結果

問題 No.426 往復漸化式
ユーザー sigma425sigma425
提出日時 2017-09-14 22:39:14
言語 C++11
(gcc 11.4.0)
結果
AC  
実行時間 1,129 ms / 5,000 ms
コード長 6,518 bytes
コンパイル時間 3,023 ms
コンパイル使用メモリ 211,952 KB
実行使用メモリ 284,248 KB
最終ジャッジ日時 2024-04-25 09:35:00
合計ジャッジ時間 19,173 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge3
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 3 ms
5,376 KB
testcase_02 AC 3 ms
5,376 KB
testcase_03 AC 21 ms
5,504 KB
testcase_04 AC 20 ms
5,504 KB
testcase_05 AC 182 ms
36,948 KB
testcase_06 AC 178 ms
36,948 KB
testcase_07 AC 818 ms
283,988 KB
testcase_08 AC 832 ms
284,120 KB
testcase_09 AC 987 ms
284,116 KB
testcase_10 AC 993 ms
284,120 KB
testcase_11 AC 808 ms
284,120 KB
testcase_12 AC 947 ms
284,120 KB
testcase_13 AC 1,060 ms
284,120 KB
testcase_14 AC 949 ms
284,116 KB
testcase_15 AC 824 ms
284,248 KB
testcase_16 AC 964 ms
284,120 KB
testcase_17 AC 963 ms
284,124 KB
testcase_18 AC 973 ms
284,120 KB
testcase_19 AC 786 ms
283,992 KB
testcase_20 AC 903 ms
284,116 KB
testcase_21 AC 1,129 ms
284,124 KB
testcase_22 AC 920 ms
283,992 KB
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ソースコード

diff # 

/*
	あのさぁ・・・
*/


#include <bits/stdc++.h>
#define rep(i,n) for(int i=0;i<(int)(n);i++)
#define rep1(i,n) for(int i=1;i<=(int)(n);i++)
#define all(c) c.begin(),c.end()
#define pb push_back
#define fs first
#define sc second
#define show(x) cout << #x << " = " << x << endl
#define chmin(x,y) x=min(x,y)
#define chmax(x,y) x=max(x,y)
using namespace std;
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){return o<<"("<<p.fs<<","<<p.sc<<")";}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){o<<"sz = "<<vc.size()<<endl<<"[";for(const T& v:vc) o<<v<<",";o<<"]";return o;}

template<unsigned int mod_>
struct ModInt{
	using uint = unsigned int;
	using ll = long long;
	using ull = unsigned long long;

	constexpr static uint mod = mod_;

	uint v;
	ModInt():v(0){}
	ModInt(ll v):v(normS(v%mod+mod)){}
	explicit operator bool() const {return v!=0;}
	static uint normS(const uint &x){return (x<mod)?x:x-mod;}		// [0 , 2*mod-1] -> [0 , mod-1]
	static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
	ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
	ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
	ModInt operator-() const { return make(normS(mod-v)); }
	ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
	ModInt operator/(const ModInt& b) const { return *this*b.inv();}
	ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
	ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
	ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
	ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
	ll extgcd(ll a,ll b,ll &x,ll &y) const{
		ll u[]={a,1,0},v[]={b,0,1};
		while(*v){
			ll t=*u/ *v;
			rep(i,3) swap(u[i]-=t*v[i],v[i]);
		}
		if(u[0]<0) rep(i,3) u[i]=-u[i];
		x=u[1],y=u[2];
		return u[0];
	}
	ModInt inv() const{
		ll x,y;
		extgcd(v,mod,x,y);
		return make(normS(x+mod));
	}
	bool operator==(const ModInt& b) const { return v==b.v;}
	bool operator!=(const ModInt& b) const { return v!=b.v;}
	friend istream& operator>>(istream &o,ModInt& x){
		ll tmp;
		o>>tmp;
		x=ModInt(tmp);
		return o;
	}
	friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
};
using mint = ModInt<1000000007>;

template<class T>
struct Matrix{
	int H,W;
	vector< vector<T> > m;
	Matrix():H(0),W(0){}
	Matrix(int H,int W):H(H),W(W),m( vector< vector<T> >(H,vector<T>(W,0)) ){}
	vector<T> const& operator[](const int& i) const {return m[i];}
	vector<T>& operator[](const int& i) {return m[i];}
	Matrix operator+=(const Matrix& b){
		assert(H==b.H&&W==b.W);
		rep(i,H) rep(j,W) m[i][j]+=b[i][j];
		return *this;
	}
	Matrix operator-=(const Matrix& b){
		assert(H==b.H&&W==b.W);
		rep(i,H) rep(j,H) m[i][j]-=b[i][j];
		return *this;
	}
	Matrix operator+(const Matrix& b) const {return Matrix(*this)+=b;}
	Matrix operator-(const Matrix& b) const {return Matrix(*this)-=b;}
	Matrix operator*(const Matrix& b) const {
		assert(W==b.H);
		Matrix c(H,b.W);
		rep(i,H) rep(j,b.W) rep(k,W) c[i][j]+=m[i][k]*b[k][j];
		return c;
	}
	Matrix operator*=(const Matrix& b){return (*this)=(*this)*b;}
	vector<T> operator*(const vector<T>& b) const {
		assert(W==b.size());
		vector<T> c(H);
		rep(i,H) rep(j,W) c[i]+=m[i][j]*b[j];
		return c;
	}
	static Matrix E(int N){
		Matrix a(N,N);
		rep(i,N) a[i][i]=1;
		return a;
	}
	friend ostream& operator<<(ostream &o,const Matrix& m){
		o<<m.H<<" * "<<m.W<<endl;
		rep(i,m.H){
			o<<"[";
			rep(j,m.W) o<<m[i][j]<<" ";
			o<<"]"<<endl;
		}
		return o;
	}
};

template<class D>
struct segtree_simple{
	int N;
	vector<D> val;

	segtree_simple(){}
	segtree_simple(int n){
		N=1;
		while(N<n) N*=2;
		val.assign(N*2,D::e());
	}
	segtree_simple(const vector<D>& ds){
		int n = ds.size();
		N=1;
		while(N<n) N*=2;
		val.assign(N*2,D::e());
		rep(i,n) val[i+N] = ds[i];
		for(int i=N-1;i>0;i--) val[i] = val[i*2] + val[i*2+1];
	}
	void assign(int k,D d){
		k+=N;
		val[k]=d;
		k/=2;
		while(k){
			val[k] = val[k*2] + val[k*2+1];
			k/=2;
		}
	}
	D query(int a,int b){		//non-commutative & unrecursive
		D L = D::e() , R = D::e();
		a+=N,b+=N;
		while(a<b){
			if(a&1) L = L + val[a++];
			if(b&1) R = val[--b] + R;
			a/=2,b/=2;
		}
		return L+R;
	}
};

struct MA{
	static const int N = 3;
	Matrix<mint> a;
	MA(){}
	MA(Matrix<mint> a):a(a){}
	const static MA e(){
		return Matrix<mint>::E(N);
	}
	MA operator+(const MA& r) const {
		return MA(r.a*a);
	};
};

struct MB{
	static const int N = 2;
	Matrix<mint> a;
	MB(){}
	MB(Matrix<mint> a):a(a){}
	const static MB e(){
		return Matrix<mint>::E(N);
	}
	MB operator+(const MB& r) const {
		return MB(a*r.a);
	};
};

struct D{	//? -> b?a + x
	using Mat = Matrix<mint>;
	Mat b,a,x;
	D(){*this = e();}
	D(Mat b,Mat a,Mat x):b(b),a(a),x(x){}
	const static D e(){
		return D(Mat::E(2),Mat::E(3),Mat(2,3));
	}
	D operator+(const D& r) const {
		// puts("plus");
		// show(b);
		// show(r.x);
		// show(b*r.x);
		auto ret = D(b*r.b,r.a*a,b*r.x*a+x);
		// puts("done");
		return ret;
	};
};


Matrix<mint> X(int x){
	Matrix<mint> res(2,3);
	rep(i,2) rep(j,3) res[i][j] = mint(6*x+i*3+j);
	return res;
}


segtree_simple<MA> sega;
segtree_simple<MB> segb;
segtree_simple<D> segd;

int main(){
	int N;
	cin>>N;
	vector<mint> a0,bn;
	rep(i,3){
		int x;
		cin>>x;
		a0.pb(mint(x));
	}
	rep(i,2){
		int x;
		cin>>x;
		bn.pb(mint(x));
	}

	sega = segtree_simple<MA>(N+1);
	segb = segtree_simple<MB>(N+1);
	segd = [&]{
		vector<D> vs;
		rep1(i,N+1){
			D v;
			v.x = X(i);
			vs.pb(v);
		}
		return segtree_simple<D>(vs);
	}();

	int Q;
	cin>>Q;
	rep(qt,Q){
		string s;
		cin>>s;
		if(s == "a"){
			int i;
			cin>>i;
			Matrix<mint> x(3,3);
			rep(i,3) rep(j,3){
				int v;
				cin>>v;
				x.m[i][j] = mint(v);
			}
			MA A(x);
			sega.assign(i,A);
			MB B = segb.query(i,i+1);
			D v(B.a,A.a,B.a*X(i+1)*A.a);
			segd.assign(i,v);
		}
		if(s == "b"){
			int i;
			cin>>i;
			Matrix<mint> x(2,2);
			rep(i,2) rep(j,2){
				int v;
				cin>>v;
				x.m[i][j] = mint(v);
			}
			MB B(x);
			segb.assign(i,B);
			MA A = sega.query(i,i+1);
			D v(B.a,A.a,B.a*X(i+1)*A.a);
			segd.assign(i,v);
		}
		if(s == "ga"){
			int i;
			cin>>i;
			auto v = sega.query(0,i).a * a0;
			cout<<v[0]<<" "<<v[1]<<" "<<v[2]<<endl;
		}
		if(s == "gb"){
			int i;
			cin>>i;
			if(i == N){
				cout<<bn[0]<<" "<<bn[1]<<endl;
				continue;
			}
			auto x = segd.query(i+1,N).x;
			x += X(i+1);
			auto v = x * sega.query(0,i+1).a * a0;
			auto u = segb.query(i+1,N+1).a * bn;
			cout<<v[0]+u[0]<<" "<<v[1]+u[1]<<endl;
		}

	}

}
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