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QOJ
ID | 题目 | 提交者 | 结果 | 用时 | 内存 | 语言 | 文件大小 | 提交时间 | 测评时间 |
---|---|---|---|---|---|---|---|---|---|
#706692 | #9526. Subsequence Counting | ucup-team5243 | TL | 1ms | 3692kb | C++17 | 15.9kb | 2024-11-03 13:00:22 | 2024-11-03 13:00:23 |
Judging History
answer
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
using i64 = long long;
#define rep(i,n) for(int i=0; i<int(n); i++)
using namespace std;
#include <cassert>
#include <utility>
namespace nachia{
template<class Elem>
struct MatrixModulo{
private:
int h;
int w;
std::vector<Elem> elems;
public:
MatrixModulo(int new_h=0, int new_w=0)
: h(new_h), w(new_w), elems(h*w, Elem(0)){}
MatrixModulo(const MatrixModulo &) = default;
int numRow() const { return h; }
int numColumn() const { return w; }
int height() const { return numRow(); }
int width() const { return numColumn(); }
typename std::vector<Elem>::iterator operator[](int y){ return elems.begin() + (y*w); }
typename std::vector<Elem>::const_iterator operator[](int y) const { return elems.begin() + (y*w); }
static MatrixModulo Identity(int n){
auto res = MatrixModulo(n,n);
for(int i=0; i<n; i++) res[i][i]=Elem(1);
return res;
}
MatrixModulo transposed() const {
auto res = MatrixModulo(w,h);
for(int i=0; i<h; i++) for(int j=0; j<w; j++) res[j][i] = elems[i*w+j];
return res;
}
void swapColumns(int x1, int x2){
assert(0 <= x1 && x1 < numColumn());
assert(0 <= x2 && x2 < numColumn());
for(int y=0; y<numRow(); y++) std::swap((*this)[y][x1], (*this)[y][x2]);
}
void swapRows(int y1, int y2){
assert(0 <= y1 && y1 < numRow());
assert(0 <= y2 && y2 < numRow());
for(int x=0; x<numColumn(); x++) std::swap((*this)[y1][x], (*this)[y2][x]);
}
MatrixModulo operator*(const MatrixModulo& r) const {
assert(width() == r.height());
auto res = MatrixModulo(h, r.w);
for(int i=0; i<h; i++) for(int j=0; j<w; j++) for(int k=0; k<r.w; k++){
res[i][k] += (*this)[i][j] * r[j][k];
}
return res;
}
std::vector<Elem> operator*(const std::vector<Elem>& r) const {
assert(width() == int(r.size()));
auto res = std::vector<Elem>(h);
for(int i=0; i<h; i++) for(int j=0; j<w; j++){
res[i] += (*this)[i][j] * r[j];
}
return res;
}
Elem det() const {
assert(height() == width());
MatrixModulo g = *this;
Elem ans = 1;
for(int i=0; i<h; i++){
int tg = -1;
for(int j=i; j<h; j++){ if(g[j][i].val() != 0) tg = j; }
if(tg == -1) return 0;
if(tg != i) ans = -ans;
for(int j=0; j<h; j++) std::swap(g[i][j], g[tg][j]);
tg = i;
ans *= g[i][i];
Elem const_coeff = g[i][i].inv();
for(int j=0; j<h; j++) g[i][j] *= const_coeff;
for(int j=i+1; j<h; j++) for(int k=h-1; k>=i; k--) g[j][k] -= g[j][i] * g[i][k];
}
return ans;
}
int rank() const {
if(height() == 0 || width() == 0) return 0;
MatrixModulo g = *this;
int y = 0;
for(int d=0; d<w; d++){
if(y == h) break;
int tg = -1;
for(int i=y; i<h; i++){ if(g[i][d].val() != 0){ tg = i; break; } }
if(tg == -1) continue;
for(int j=d; j<w; j++) std::swap(g[y][j], g[tg][j]);
tg = y;
Elem const_coeff = g[y][d].inv();
for(int j=d; j<w; j++) g[y][j] *= const_coeff;
for(int i=y+1; i<h; i++) for(int j=w-1; j>=d; j--) g[i][j] -= g[i][d] * g[y][j];
y++;
}
return y;
}
MatrixModulo pow(unsigned long long i){
auto a = *this;
auto res = Identity(height());
while(i){
if(i%2) res = res * a;
a = a * a; i /= 2;
}
return res;
}
};
} // namespace nachia
namespace nachia{
// ax + by = gcd(a,b)
// return ( x, - )
std::pair<long long, long long> ExtGcd(long long a, long long b){
long long x = 1, y = 0;
while(b){
long long u = a / b;
std::swap(a-=b*u, b);
std::swap(x-=y*u, y);
}
return std::make_pair(x, a);
}
} // namespace nachia
namespace nachia{
template<unsigned int MOD>
struct StaticModint{
private:
using u64 = unsigned long long;
unsigned int x;
public:
using my_type = StaticModint;
template< class Elem >
static Elem safe_mod(Elem x){
if(x < 0){
if(0 <= x+MOD) return x + MOD;
return MOD - ((-(x+MOD)-1) % MOD + 1);
}
return x % MOD;
}
StaticModint() : x(0){}
StaticModint(const my_type& a) : x(a.x){}
StaticModint& operator=(const my_type&) = default;
template< class Elem >
StaticModint(Elem v) : x(safe_mod(v)){}
unsigned int operator*() const noexcept { return x; }
my_type& operator+=(const my_type& r) noexcept { auto t = x + r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
my_type operator+(const my_type& r) const noexcept { my_type res = *this; return res += r; }
my_type& operator-=(const my_type& r) noexcept { auto t = x + MOD - r.x; if(t >= MOD) t -= MOD; x = t; return *this; }
my_type operator-(const my_type& r) const noexcept { my_type res = *this; return res -= r; }
my_type operator-() const noexcept { my_type res = *this; res.x = ((res.x == 0) ? 0 : (MOD - res.x)); return res; }
my_type& operator*=(const my_type& r)noexcept { x = (u64)x * r.x % MOD; return *this; }
my_type operator*(const my_type& r) const noexcept { my_type res = *this; return res *= r; }
my_type pow(unsigned long long i) const noexcept {
my_type a = *this, res = 1;
while(i){ if(i & 1){ res *= a; } a *= a; i >>= 1; }
return res;
}
my_type inv() const { return my_type(ExtGcd(x, MOD).first); }
unsigned int val() const noexcept { return x; }
static constexpr unsigned int mod() { return MOD; }
static my_type raw(unsigned int val) noexcept { auto res = my_type(); res.x = val; return res; }
my_type& operator/=(const my_type& r){ return operator*=(r.inv()); }
my_type operator/(const my_type& r) const { return operator*(r.inv()); }
};
} // namespace nachia
namespace nachia{
template<
class F,
F composition(const F& f, const F& x)
>
struct DualSegtree {
struct Node { F f; bool propagated; };
int N;
int logN;
std::vector<Node> A;
void mapf(Node& a, F f) {
a.propagated = false;
a.f = composition(f, a.f);
}
void spread(int i) {
if(A[i].propagated || !(i < N)) return;
mapf(A[i*2], A[i].f);
mapf(A[i*2+1], A[i].f);
A[i] = A[0];
}
DualSegtree(int n, F id) {
N=1; logN=0;
while(N<n){ N *= 2; logN++; }
A.assign(N*2, { id, true });
}
DualSegtree(const std::vector<F>& a, F id) : DualSegtree(a.size(), id) {
for(int i=0; i<a.size(); i++){ A[i+N].f = a[i]; A[i+N].propagated = false; }
}
void clear(int p) {
p += N;
for(int d=logN; d; d--) spread(p >> d);
A[p] = A[0];
}
F get(int p){
p += N;
for(int d=logN; d; d--) spread(p >> d);
return A[p].f;
}
void apply(int l, int r, F f){
if(!(l < r)) return;
if(l == 0 && r == N){ mapf(A[1], f); return; }
l += N; r += N;
for(int d=logN; d; d--){
if((l >> d) << d != l) spread(l >> d);
if((r >> d) << d != r) spread(r >> d);
}
while(l < r){
if(l&1){ mapf(A[l++], f); } l /= 2;
if(r&1){ mapf(A[--r], f); } r /= 2;
}
}
void apply(int p, F f){
p += N;
for(int d=logN; d; d--) spread(p >> d);
mapf(A[p], f);
}
};
} // namespace nachia;
#include <iterator>
#include <functional>
template<class Elem> struct vec;
template<class Iter>
struct seq_view{
using Ref = typename std::iterator_traits<Iter>::reference;
using Elem = typename std::iterator_traits<Iter>::value_type;
Iter a, b;
Iter begin() const { return a; }
Iter end() const { return b; }
int size() const { return (int)(b-a); }
seq_view(Iter first, Iter last) : a(first), b(last) {}
seq_view sort() const { std::sort(a, b); return *this; }
Ref& operator[](int x) const { return *(a+x); }
template<class F = std::less<Elem>, class ret = vec<int>> ret sorti(F f = F()) const {
ret x(size()); for(int i=0; i<size(); i++) x[i] = i;
x().sort([&](int l, int r){ return f(a[l],a[r]); });
return x;
}
template<class ret = vec<Elem>> ret col() const { return ret(begin(), end()); }
template<class ret = vec<Elem>> ret cumsum() const {
auto res = ret(size() + 1, Elem(0));
for(int i=0; i<size(); i++) res[i+1] = res[i] + operator[](i);
return res;
}
template<class F = std::equal_to<Elem>, class ret = vec<std::pair<Elem, int>>>
ret rle(F eq = F()) const {
auto x = ret();
for(auto& a : (*this)){
if(x.size() == 0 || !eq(x[x.size()-1].first, a)) x.emp(a, 1); else x[x.size()-1].second++;
} return x;
}
template<class F> seq_view sort(F f) const { std::sort(a, b, f); return *this; }
Iter uni() const { return std::unique(a, b); }
Iter lb(const Elem& x) const { return std::lower_bound(a, b, x); }
Iter ub(const Elem& x) const { return std::upper_bound(a, b, x); }
int lbi(const Elem& x) const { return lb(x) - a; }
int ubi(const Elem& x) const { return ub(x) - a; }
seq_view bound(const Elem& l, const Elem& r) const { return { lb(l), lb(r) }; }
template<class F> Iter lb(const Elem& x, F f) const { return std::lower_bound(a, b, x, f); }
template<class F> Iter ub(const Elem& x, F f) const { return std::upper_bound(a, b, x, f); }
template<class F> Iter when_true_to_false(F f) const {
if(a == b) return a;
return std::lower_bound(a, b, *a,
[&](const Elem& x, const Elem&){ return f(x); });
}
seq_view same(Elem x) const { return { lb(x), ub(x) }; }
template<class F> auto map(F f) const {
vec<typename Iter::value_type> r;
for(auto& x : *this) r.emp(f(x));
return r;
}
Iter max() const { return std::max_element(a, b); }
Iter min() const { return std::min_element(a, b); }
template<class F = std::less<Elem>>
Iter min(F f) const { return std::min_element(a, b, f); }
seq_view rev() const { std::reverse(a, b); return *this; }
};
template<class Elem>
struct vec {
public:
using Base = typename std::vector<Elem>;
using Iter = typename Base::iterator;
using CIter = typename Base::const_iterator;
using View = seq_view<Iter>;
using CView = seq_view<CIter>;
vec(){}
explicit vec(int n, const Elem& value = Elem()) : a(0<n?n:0, value) {}
template <class I2> vec(I2 first, I2 last) : a(first, last) {}
vec(std::initializer_list<Elem> il) : a(std::move(il)) {}
vec(Base b) : a(std::move(b)) {}
operator Base() const { return a; }
Iter begin(){ return a.begin(); }
CIter begin() const { return a.begin(); }
Iter end(){ return a.end(); }
CIter end() const { return a.end(); }
int size() const { return a.size(); }
bool empty() const { return a.empty(); }
Elem& back(){ return a.back(); }
const Elem& back() const { return a.back(); }
vec& sortuni(){ (*this)().sort(); a.erase((*this)().uni(), end()); return *this; }
vec sortunied(){ vec x = *this; x.sortuni(); return x; }
Iter operator()(int x){ return a.begin() + x; }
CIter operator()(int x) const { return a.begin() + x; }
View operator()(int l, int r){ return { (*this)(l), (*this)(r) }; }
CView operator()(int l, int r) const { return { (*this)(l), (*this)(r) }; }
View operator()(){ return (*this)(0,size()); }
CView operator()() const { return (*this)(0,size()); }
Elem& operator[](int x){ return a[x]; }
const Elem& operator[](int x) const { return a[x]; }
Base& operator*(){ return a; }
const Base& operator*() const { return a; }
vec& push(Elem args){
a.push_back(std::move(args));
return *this;
}
template<class... Args>
vec& emp(Args &&... args){
a.emplace_back(std::forward<Args>(args) ...);
return *this;
}
template<class Range>
vec& app(Range& x){ for(auto& v : x){ emp(v); } return *this; }
Elem pop(){ Elem x = std::move(a.back()); a.pop_back(); return x; }
void resize(int sz){ a.resize(sz); }
void reserve(int sz){ a.reserve(sz); }
bool operator==(const vec& r) const { return a == r.a; }
bool operator!=(const vec& r) const { return a != r.a; }
bool operator<(const vec& r) const { return a < r.a; }
bool operator<=(const vec& r) const { return a <= r.a; }
bool operator>(const vec& r) const { return a > r.a; }
bool operator>=(const vec& r) const { return a >= r.a; }
vec<vec<Elem>> pile(int n) const { return vec<vec<Elem>>(n, *this); }
template<class F> vec& filter(F f){
int p = 0;
for(auto& x : a) if(f(x)) std::swap(a[p++],x);
resize(p); return *this;
}
vec& operator+=(const vec& r){ return app(r); }
vec operator+(const vec& r) const { vec x = *this; x += r; return x; }
vec operator*(int t) const { vec res; while(t--){ res += *this; } return res; }
private: Base a;
};
template<class IStr, class U, class T>
IStr& operator>>(IStr& is, vec<std::pair<U,T>>& v){ for(auto& x:v){ is >> x.first >> x.second; } return is; }
template<class IStr, class T>
IStr& operator>>(IStr& is, vec<T>& v){ for(auto& x:v){ is >> x; } return is; }
template<class OStr, class T>
OStr& operator<<(OStr& os, const vec<T>& v){
for(int i=0; i<v.size(); i++){
if(i){ os << ' '; } os << v[i];
} return os;
}
template<class OStr, class U, class T>
OStr& operator<<(OStr& os, const vec<std::pair<U,T>>& v){
for(int i=0; i<v.size(); i++){
if(i){ os << ' '; } os << '(' << v[i].first << ',' << v[i].second << ')';
} return os;
}
using Modint = nachia::StaticModint<998244353>;
using Mat = nachia::MatrixModulo<Modint>;
Mat opmat(const Mat& f, const Mat& x){ return x * f; }
Mat solve(int X, i64 L, i64 d, vec<pair<Mat, i64>> rle){
if(L == 1){
return rle[0].first;
}
if(d*2 < L){
vec<pair<Mat,i64>> nxrle(1, {rle[0].first,1});
nxrle += rle().rev().col();
nxrle.back().second -= 1;
if(nxrle.back().second == 0) nxrle.pop();
return solve(X, L, L-d, move(nxrle));
}
vec<i64> chp;
chp.push(0);
for(auto& [u,v] : rle) chp.push(chp.back() + v);
vec<i64> chp_ds = chp().map([&](i64 x){ return x % d; }).sortunied();
chp_ds.push(d);
i64 ds_sz = chp_ds.size() - 1;
nachia::DualSegtree<Mat, opmat> ds(ds_sz, Mat::Identity(X));
rep(i,rle.size()){
i64 l = chp[i];
i64 r = chp[i+1];
i64 lpds = chp_ds().lbi(l%d);
i64 rpds = chp_ds().lbi(r%d);
if(r/d == l/d){
ds.apply(lpds, rpds, rle[i].first);
} else {
ds.apply(lpds, ds_sz, rle[i].first);
ds.apply(0, ds_sz, rle[i].first.pow(r/d-l/d-1));
ds.apply(0, rpds, rle[i].first);
}
}
vec<pair<Mat, i64>> nxrle;
rep(i,ds_sz) nxrle.push({ ds.get(i), chp_ds[i+1] - chp_ds[i] });
return solve(X, d, d-L%d, move(nxrle));
}
void testcase(){
i64 N, M, K, L; cin >> N >> M >> K >> L;
vec<i64> A(M); cin >> A;
vec<pair<Mat, i64>> rle;
rep(i,N){
i64 a,b; cin >> a >> b;
Mat m = Mat::Identity(M+1);
rep(j,M) if(A[j] == b) m[j][j+1] = 1;
rle.push({ m, a });
}
i64 d = nachia::ExtGcd(K, L).first;
auto mp = solve(M+1, L, d, rle);
auto ans = mp[0][M];
cout << ans.val() << '\n';
}
int main(){
ios::sync_with_stdio(false); cin.tie(nullptr);
testcase();
return 0;
}
詳細信息
Test #1:
score: 100
Accepted
time: 1ms
memory: 3660kb
input:
4 2 17 27 3 1 10 3 6 1 10 3 1 1
output:
76
result:
ok single line: '76'
Test #2:
score: 0
Accepted
time: 0ms
memory: 3692kb
input:
5 3 1789 15150 555 718 726 72 555 1029 718 5807 726 1002 718 7240 555
output:
390415327
result:
ok single line: '390415327'
Test #3:
score: -100
Time Limit Exceeded
input:
1 1 1 1000000000 1000 1000000000 1000