#276815 (C++14) No.510 二次漸化式

提出ソース

結果

問題	No.510 二次漸化式
ユーザー	FF256grhy
提出日時	2018-08-04 16:59:51
言語	C++14 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	1,273 ms / 3,000 ms
コード長	7,894 bytes
コンパイル時間	2,589 ms
コンパイル使用メモリ	190,776 KB
実行使用メモリ	87,552 KB
最終ジャッジ日時	2024-09-19 17:52:49
合計ジャッジ時間	28,677 ms
ジャッジサーバーID （参考情報）	judge1 / 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	2 ms 5,376 KB
testcase_02	AC	420 ms 5,376 KB
testcase_03	AC	413 ms 5,376 KB
testcase_04	AC	410 ms 5,376 KB
testcase_05	AC	407 ms 5,376 KB
testcase_06	AC	606 ms 13,952 KB
testcase_07	AC	608 ms 13,952 KB
testcase_08	AC	609 ms 13,952 KB
testcase_09	AC	600 ms 13,952 KB
testcase_10	AC	193 ms 5,376 KB
testcase_11	AC	196 ms 5,376 KB
testcase_12	AC	193 ms 5,376 KB
testcase_13	AC	187 ms 5,376 KB
testcase_14	AC	196 ms 5,376 KB
testcase_15	AC	191 ms 5,376 KB
testcase_16	AC	777 ms 87,408 KB
testcase_17	AC	791 ms 87,424 KB
testcase_18	AC	787 ms 87,484 KB
testcase_19	AC	784 ms 87,504 KB
testcase_20	AC	796 ms 87,472 KB
testcase_21	AC	794 ms 87,424 KB
testcase_22	AC	806 ms 87,424 KB
testcase_23	AC	1,123 ms 87,388 KB
testcase_24	AC	1,132 ms 87,424 KB
testcase_25	AC	1,097 ms 87,424 KB
testcase_26	AC	1,102 ms 87,440 KB
testcase_27	AC	1,119 ms 87,424 KB
testcase_28	AC	1,107 ms 87,552 KB
testcase_29	AC	1,104 ms 87,404 KB
testcase_30	AC	1,118 ms 87,484 KB
testcase_31	AC	1,253 ms 87,552 KB
testcase_32	AC	1,240 ms 87,424 KB
testcase_33	AC	1,273 ms 87,424 KB
testcase_34	AC	908 ms 87,516 KB
testcase_35	AC	815 ms 87,296 KB

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ソースコード

raw source code

#include <bits/stdc++.h>
using namespace std;

typedef long long   signed int LL;
typedef long long unsigned int LU;

#define incID(i, l, r) for(int i = (l)    ; i <  (r); i++)
#define incII(i, l, r) for(int i = (l)    ; i <= (r); i++)
#define decID(i, l, r) for(int i = (r) - 1; i >= (l); i--)
#define decII(i, l, r) for(int i = (r)    ; i >= (l); i--)
#define  inc(i, n) incID(i, 0, n)
#define inc1(i, n) incII(i, 1, n)
#define  dec(i, n) decID(i, 0, n)
#define dec1(i, n) decII(i, 1, n)

#define inII(v, l, r) ((l) <= (v) && (v) <= (r))
#define inID(v, l, r) ((l) <= (v) && (v) <  (r))

#define PB push_back
#define EB emplace_back
#define MP make_pair
#define FI first
#define SE second
#define UB upper_bound
#define LB lower_bound
#define PQ priority_queue

#define  ALL(v)  v.begin(),  v.end()
#define RALL(v) v.rbegin(), v.rend()
#define  FOR(it, v) for(auto it =  v.begin(); it !=  v.end(); ++it)
#define RFOR(it, v) for(auto it = v.rbegin(); it != v.rend(); ++it)

template<typename T> bool   setmin(T & a, T b) { if(b <  a) { a = b; return true; } else { return false; } }
template<typename T> bool   setmax(T & a, T b) { if(b >  a) { a = b; return true; } else { return false; } }
template<typename T> bool setmineq(T & a, T b) { if(b <= a) { a = b; return true; } else { return false; } }
template<typename T> bool setmaxeq(T & a, T b) { if(b >= a) { a = b; return true; } else { return false; } }
template<typename T> T gcd(T a, T b) { return (b == 0 ? a : gcd(b, a % b)); }
template<typename T> T lcm(T a, T b) { return a / gcd(a, b) * b; }

// ---- ----

template<typename T> class SegmentTree {
private:
	T * a = NULL;
	int N = -1, S;
	function<T(T, T)> F;
	T I;
	bool is_available = false;
public:
	SegmentTree() { }
	SegmentTree(int n, function<T(T, T)> func, T id) { init(n, func, id); }
	void init(int size, function<T(T, T)> func, T id) {
		assert(size > 0);
		N = size;
		F = func;
		I = id;
		S = 1;
		while(S < size) { S *= 2; }
		delete[] a;
		a = new T[S * 2];
		inc(i, S * 2) { a[i] = I; }
		is_available = true;
	}
	T operator[](int p) {
		assert(inID(p, 0, N));
		p += S;
		return a[p];
	}
	T & ref(int p) {
		is_available = false;
		assert(inID(p, 0, N));
		p += S;
		return a[p];
	}
	void calc() {
		decID(i, 1, S) { a[i] = F(a[i * 2], a[i * 2 + 1]); }
		is_available = true;
	}
	void apply(int p, function<void(T &)> op) {
		assert(inID(p, 0, N));
		p += S;
		op(a[p]);
		while(p != 1) {
			p /= 2;
			a[p] = F(a[p * 2], a[p * 2 + 1]);
		}
	}
	T fold_ID(int l, int r, bool loop = false) {
		assert(is_available);
		assert(inII(l, 0, N));
		assert(inII(r, 0, N));
		if(loop && l >= r) { return F(fold_ID(l, N), fold_ID(0, r)); }
		assert(l <= r);
		l += S;
		r += S;
		T v = I, w = I;
		while(l < r) {
			if(l + 1 == r) { v = F(v, a[l]); break; }
			
			if(l % 2 == 1) { v = F(v, a[l]); }
			if(r % 2 == 1) { w = F(a[r - 1], w); }
			
			l = (l + 1) / 2;
			r = r / 2;
		}
		return F(v, w);
	}
	T fold_II(int l, int r, bool loop = false) { return fold_ID(l    , r + 1, loop); }
	T fold_CD(int l, int r, bool loop = false) { return fold_ID(l + 1, r    , loop); }
	T fold_CI(int l, int r, bool loop = false) { return fold_ID(l + 1, r + 1, loop); }
};

#define OP(op) [&](auto A, auto B) { return op; }
#define AP(op) [&](auto & A) { op; }

// ---- ----

template<typename T, int N> struct Matrix {
	vector<vector<T>> a;
	Matrix(const vector<vector<T>> & v = { }) { init(v); }
	void init(const vector<vector<T>> & v) {
		a = vector<vector<T>>(N, vector<T>(N, 0));
		assert(v.size() <= N);
		inc(i, v.size()) { assert(v[i].size() <= N);
		inc(j, v[i].size()) {
			a[i][j] = v[i][j];
		}
		}
	}
	vector<T> & operator[](int i) { return a[i]; }
	Matrix id() {
		Matrix e;
		inc(i, N) { e[i][i] = 1; }
		return e;
	}
	Matrix tp() {
		Matrix b;
		inc(i, N) {
		inc(j, N) {
			b[j][i] = a[i][j];
		}
		}
		return b;
	}
	Matrix & operator+=(const Matrix & b) {
		inc(i, N) {
		inc(j, N) {
			a[i][j] += b.a[i][j];
		}
		}
		return (*this);
	}
	Matrix & operator*=(T b) {
		inc(i, N) {
		inc(j, N) {
			a[i][j] *= b;
		}
		}
		return (*this);
	}
	Matrix & operator*=(const Matrix & b) {
		Matrix c;
		inc(i, N) {
		inc(j, N) {
		inc(k, N) {
			c[i][j] += a[i][k] * b.a[k][j];
		}
		}
		}
		return (*this) = c;
	}
	Matrix & operator^=(LU b) {
		Matrix t[64], c = id();
		int D = 64;
		inc(i, D) { if((b >> i) == 0) { D = i; break; } }
		inc(i, D) { t[i] = (i == 0 ? (*this) : t[i - 1] * t[i - 1]); }
		inc(i, D) { if((b >> i) & 1) { c *= t[i]; } }
		return (*this) = c;
	}
	Matrix operator+(const Matrix & b) const { Matrix c = a; return c += b; }
	Matrix operator*(             T b) const { Matrix c = a; return c *= b; }
	Matrix operator*(const Matrix & b) const { Matrix c = a; return c *= b; }
	Matrix operator^(            LU b) const { Matrix c = a; return c ^= b; }
};
template<typename T, int N> Matrix<T, N> operator*(T a, const Matrix<T, N> & b) { return b * a; }
template<typename T, int N> ostream & operator<<(ostream & os, const Matrix<T, N> & m) {
	inc(i, N) {
	inc(j, N) {
		os << m.a[i][j] << " ";
	} os << endl;
	}
	return os;
}

// ---- ----

template<int N> class ModInt {
private:
	LL v;
	static LL m;
public:
	ModInt(LL vv = 0) { setval(vv); }
	ModInt & setval(LL vv) { v = vv % m; if(v < 0) { v += m; } return (*this); }
	static void setmod(LL mm) { m = mm; }
	LL getval() const { return v; }
	ModInt & operator+=(const ModInt & b)       { return setval(v + b.v); }
	ModInt & operator-=(const ModInt & b)       { return setval(v - b.v); }
	ModInt & operator*=(const ModInt & b)       { return setval(v * b.v); }
	ModInt & operator/=(const ModInt & b)       { return setval(v * b.inv()); }
	ModInt & operator^=(            LU b)       { return setval(ex(v, b)); }
	ModInt   operator+ (                ) const { return ModInt(+v); }
	ModInt   operator- (                ) const { return ModInt(-v); }
	ModInt   operator+ (const ModInt & b) const { return ModInt(v + b.v); }
	ModInt   operator- (const ModInt & b) const { return ModInt(v - b.v); }
	ModInt   operator* (const ModInt & b) const { return ModInt(v * b.v); }
	ModInt   operator/ (const ModInt & b) const { return ModInt(v * b.inv()); }
	ModInt   operator^ (            LU b) const { return ModInt(ex(v, b)); }
	LL inv() const {
		LL x = (ex_gcd(v, m).FI + m) % m;
		assert(x * v % m == 1);
		return x;
	}
	LL ex(LL a, LU b) const {
		LL D = 64, x[64], y = 1;
		inc(i, D) { if((b >> i) == 0) { D = i; break; } }
		inc(i, D) { x[i] = (i == 0 ? a : x[i - 1] * x[i - 1]) % m; }
		inc(i, D) { if((b >> i) & 1) { (y *= x[i]) %= m; } }
		return y;
	}
	pair<LL, LL> ex_gcd(LL a, LL b) const {
		if(b == 0) { return MP(1, 0); }
		auto p = ex_gcd(b, a % b);
		return MP(p.SE, p.FI - (a / b) * p.SE);
	}
};
template<int N> LL ModInt<N>::m;
template<int N> ModInt<N> operator+(LL a, const ModInt<N> & b) { return  b + a; }
template<int N> ModInt<N> operator-(LL a, const ModInt<N> & b) { return -b + a; }
template<int N> ModInt<N> operator*(LL a, const ModInt<N> & b) { return  b * a; }
template<int N> ModInt<N> operator/(LL a, const ModInt<N> & b) { return  a * b.inv(); }
template<int N> istream & operator>>(istream & is, ModInt<N> & b) { LL v; is >> v; b.setval(v); return is; }
template<int N> ostream & operator<<(ostream & os, const ModInt<N> & b) { return (os << b.getval()); }

// ---- ----

int main() {
	int n, q;
	cin >> n >> q;
	
	ModInt<0>::setmod(1e9 + 7);
	typedef Matrix<ModInt<0>, 4> MM;
	SegmentTree<MM> st(n, OP(B * A), MM().id());
	
	inc(i, n) { st.ref(i).init({ {1}, {0, 1}, {1}, {1} }); }
	st.calc();
	
	inc(qq, q) {
		char c; LL i, v;
		cin >> c;
		
		if(c == 'x') {
			cin >> i >> v;
			st.apply(i, AP(A.a[1][3] = v));
		}
		if(c == 'y') {
			cin >> i >> v;
			st.apply(i, AP(
				A.a[2][2] = v;
				A.a[3][2] = 2 * v;
				A.a[3][3] = v * v;
			));
		}
		if(c == 'a') {
			cin >> i;
			cout << (st.fold_ID(0, i) * MM({ {1}, {1}, {1}, {1} }))[1][0] << "\n";
		}
	}
	
	return 0;
}

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結果

テストケース

ソースコード