cpp_library
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math/verify/verify_math_024_fixed_matrix.cpp
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- Last update: 2020-01-06 07:57:20+09:00
Depends on
math/math_017_modint.cpp
- math/math_024_fixed_matrix.cpp
遅延伝播セグメント木 (Lazy Segment Tree)
(structure/strc_009_abst_lazy_segtree.cpp)
Code
#include <iostream>
#include <cstdio>
#include <valarray>
#include <vector>
#include <functional>
using namespace std;
#include "../math_024_fixed_matrix.cpp"
#include "../math_017_modint.cpp"
#include "../../structure/strc_009_abst_lazy_segtree.cpp"
void CF373_div2_E() {
using mint = ModInt<1000000007>;
using Mat = FixedMatrix<mint, 2, 2>;
using Vec = FixedMatrix<mint, 2, 1>;
auto f = [](Vec a, Mat b) { return b * a; };
auto g = [](Vec a, Vec b) {
return a + b;
};
auto h = [](Mat a, Mat b) {
return a * b;
};
auto p = [](Mat a, int x) {
return a;
};
Vec E0; E0.at(0, 0) = 0, E0.at(1, 0) = 0;
Mat E1 = eigen<mint, 2, 2>();
Mat fib;
fib.at(0, 0) = fib.at(0, 1) = fib.at(1, 0) = 1;
fib.at(1, 1) = 0;
Vec vec;
vec.at(0, 0) = 1, vec.at(1, 0) = 0;
int N, Q; scanf("%d%d", &N, &Q);
vector<Vec> matrices(N);
for(int i=0; i<N; i++) {
int v; scanf("%d", &v);
Mat pow_fib = pow(fib, v - 1);
matrices[i] = pow_fib * vec;
}
LazySegmentTree<Vec, Mat> seg(N, E0, E1, f, g, h, p, matrices);
while(Q--) {
int type; scanf("%d", &type);
if(type == 1) {
int l, r, x; scanf("%d%d%d", &l, &r, &x); l--;
Mat pow_fib = pow(fib, x);
seg.update(l, r, pow_fib);
}
if(type == 2) {
int l, r; scanf("%d%d", &l, &r); l--;
auto res = seg.query(l, r);
printf("%lld\n", res.at(0, 0).v);
}
}
}
int main() {
CF373_div2_E();
}#line 1 "math/verify/verify_math_024_fixed_matrix.cpp"
#include <iostream>
#include <cstdio>
#include <valarray>
#include <vector>
#include <functional>
using namespace std;
#line 1 "math/math_024_fixed_matrix.cpp"
// 行列ライブラリ
// 演算子: 複合代入 (+=, -=), 単項 (-), 二項 (+, -, *, ==)
// eigen(N): N*N 単位行列を返す
// pow(mat, k): mat の k 乗を返す
template <typename T, int h, int w>
struct FixedMatrix {
using array_type = array<T, h * w>;
array_type mat;
FixedMatrix(T val = T(0)) { mat.fill(val); }
const T& at(int i, int j) const { return mat[i*w + j]; }
T& at(int i, int j) { return mat[i*w + j]; }
FixedMatrix<T, h, w> &operator+=(const FixedMatrix<T, h, w>& rhs) {
for(size_t i=0; i<h; i++) {
for(size_t j=0; j<w; j++) {
this->at(i, j) += rhs.at(i, j);
}
}
return *this;
}
FixedMatrix<T, h, w> operator-() const {
FixedMatrix<T, h, w> res(*this);
for(size_t i=0; i<h; i++) {
for(size_t j=0; j<w; j++) {
res.at(i, j) *= T(-1);
}
}
return res;
}
FixedMatrix<T, h, w> &operator-=(const FixedMatrix<T, h, w>& rhs) {
return (FixedMatrix<T, h, w>(*this) += -rhs);
}
template <int wr>
FixedMatrix<T, h, wr> operator*(const FixedMatrix<T, w, wr>& rhs) {
size_t H = h, W = wr, C = w;
FixedMatrix<T, h, wr> res;
for(size_t i=0; i<H; i++) {
for(size_t j=0; j<W; j++) {
for(size_t k=0; k<C; k++) {
res.at(i, j) += this->at(i, k) * rhs.at(k, j);
}
}
}
return res;
}
FixedMatrix<T, h, w> operator+(const FixedMatrix<T, h, w>& rhs) {
return (FixedMatrix<T, h, w>(*this) += rhs);
}
FixedMatrix<T, h, w> operator-(const FixedMatrix<T, h, w> &rhs) {
return (FixedMatrix<T, h, w>(*this) -= rhs);
}
bool operator==(const FixedMatrix<T, h, w> &rhs) const {
return this->mat == rhs.mat;
}
bool operator!=(const FixedMatrix<T, h, w> &rhs) const {
return !(*this == rhs);
}
};
template <typename T, int h, int w>
FixedMatrix<T, h, w> eigen() {
FixedMatrix<T, h, w> res(0);
for(size_t i=0; i<h; i++) res.at(i, i) = T(1);
return res;
}
template <typename T, int h, int w>
FixedMatrix<T, h, w> pow(FixedMatrix<T, h, w> mat, long long int k) {
FixedMatrix<T, h, w> res = eigen<T, h, w>();
for(; k>0; k>>=1) {
if(k & 1) res = res * mat;
mat = mat * mat;
}
return res;
}
template <typename T, int h, int w>
ostream& operator<< (ostream& out, FixedMatrix<T, h, w> mat) {
int H = mat.h, W = mat.w;
out << "[" << endl;
for(int i=0; i<H; i++) {
out << " [ ";
for(int j=0; j<W; j++) out << mat.at(i, j) << " ";
out << "]" << endl;
}
out << "]" << endl;
return out;
}
#line 1 "math/math_017_modint.cpp"
// ModInt begin
using ll = long long;
template<ll mod>
struct ModInt {
ll v;
ll mod_pow(ll x, ll n) const {
return (!n) ? 1 : (mod_pow((x*x)%mod,n/2) * ((n&1)?x:1)) % mod;
}
ModInt(ll a = 0) : v((a %= mod) < 0 ? a + mod : a) {}
ModInt operator+ ( const ModInt& b ) const {
return (v + b.v >= mod ? ModInt(v + b.v - mod) : ModInt(v + b.v));
}
ModInt operator- () const {
return ModInt(-v);
}
ModInt operator- ( const ModInt& b ) const {
return (v - b.v < 0 ? ModInt(v - b.v + mod) : ModInt(v - b.v));
}
ModInt operator* ( const ModInt& b ) const {return (v * b.v) % mod;}
ModInt operator/ ( const ModInt& b ) const {return (v * mod_pow(b.v, mod-2)) % mod;}
bool operator== ( const ModInt &b ) const {return v == b.v;}
bool operator!= ( const ModInt &b ) const {return !(*this == b); }
ModInt& operator+= ( const ModInt &b ) {
v += b.v;
if(v >= mod) v -= mod;
return *this;
}
ModInt& operator-= ( const ModInt &b ) {
v -= b.v;
if(v < 0) v += mod;
return *this;
}
ModInt& operator*= ( const ModInt &b ) {
(v *= b.v) %= mod;
return *this;
}
ModInt& operator/= ( const ModInt &b ) {
(v *= mod_pow(b.v, mod-2)) %= mod;
return *this;
}
ModInt pow(ll x) { return ModInt(mod_pow(v, x)); }
// operator int() const { return int(v); }
// operator long long int() const { return v; }
};
template<ll mod>
ModInt<mod> pow(ModInt<mod> n, ll k) {
return ModInt<mod>(n.mod_pow(n.v, k));
}
template<ll mod>
ostream& operator<< (ostream& out, ModInt<mod> a) {return out << a.v;}
template<ll mod>
istream& operator>> (istream& in, ModInt<mod>& a) {
in >> a.v;
return in;
}
// ModInt end
#line 1 "structure/strc_009_abst_lazy_segtree.cpp"
// @category セグメント木 (Segment Tree)
// @title 遅延伝播セグメント木 (Lazy Segment Tree)
template <typename MonoidType, typename OperatorType>
struct LazySegmentTree {
using MMtoM = function< MonoidType(MonoidType, MonoidType) >;
using OOtoO = function< OperatorType(OperatorType, OperatorType) >;
using MOtoM = function< MonoidType(MonoidType, OperatorType) >;
using OItoO = function< OperatorType(OperatorType, int) >;
// node, lazy, update flag (for lazy), identity element
int n;
vector<MonoidType> node;
vector<OperatorType> lazy;
vector<bool> need_update;
MonoidType E0;
OperatorType E1;
// update / combine / lazy / accumulate function
MOtoM upd_f;
MMtoM cmb_f;
OOtoO lzy_f;
OItoO acc_f;
void build(int m, vector<MonoidType> v = vector<MonoidType>()) {
if(v != vector<MonoidType>()) m = v.size();
n = 1; while(n < m) n *= 2;
node = vector<MonoidType>(2*n-1, E0);
lazy = vector<OperatorType>(2*n-1, E1);
need_update = vector<bool>(2*n-1, false);
if(v != vector<MonoidType>()) {
for(int i=0; i<m; i++) {
node[n-1+i] = v[i];
}
for(int i=n-2; i>=0; i--) {
node[i] = cmb_f(node[2*i+1], node[2*i+2]);
}
}
}
// initialize
LazySegmentTree() {}
LazySegmentTree(int n_, MonoidType E0_, OperatorType E1_,
MOtoM upd_f_, MMtoM cmb_f_, OOtoO lzy_f_, OItoO acc_f_,
vector<MonoidType> v = vector<MonoidType>()) :
E0(E0_), E1(E1_),
upd_f(upd_f_), cmb_f(cmb_f_), lzy_f(lzy_f_), acc_f(acc_f_) {
build(n_, v);
}
void eval(int k, int l, int r) {
if(!need_update[k]) return;
node[k] = upd_f(node[k], acc_f(lazy[k], r - l));
if(r - l > 1) {
lazy[2*k+1] = lzy_f(lazy[2*k+1], lazy[k]);
lazy[2*k+2] = lzy_f(lazy[2*k+2], lazy[k]);
need_update[2*k+1] = need_update[2*k+2] = true;
}
lazy[k] = E1;
need_update[k] = false;
}
void update(int a, int b, OperatorType x, int l, int r, int k) {
eval(k, l, r);
if(b <= l or r <= a) return;
if(a <= l and r <= b) {
lazy[k] = lzy_f(lazy[k], x);
need_update[k] = true;
eval(k, l, r);
}
else {
int mid = (l + r) / 2;
update(a, b, x, l, mid, 2*k+1);
update(a, b, x, mid, r, 2*k+2);
node[k] = cmb_f(node[2*k+1], node[2*k+2]);
}
}
MonoidType query(int a, int b, int l, int r, int k) {
if(b <= l or r <= a) return E0;
eval(k, l, r);
if(a <= l and r <= b) return node[k];
int mid = (l + r) / 2;
MonoidType vl = query(a, b, l, mid, 2*k+1);
MonoidType vr = query(a, b, mid, r, 2*k+2);
return cmb_f(vl, vr);
}
// update [a, b)-th element (applied value, x)
void update(int a, int b, OperatorType x) {
update(a, b, x, 0, n, 0);
}
// range query for [a, b)
MonoidType query(int a, int b) {
return query(a, b, 0, n, 0);
}
void dump() {
fprintf(stderr, "[lazy]\n");
for(int i=0; i<2*n-1; i++) {
if(i == n-1) fprintf(stderr, "xxx ");
if(lazy[i] == E1) fprintf(stderr, " E ");
else fprintf(stderr, "%3d ", lazy[i]);
}
fprintf(stderr, "\n");
fprintf(stderr, "[node]\n");
for(int i=0; i<2*n-1; i++) {
if(i == n-1) fprintf(stderr, "xxx ");
if(node[i] == E0) fprintf(stderr, " E ");
else fprintf(stderr, "%3d ", node[i]);
}
fprintf(stderr, "\n");
}
};
#line 10 "math/verify/verify_math_024_fixed_matrix.cpp"
void CF373_div2_E() {
using mint = ModInt<1000000007>;
using Mat = FixedMatrix<mint, 2, 2>;
using Vec = FixedMatrix<mint, 2, 1>;
auto f = [](Vec a, Mat b) { return b * a; };
auto g = [](Vec a, Vec b) {
return a + b;
};
auto h = [](Mat a, Mat b) {
return a * b;
};
auto p = [](Mat a, int x) {
return a;
};
Vec E0; E0.at(0, 0) = 0, E0.at(1, 0) = 0;
Mat E1 = eigen<mint, 2, 2>();
Mat fib;
fib.at(0, 0) = fib.at(0, 1) = fib.at(1, 0) = 1;
fib.at(1, 1) = 0;
Vec vec;
vec.at(0, 0) = 1, vec.at(1, 0) = 0;
int N, Q; scanf("%d%d", &N, &Q);
vector<Vec> matrices(N);
for(int i=0; i<N; i++) {
int v; scanf("%d", &v);
Mat pow_fib = pow(fib, v - 1);
matrices[i] = pow_fib * vec;
}
LazySegmentTree<Vec, Mat> seg(N, E0, E1, f, g, h, p, matrices);
while(Q--) {
int type; scanf("%d", &type);
if(type == 1) {
int l, r, x; scanf("%d%d%d", &l, &r, &x); l--;
Mat pow_fib = pow(fib, x);
seg.update(l, r, pow_fib);
}
if(type == 2) {
int l, r; scanf("%d%d", &l, &r); l--;
auto res = seg.query(l, r);
printf("%lld\n", res.at(0, 0).v);
}
}
}
int main() {
CF373_div2_E();
}