結果
問題 | No.2206 Popcount Sum 2 |
ユーザー |
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提出日時 | 2024-05-05 19:02:57 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 790 ms / 4,000 ms |
コード長 | 6,374 bytes |
コンパイル時間 | 2,584 ms |
コンパイル使用メモリ | 213,836 KB |
最終ジャッジ日時 | 2025-02-21 11:03:03 |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
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ファイルパターン | 結果 |
---|---|
sample | AC * 1 |
other | AC * 18 |
ソースコード
#include<bits/stdc++.h>using namespace std;template<long long mod_>struct modint{modint():value(0){}modint(long long v){long long x=(long long)(v%m());if(x<0)x+=m();value=x;}static modint raw(long long v){modint x;x.value=v;return x;}static constexpr long long mod()noexcept{return m();}long long val()const{return value;}modint& operator++(){value++;if(value==m())value=0;return *this;}modint& operator--(){if(value==0)value=m();value--;return *this;}modint operator++(int){modint res=*this;++*this;return res;}modint operator--(int){modint res=*this;--*this;return res;}modint& operator+=(const modint& a){value+=a.value;if(value>=m())value-=m();return *this;}modint& operator-=(const modint& a){value-=a.value;if(value<0)value+=m();return *this;}modint& operator*=(const modint& a){unsigned long long x=value;x*=a.value;x%=m();if(x<0)x+=m();value=x;return *this;}modint& operator/=(const modint& a){return *this=(*this)*a.inv();}modint operator+()const{return *this;}modint operator-()const{return modint()-*this;}modint pow(long long n)const{modint x=*this,res=1;while(n){if(n&1)res*=x;x*=x;n>>=1;}return res;}modint inv()const{long long a=value,b=m(),u=1,v=0;while(b){long long t=a/b;a-=t*b;swap(a,b);u-=t*v;swap(u,v);}return modint(u);}friend modint operator+(const modint& a, const modint& b){modint res=a;res+=b;return res;}friend modint operator-(const modint& a, const modint& b){modint res=a;res-=b;return res;}friend modint operator*(const modint& a, const modint& b){modint res=a;res*=b;return res;}friend modint operator/(const modint& a, const modint& b){modint res=a;res/=b;return res;}friend bool operator==(const modint& a, const modint& b){return a.value==b.value;}friend bool operator!=(const modint& a, const modint& b){return a.value!=b.value;}private:long long value;static constexpr long long m(){return mod_;}};template<typename mint>struct combination{combination(int n=0):inner_fac(1,1),inner_finv(1,1){init(n);}mint fac(int n){init(n);return inner_fac[n];}mint finv(int n){init(n);return inner_finv[n];}mint inv(int n){if(n==0)return 0;init(n);return inner_fac[n-1]*inner_finv[n];}mint C(int n, int r){if(r<0)return 0;if(n<0){n=-n;mint res=C(n-1+r,r);if(r&1)res=-res;return res;}if(n<r)return 0;if(n<bound){init(n);return inner_fac[n]*inner_finv[n-r]*inner_finv[r];}init(r);mint res=1;for(int i=0;i<r;i++)res*=(n-i);return res*inner_finv[r];}mint P(int n, int r){if(n<0||r<0||n<r)return 0;if(n<bound){init(n);return inner_fac[n]*inner_finv[n-r];}mint res=1;for(int i=0;i<r;i++)res*=(n-i);return res;}mint H(int n, int r){return C(n-1+r,r);}private:const int bound=1<<25;vector<mint>inner_fac,inner_finv;void init(int n){int sz=inner_fac.size();if(sz>n)return;n=min(max(n,2*sz),bound);inner_fac.resize(n+1);inner_finv.resize(n+1);for(int i=sz;i<=n;i++)inner_fac[i]=inner_fac[i-1]*i;inner_finv[n]=inner_fac[n].inv();for(int i=n;i>sz;i--)inner_finv[i-1]=inner_finv[i]*i;}};struct Mo{Mo(int _n, int _q):n(_n),q(_q){querys.reserve(_n);}void add(int l, int r){querys.emplace_back(l,r);}template<typename ExL,typename ShL,typename ExR,typename ShR,typename O>void build(const ExL&exl, const ShL&shl, const ExR&exr, const ShR&shr, const O&out){const int b=n/min(n,(int)sqrt(n));vector<int>idx(q);for(int i=0;i<q;i++)idx[i]=i;sort(idx.begin(),idx.end(),[&](int i, int j){auto[li,ri]=querys[i];auto[lj,rj]=querys[j];int bi=li/b,bj=lj/b;return bi==bj?bi&1?ri<rj:ri>rj:bi<bj;});int l=0,r=0;for(int i:idx){auto[li,ri]=querys[i];while(l>li)exl(--l);while(r<ri)exr(r++);while(l<li)shl(l++);while(r>ri)shr(--r);out(i);}}private:int n,q;vector<pair<int,int>>querys;};using mint=modint<998244353>;combination<mint>C;vector<mint>multipoint_binomial_sum(const vector<pair<int,int>>& qs){auto binom=[&](int n, int k){return C.C(n,k);};int n_max=2,q=qs.size();for(auto[n,k]:qs)n_max=max(n_max,n);Mo mo(n_max,q);for(auto[n,k]:qs)mo.add(k,n);vector<mint>res(q);int n=0,k=0;mint ans=1;const mint inv2=mint(2).inv();auto exl=[&](int i){ans-=binom(n,k--);};auto shl=[&](int i){ans+=binom(n,++k);};auto exr=[&](int i){ans+=ans-binom(n++,k);};auto shr=[&](int i){ans=(ans+binom(--n,k))*inv2;};auto out=[&](int i){res[i]=ans;};mo.build(exl,shl,exr,shr,out);return res;}int main(){ios::sync_with_stdio(false);cin.tie(nullptr);int Q;cin>>Q;vector<pair<int,int>>qs(Q);for(auto&p:qs){int n,k;cin>>n>>k;p=make_pair(n-1,k-1);}auto binom=multipoint_binomial_sum(qs);for(int i=0;i<Q;i++){mint ans=mint(2).pow(qs[i].first+1)-1;ans*=binom[i];cout<<ans.val()<<'\n';}}