結果

問題 No.2605 Pickup Parentheses
ユーザー Jeroen Op de Beek
提出日時 2024-01-12 21:54:07
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 374 ms / 2,000 ms
コード長 5,054 bytes
コンパイル時間 6,240 ms
コンパイル使用メモリ 200,940 KB
最終ジャッジ日時 2025-02-18 18:09:57
ジャッジサーバーID
(参考情報)
judge3 / judge3
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
sample AC * 3
other AC * 68
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#include "bits/stdc++.h"
using namespace std;
#define all(x) begin(x),end(x)
template<typename A, typename B> ostream& operator<<(ostream &os, const pair<A, B> &p) { return os << '(' << p.first << ", " << p.second << ')'; }
template<typename T_container, typename T = typename enable_if<!is_same<T_container, string>::value, typename T_container::value_type>::type>
    ostream& operator<<(ostream &os, const T_container &v) { string sep; for (const T &x : v) os << sep << x, sep = " "; return os; }
#define debug(a) cerr << "(" << #a << ": " << a << ")\n";
typedef long long ll;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef pair<int,int> pi;
const int mxN = 1<<20, oo = 1e9;
const long long MD = 998244353;
template<long long MOD=MD> struct mdint {
int d;
mdint () {d=0;}
mdint (long long _d) : d(_d%MOD){
if(d<0) d+=MOD;
};
friend mdint& operator+=(mdint& a, const mdint& o) {
a.d+=o.d; if(a.d>=MOD) a.d-=MOD;
return a;
}
friend mdint& operator-=(mdint& a, const mdint& o) {
a.d-=o.d; if(a.d<0) a.d+=MOD;
return a;
}
friend mdint& operator*=(mdint& a, const mdint& o) {
return a = mdint((ll)a.d*o.d);
}
mdint operator*(const mdint& o) const {
mdint res = *this;
res*=o;
return res;
}
mdint operator+(const mdint& o) const {
mdint res = *this;
res+=o;
return res;
}
mdint operator-(const mdint& o) const {
mdint res = *this;
res-=o;
return res;
}
mdint operator^(long long b) const {
mdint tmp = 1;
mdint power = *this;
while(b) {
if(b&1) {
tmp = tmp*power;
}
power = power*power;
b/=2;
}
return tmp;
}
friend mdint operator/=(mdint& a, const mdint& o) {
a *= (o^(MOD-2));
return a;
}
mdint operator/(const mdint& o) {
mdint res = *this;
res/=o;
return res;
}
bool operator==(const mdint& o) { return d==o.d;}
bool operator!=(const mdint& o) { return d!=o.d;}
friend istream& operator>>(istream& c, mdint& a) {return c >> a.d;}
friend ostream& operator<<(ostream& c, const mdint& a) {return c << a.d;}
};
using mint = mdint<MD>;
const int mxF = 2e6+2;
mint fact[mxF], ifact[mxF];
mint ncr(int a, int b) {
if(b>a or a<0 or b<0) return 0;
return fact[a]*ifact[b]*ifact[a-b];
}
void precomp() {
fact[0]=1;
for(int i=1;i<mxF;++i) {
fact[i]=fact[i-1]*i;
}
ifact[mxF-1] = mint(1)/fact[mxF-1];
for(int i=mxF-2;i>=0;--i) {
ifact[i]=ifact[i+1]*(i+1);
}
}
typedef mint cd;
void revperm(cd* in, int n) {
for(int i=0,j=0;i<n;++i) {
if(i<j) swap(in[i],in[j]);
for(int k = n >> 1; (j ^= k) < k; k >>= 1);
}
}
cd w[mxN+1]; // stores w^j for each j in [0,n-1]
void precomp2() {
w[0] = 1;
int pw = (MD-1)/mxN;
w[1] = mint(3)^pw;
for(int i= 2;i<=mxN;++i) {
w[i] = w[i-1]*w[1];
}
}
void fft(cd* in, int n, bool reverse=false) {
int lg = __lg(n);
assert(1<<lg == n);
int stride = mxN/n;
revperm(in,n);
for(int s=1;s<=lg;++s) {
int pw = 1<<s;
int mstride = stride*(n>>s);
for(int j=0;j<n;j+=pw) {
// do FFT merging on out array
cd* even = in+j, *odd = in+j+pw/2;
for(int i=0;i<pw/2;++i) {
cd& power = w[reverse?mxN-mstride*i:mstride*i];
auto tmp = power*odd[i];
odd[i] = even[i] - tmp;
even[i] = even[i] + tmp;
}
}
}
if(reverse) {
mint fac = mint(1)/n;
for(int i=0;i<n;++i) in[i]=in[i]*fac;
}
}
vector<cd> polymul(vector<cd> a, vector<cd> b) {
int n = a.size(), m = b.size(), ptwo = 1;
while(ptwo<(n+m)) ptwo*=2;
a.resize(ptwo), b.resize(ptwo);
fft(a.data(),ptwo);
fft(b.data(),ptwo);
for(int i=0;i<ptwo;++i)
a[i] = a[i]*b[i];
fft(a.data(),ptwo,true);
a.resize(n+m-1);
return a;
}
mint catalan(int n) {
if(n%2==1) return 0;
n/=2;
return ncr(2*n,n)/(n+1);
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
precomp();
precomp2();
int n,m; cin >> n >> m;
vi ws;
for(int i=0;i<m;++i) {
int l,r; cin >> l >> r;
--l,--r;
if((r-l+1)%2==0) {
ws.push_back(r-l+1);
}
}
m = ws.size();
auto mul = [&](auto&& self, int l, int r) -> vector<mint> {
if(l==r) return {1};
// cerr << l << ' ' << r << '\n';
if(l+1==r) {
vector<mint> v( (ws[l]/2+1));
v[ws[l]/2]=mint(0)-catalan(ws[l]);
v[0]+=1;
return v;
}
auto mid = (l+r)/2;
return polymul(self(self,l,mid), self(self,mid,r));
};
vector<mint> res = mul(mul,0,m);
// normally: n brackets
mint ans=0;
for(int i=0;i<res.size();++i) {
ans+=catalan(n-i*2)*res[i];
}
cout << ans << '\n';
}
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