC	3 ms 6,820 KB
testcase_62	AC	4 ms 6,816 KB
testcase_63	AC	4 ms 6,816 KB
testcase_64	AC	3 ms 6,816 KB
testcase_65	AC	3 ms 6,816 KB
testcase_66	AC	4 ms 6,820 KB
testcase_67	AC	4 ms 6,816 KB

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ソースコード

raw source code

// need
#include <iostream>
#include <algorithm>

// data structure
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
//#include <array>
//#include <unordered_map>
//#include <complex>
//#include <deque>
#include <valarray>

// stream
//#include <istream>
//#include <sstream>
//#include <ostream>
#include <fstream>

// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { std::cin >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest&...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int i=0; i<n; ++i){MACRO_VEC_ROW_Scan(i, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest&...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest&...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)std::cin>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& r:c)for(auto& i:r)std::cin>>i;

// output
#define OUT(d) std::cout<<d;
#define FOUT(n, d) std::cout<<std::fixed<<std::setprecision(n)<<d;
#define SOUT(n, c, d) std::cout<<std::setw(n)<<std::setfill(c)<<d;
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(i, n) std::cout<<(i + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(d) {std::cerr << #d << "\t:" << d << "\n";}
#define SHOWVECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOWVECTOR2(v) {std::cerr << #v << "\t:\n";for(const auto& xxx : v){for(const auto& yyy : xxx){std::cerr << yyy << " ";}std::cerr << "\n";}}
#define SHOWQUEUE(a) {auto tmp(a);std::cerr << #a << "\t:";while(!tmp.empty()){std::cerr << tmp.front() << " ";tmp.pop();}std::cerr << "\n";}

// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(i, a, b) for(int i=(a);i<(b);++i)
#define RFOR(i, a, b) for(int i=(b)-1;i>=(a);--i)
#define REP(i, n) for(int i=0;i<int(n);++i)
#define RREP(i, n) for(int i=int(n)-1;i>=0;--i)
#define FORLL(i, a, b) for(ll i=ll(a);i<ll(b);++i)
#define RFORLL(i, a, b) for(ll i=ll(b)-1;i>=ll(a);--i)
#define REPLL(i, n) for(ll i=0;i<ll(n);++i)
#define RREPLL(i, n) for(ll i=ll(n)-1;i>=0;--i)
#define IN(a, x, b) (a<=x && x<b)
template<typename T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<typename T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
#define EXCEPTION(msg) throw std::string("Exception : " msg " [ in ") + __func__ + " : " + std::to_string(__LINE__) + " lines ]"
#define TRY(cond, msg) try {if (cond) EXCEPTION(msg);}catch (std::string s) {std::cerr << s << std::endl;}
void CHECKTIME(std::function<void()> f) { auto start = std::chrono::system_clock::now(); f(); auto end = std::chrono::system_clock::now(); auto res = std::chrono::duration_cast<std::chrono::nanoseconds>((end - start)).count(); std::cerr << "[Time:" << res << "ns  (" << res / (1.0e9) << "s)]\n"; }

// test
template<class T> std::vector<std::vector<T>> VV(int n) {
	return std::vector<std::vector<T>>(n);
}
template<class T> std::vector<std::vector<T>> VV(int n, int m, T init = T()) {
	return std::vector<std::vector<T>>(n, std::vector<T>(m, init));
}
template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, std::pair<S, T> p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}

// type/const

#define int ll
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = 1 << 30;                          // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-9;
constexpr int MOD = 1000000007;
constexpr double PI = 3.141592653589793238462643383279;

template<class T>
class MatrixMOD {
private:
	std::valarray<std::valarray<T>> mat;
public:
	MatrixMOD(size_t m = 0, size_t n = 0, T init = 0) {
		if (n == 0) n = m;
		mat.resize(m);
		for (size_t i = 0; i < m; ++i) mat[i].resize(n, init);
	}
	MatrixMOD(std::valarray<std::valarray<T>> a) { mat = a; }
	MatrixMOD<T> init(size_t m = 0, size_t n = 0, T init = 0) {
		if (n == 0) n = m;
		mat.resize(m);
		for (size_t i = 0; i < m; ++i) mat[i].resize(n, init);
		return *this;
	}
	std::valarray<T>& operator[](size_t i) { return mat[i]; }
	const std::valarray<T>& operator[](size_t i) const { return mat[i]; }
	MatrixMOD<T>& operator=(const MatrixMOD<T>& r) {
		for (size_t i = 0; i < mat.size(); ++i) mat[i] = r[i];
		return *this;
	}
	MatrixMOD<T> operator+() const { return mat; }
	MatrixMOD<T> operator-() const {
		MatrixMOD<T> res(mat.size());
		for (size_t i = 0; i < mat.size(); ++i) res[i] = (MOD - mat[i]) %= MOD;
		return res;
	}
	MatrixMOD<T>& operator+=(const MatrixMOD<T>& r) {
		for (size_t i = 0; i < mat.size(); ++i) (mat[i] += r[i]) %= MOD;
		return *this;
	}
	MatrixMOD<T>& operator+=(const T& x) {
		for (size_t i = 0; i < mat.size(); ++i) (mat[i] += x) %= MOD;
		return *this;
	}
	MatrixMOD<T>& operator-=(const MatrixMOD<T>& r) { return *this += MOD - r; }
	MatrixMOD<T>& operator-=(const T& x) { return *this += MOD - x; }
	MatrixMOD<T>& operator*=(const MatrixMOD<T>& r) { // O(N^3)
		MatrixMOD<T> res(*this);
		for (size_t i = 0; i < mat.size(); ++i) {
			for (size_t j = 0; j < r[0].size(); ++j) {
				res[i][j] = 0;
				for (size_t k = 0; k < mat[0].size(); ++k) {
					(res[i][j] += mat[i][k] * r[k][j] % MOD) %= MOD;
				}
			}
		}
		return *this = res;
	}
	MatrixMOD<T>& operator*=(const T& x) {
		for (size_t i = 0; i < mat.size(); ++i) (mat[i] *= x) %= MOD;
		return *this;
	}
	MatrixMOD<T>& operator%=(const T& mod) {
		for (size_t i = 0; i < mat.size(); ++i) mat[i] %= MOD;
		return *this;
	}
	MatrixMOD<T>& operator^=(ll p) { // O(N^3 logP)
		MatrixMOD<T> res(*this);

		for (size_t i = 0; i < mat.size(); ++i) {
			for (size_t j = 0; j < mat[0].size(); ++j) {
				res[i][j] = i == j;
			}
		}
		while (p) {
			if (p & 1) (res *= (*this)) %= MOD;
			((*this) *= (*this)) %= MOD;
			p >>= 1;
		}
		for (size_t i = 0; i < mat.size(); ++i) mat[i] = res[i];
		return *this;
	}
	MatrixMOD<T> operator+(const MatrixMOD& r) const {
		MatrixMOD<T> res(mat);
		return res += r;
	}
	MatrixMOD<T> operator-(const MatrixMOD& r) const {
		MatrixMOD<T> res(mat);
		return res -= r;
	}
	MatrixMOD<T> operator*(const MatrixMOD& r) const {
		MatrixMOD<T> res(mat);
		return res *= r;
	}
	MatrixMOD<T> operator*(const T& r) const {
		MatrixMOD<T> res(mat);
		return res *= r;
	}
	MatrixMOD<T> operator^(const int& p) const {
		MatrixMOD<T> res(mat);
		return res ^= p;
	}
	MatrixMOD<T> t() const {
		MatrixMOD<T> res(mat[0].size(), mat.size(), 0);
		for (size_t i = 0; i < mat[0].size(); ++i) {
			for (size_t j = 0; j < mat.size(); ++j) {
				res[i][j] = mat[j][i];
			}
		}
		return res;
	}
	static MatrixMOD<T> getUnit(size_t n) {
		MatrixMOD<T> res(n, n, 0);
		for (size_t i = 0; i < n; ++i) res[i][i] = 1;
		return res;
	}
	void show() const {
		for (const auto& r : mat) {
			for (const auto & x : r) {
				std::cerr << x << "\t";
			}
			std::cerr << std::endl;
		}
	}
};

int a[] = { 2, 5, 22, 75, 264, 941, 3286, 11623, 40960, 144267, 508812, 1792981, 6319994, 22277291, 78518760, 276763545};

signed main() {
	INIT;
	VAR(int, n);
	if (n <= 15) {
		OUT(a[n - 1] % MOD)BR;
		return 0;
	}
	MatrixMOD<ll> A(std::valarray<std::valarray<ll>>({
		{ 1,5,11,5,14,8,3,0,MOD-5,MOD-11,MOD-1,2,0,0,1 },
		{ 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0 },
		{ 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0 },
		{ 0,0,1,0,0,0,0,0,0,0,0,0,0,0,0 },
		{ 0,0,0,1,0,0,0,0,0,0,0,0,0,0,0 },
		{ 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0 },
		{ 0,0,0,0,0,1,0,0,0,0,0,0,0,0,0 },
		{ 0,0,0,0,0,0,1,0,0,0,0,0,0,0,0 },
		{ 0,0,0,0,0,0,0,1,0,0,0,0,0,0,0 },
		{ 0,0,0,0,0,0,0,0,1,0,0,0,0,0,0 },
		{ 0,0,0,0,0,0,0,0,0,1,0,0,0,0,0 },
		{ 0,0,0,0,0,0,0,0,0,0,1,0,0,0,0 },
		{ 0,0,0,0,0,0,0,0,0,0,0,1,0,0,0 },
		{ 0,0,0,0,0,0,0,0,0,0,0,0,1,0,0 },
		{ 0,0,0,0,0,0,0,0,0,0,0,0,0,1,0 },
	}));
	n -= 15;
	A ^= n;
	int ans = 0;
	REP(i, 15) {
		(ans += A[0][i] * (a[14 - i] % MOD) % MOD) %= MOD;
	}
	OUT(ans)BR;
	return 0;
}

yukicoder

結果

テストケース

ソースコード