#252804 (C++14) No.673 カブトムシ

提出ソース

結果

問題	No.673 カブトムシ
ユーザー	sntea
提出日時	2018-04-21 01:21:21
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	2 ms / 2,000 ms
コード長	10,427 bytes
コンパイル時間	1,991 ms
コンパイル使用メモリ	182,020 KB
実行使用メモリ	6,944 KB
最終ジャッジ日時	2024-06-30 06:09:34
合計ジャッジ時間	2,668 ms
ジャッジサーバーID （参考情報）	judge2 / judge4

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	1 ms 6,816 KB
testcase_01	AC	2 ms 6,816 KB
testcase_02	AC	2 ms 6,812 KB
testcase_03	AC	2 ms 6,812 KB
testcase_04	AC	2 ms 6,944 KB
testcase_05	AC	2 ms 6,944 KB
testcase_06	AC	2 ms 6,944 KB
testcase_07	AC	2 ms 6,940 KB
testcase_08	AC	2 ms 6,940 KB
testcase_09	AC	2 ms 6,944 KB
testcase_10	AC	2 ms 6,944 KB
testcase_11	AC	2 ms 6,940 KB
testcase_12	AC	2 ms 6,940 KB
testcase_13	AC	2 ms 6,944 KB
testcase_14	AC	2 ms 6,940 KB
testcase_15	AC	2 ms 6,944 KB
testcase_16	AC	2 ms 6,940 KB
testcase_17	AC	2 ms 6,940 KB

権限があれば一括ダウンロードができます

ソースコード

raw source code

#ifdef LOCAL111
	#define _GLIBCXX_DEBUG
#else
	#define NDEBUG
#endif
#define _USE_MATH_DEFINES
#ifndef _GLIBCXX_NO_ASSERT
#include <cassert>
#endif
#include <cctype>
#include <cerrno>
#include <cfloat>
#include <ciso646>
#include <climits>
#include <clocale>
#include <cmath>
#include <csetjmp>
#include <csignal>
#include <cstdarg>
#include <cstddef>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>

#if __cplusplus >= 201103L
#include <ccomplex>
#include <cfenv>
#include <cinttypes>
#include <cstdbool>
#include <cstdint>
#include <ctgmath>
#include <cwchar>
#include <cwctype>
#endif

// C++
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <exception>
#include <fstream>
#include <functional>
#include <iomanip>
#include <ios>
#include <iosfwd>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <locale>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <stdexcept>
#include <streambuf>
#include <string>
#include <typeinfo>
#include <utility>
#include <valarray>
#include <vector>

#if __cplusplus >= 201103L
#include <array>
#include <atomic>
#include <chrono>
#include <condition_variable>
#include <forward_list>
#include <future>
#include <initializer_list>
#include <mutex>
#include <random>
#include <ratio>
#include <regex>
#include <scoped_allocator>
#include <system_error>
#include <thread>
#include <tuple>
#include <type_traits>
#include <typeindex>
#include <unordered_map>
#include <unordered_set>
#endif
const int INF = 1e9;
using namespace std;
template<typename T, typename U> ostream& operator<< (ostream& os, const pair<T,U>& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; }

#define endl '\n'
#define ALL(a)  (a).begin(),(a).end()
#define SZ(a) int((a).size())
#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(i,0,n)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#ifdef LOCAL111
	#define DEBUG(x) cout<<#x<<": "<<(x)<<endl
	template<typename T> void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
#else
	#define DEBUG(x) true
	template<typename T> void dpite(T a, T b){ return; }
#endif
#define F first
#define S second
#define SNP string::npos
#define WRC(hoge) cout << "Case #" << (hoge)+1 << ": "
template<typename T> void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
template<typename T> bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;}
template<typename T> bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;}

typedef long long int LL;
typedef unsigned long long ULL;
typedef pair<int,int> P;

void ios_init(){
	//cout.setf(ios::fixed);
	//cout.precision(12);
#ifdef LOCAL111
	return;
#endif
	ios::sync_with_stdio(false); cin.tie(0);
}

#define EPS 1e-9

//library
template<typename T>
class Matrix {
public:
	vector<vector<T> > v;
	int n,m;
	Matrix(int n){
		this->n = this->m = n;
		v.resize(n,vector<T>(n,0));
	}

	Matrix(int n, int m){
		this -> n = n;
		this -> m = m;
		v.resize(n,vector<T>(m,0));
	}

	size_t size() const {
		return v.size();
	}

	int row() const {
		return n;
	}

	int col() const {
		return m;
	}

	Matrix operator+ (Matrix x) const {
		Matrix res(n,m);
		for(int i = 0; i < n; i++){
			for(int j = 0; j < m; j++){
				res.v[i][j] = x.v[i][j]+v[i][j];
			}
		}
		return res;
	}

	Matrix operator-(Matrix x) const {
		Matrix res(n,m);
		for(int i = 0; i < n; i++){
			for(int j = 0; j < m; j++){
				res.v[i][j] = v[i][j]-x.v[i][j];
			}
		}
	}

	Matrix operator*(Matrix x) const {
		Matrix res(n,x.m);
		for(int i = 0; i < n; i++){
			for(int j = 0; j < x.m; j++){
				for(int k = 0; k < m; k++){
					res.v[i][j] += v[i][k]*x.v[k][j];
				}
			}
		}
		return res;
	}

	Matrix operator-() const  {
		Matrix res = *this;
		for(int i = 0; i < (int)v.size(); ++i) {
			for(int j = 0; j < (int)v[i].size(); ++j) {
				res [i][j] *= -1;
			}
		}
		return res;
	}

	vector<T> operator*(vector<T> x) const {
		assert(x.size() == v.size());
		vector<T> res(v.size());
		for(int i = 0; i < n; i++){
			T tmp = 0;
			for(int j = 0; j < m; j++){
				tmp += v[i][j]*x[j];
			}
			res[i] = tmp;
		}
		return res;
	}

	Matrix pow(long long x) const {
		assert(n == m);
		Matrix m = (*this);
		Matrix res(n);
		for(int i = 0; i < n; i++) res[i][i] = 1;
		while(x != 0) {
			if(x&1) {
				res = res*m;
			}
			m = m*m;
			x >>= 1;
		}
		return res;
	}

	vector<T>& operator[](int x){
		return v[x];
	}

	const vector<T>& operator[](int x) const {
		return v[x];
	}

	Matrix<T> inverse() const{
		assert(n == m);
		Matrix res(n);
		for(int i = 0; i < n; ++i) {
			res[i][i] = 1;
		}
		
		// vector<pair<int,int>> swap_log;
		Matrix<T> mat = *this;
		for(int k = 0; k < n; ++k) {
			T max_val = abs(mat[k][k]);
			int max_point = k;
			for(int i = k+1; i < n; ++i) {
				if(max_val < abs(mat[i][k])){
					max_val = abs(mat[i][k]);
					max_point = i;
				}
			}
			swap(mat[k],mat[max_point]);
			swap(res[k],res[max_point]);
			// swap_log.emplace_back(k,max_point);
			for(int i = k+1; i < n; ++i) {
				T m = mat[i][k]/mat[k][k];
				for(int j = 0; j < n; ++j) {
					mat[i][j] -= m*mat[k][j];
					res[i][j] -= m*res[k][j];
				}
			}
		}
		
		for(int k = n-1; k >= 0; --k) {
			for(int i = 0; i < k; ++i) {
				T m = mat[i][k]/mat[k][k];
				for(int j = 0; j < n; ++j) {
					// mat[i][j] -= mat[k][j]*m;
					res[i][j] -= res[k][j]*m;
				}
			}
		}
		for(int i = 0; i < n; ++i) {
			for(int j = 0; j < n; ++j) {
				res[i][j] /= mat[i][i];
			}
		}
		// for(auto&& e : swap_log) {
		// 	swap(res[e.first],res[e.second]);
		// }
		return res;
	}

	T det() const {
		Matrix<T> mat = *this;
		T res = 1;
		for(int k = 0; k < n; ++k) {
			T max_val = abs(mat[k][k]);
			int max_point = k;
			for(int i = k+1; i < n; ++i) {
				if(max_val < abs(mat[i][k])){
					max_val = abs(mat[i][k]);
					max_point = i;
				}
			}
			swap(mat[k],mat[max_point]);
			if(k != max_point) res *= -1;
			for(int i = k+1; i < n; ++i) {
				T m = mat[i][k]/mat[k][k];
				for(int j = 0; j < n; ++j) {
					mat[i][j] -= m*mat[k][j];
				}
			}
		}
		for(int i = 0; i < n; ++i) {
			res *= mat[i][i];
		}
		return res;
	}

	pair<T, vector<T>> getMaxEigenvalue(int iterNum = 10) const {
		assert(n == m);
		vector<T> xk_(n, 1);
		xk_ = (*this).pow(iterNum)*xk_;
		auto xk = (*this)*xk_;
		T xk_xk = 0, xk_xk_ = 0;
		for(int i = 0; i < n; i++) {
			xk_xk += xk[i]*xk[i];
			xk_xk_ += xk[i]*xk_[i];
		}
		T xkAbs = sqrt(xk_xk);
		auto res = xk;
		for(auto&& e : res) {
			e /= xkAbs;
		}
		return { xk_xk/xk_xk_, res };
	}

	void debug() const {
		for(auto&& ee : v) {
			for(auto&& e : ee) {
				cout << e << ' ';
			}
			cout << endl;
		}
		cout << endl;
	}
};

template<typename T>
Matrix<T> companion_pow(const Matrix<T>& A, long long m) {
	assert(A.col() == A.row());
	int n = A.col();
	Matrix<T> u(1, n), Ak = A;
	u[0][n-1] = 1;
	while(m > 0) {
		if(m&1) {
			u = u*Ak;
		}
		Matrix<T> a(1, n);
		for(int i = 0; i < n; ++i) {
			a[0][i] = Ak[n-1][i];
		}
		a = a*Ak;
		for(int i = n-1; i >= 0; --i) {
			for(int j = 0; j < n; ++j) {
				Ak[i][j] = a[0][j];
			}
			auto a00 = a[0][0];
			for(int j = 0; j < n-1; ++j) {
				a[0][j] = a[0][j+1]+A[0][j]*a00;
			}
			a[0][n-1] = A[0][n-1]*a00;
		}
		m >>= 1;
	}
	Matrix<T> res(n);
	for(int i = n-1; i >= 0; --i) {
		for(int j = 0; j < n; ++j) {
			res[i][j] = u[0][j];
		}
		auto u00 = u[0][0];
		for(int j = 0; j < n-1; ++j) {
			u[0][j] = u[0][j+1]+A[0][j]*u00;
		}
		u[0][n-1] = A[0][n-1]*u00;
	}
	return res;
}

//libary

template<long long MOD>
class ModInt {
public:
	const static long long mod = MOD;
	long long x;
	
	ModInt() {
		x = 0;
	}

	ModInt(long long x) {
		x %= mod;
		this->x = x < 0 ? x+mod : x;
	}

	int get() const {
		return (int)x;
	}

	ModInt &operator+=(ModInt that) {
		if((x += that.get()) >= mod) x -= mod;
		return *this;
	}

	ModInt &operator-=(ModInt that) {
		if((x += mod-that.get()) >= mod) x -= mod;
		return *this;
	}

	ModInt &operator*=(ModInt that) {
		x = x*that.get()%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 {
		using std::swap;
		long long a = x, b = mod, u = 1, v = 0;
		while(b) {
			long long t = a/b;
			a -= t*b; swap(a,b);
			u -= t*v; swap(u,v);
		}
		return ModInt(u);
	}

	ModInt pow(int n) const {
		ModInt b = *this;
		ModInt res = 1;
		while(n != 0) {
			if(n&1){
				res *= b;
			}
			b *= b;
			n >>= 1;
		}
		return res;
	}

	bool operator==(ModInt that) const { return x == that.get(); }
	bool operator!=(ModInt that) const { return x != that.get(); }
	ModInt operator-() const { return x == 0 ? 0 : ModInt(mod-x); }
};

template<long long MOD> ostream& operator<< (ostream& os, const ModInt<MOD>& m) { os << m.get(); return os; }
template<long long MOD> istream& operator>> (istream& is, ModInt<MOD>& m){ long long n; is >> n; m = n; return is;}
typedef ModInt<1000000007> mint;



typedef double Num;
typedef vector<Num> Vec;
typedef vector<Vec> Mat;

int mrank(Mat A) {
	int n = A.size();
	int m = A[0].size();
	int ret = 0;
	for(int i = 0; i < n; i ++) {
		//DEBUG(i);
		int pivot = i;
		for(int j = i+1; j < n; j ++)
			if(abs(A[pivot][i]) < abs(A[j][i])) pivot = j;
		swap(A[i], A[pivot]);
		if(abs(A[i][i]) < EPS) continue;
		Num r = Num(1) / A[i][i];
		for(int j = i+1; j < n; j ++) {
			Num u = A[j][i] * r;
			for(int k = n-1; k >= i; k --)
				A[j][k] -= u * A[i][k];
		}
	}
	for(int i = 0; i < n; i++){
		if(abs(A[i][m-1]) > EPS)	ret = i;
	}
	/*REP(i,n) pite(ALL(A[i]));
	cout << endl;*/
	return ret;
}
//libary


int main()
{
	ios_init();
	LL b, c, d;
    while(cin >> b >> c >> d) {
        Matrix<mint> m(2, 2);
        m[0][0] = c;
        m[0][1] = b;
        m[1][1] = 1;
        auto po = m.pow(d);
        REP(i, 2) dpite(ALL(po[i]));
        auto ans = (po*vector<mint>({b, 1}))[0];
        cout << ans-mint(b) << endl;
    }
	return 0;
}

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結果

テストケース

ソースコード