結果
| 問題 |
No.510 二次漸化式
|
| コンテスト | |
| ユーザー |
 FF256grhy
|
| 提出日時 | 2018-08-04 16:51:06 |
| 言語 | C++14 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,992 ms / 3,000 ms |
| コード長 | 7,882 bytes |
| コンパイル時間 | 2,308 ms |
| コンパイル使用メモリ | 191,104 KB |
| 実行使用メモリ | 87,556 KB |
| 最終ジャッジ日時 | 2024-09-19 17:51:26 |
| 合計ジャッジ時間 | 42,344 ms |
|
ジャッジサーバーID （参考情報） |
judge2 / judge4 |
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| ファイルパターン | 結果 |
|---|---|
| sample | AC * 2 |
| other | AC * 34 |
ソースコード
#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 + m) % 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;
}