結果
問題 | No.2605 Pickup Parentheses |
ユーザー |
|
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 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 68 |
ソースコード
#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 arraycd* 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 bracketsmint ans=0;for(int i=0;i<res.size();++i) {ans+=catalan(n-i*2)*res[i];}cout << ans << '\n';}