結果

問題 No.616 へんなソート
ユーザー mugen_1337mugen_1337
提出日時 2020-12-20 17:48:26
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 240 ms / 2,000 ms
コード長 10,603 bytes
コンパイル時間 2,519 ms
コンパイル使用メモリ 212,284 KB
実行使用メモリ 98,608 KB
最終ジャッジ日時 2024-09-21 11:54:31
合計ジャッジ時間 10,995 ms
ジャッジサーバーID
（参考情報） 		judge2 / judge5
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テストケース

テストケース表示
入力 結果 実行時間
実行使用メモリ
testcase_00 AC 218 ms
97,280 KB
testcase_01 AC 227 ms
97,284 KB
testcase_02 AC 229 ms
97,252 KB
testcase_03 AC 237 ms
97,260 KB
testcase_04 AC 227 ms
97,280 KB
testcase_05 AC 230 ms
97,224 KB
testcase_06 AC 226 ms
97,160 KB
testcase_07 AC 221 ms
97,240 KB
testcase_08 AC 226 ms
97,400 KB
testcase_09 AC 224 ms
97,244 KB
testcase_10 AC 224 ms
97,152 KB
testcase_11 AC 222 ms
97,392 KB
testcase_12 AC 223 ms
97,288 KB
testcase_13 AC 240 ms
98,196 KB
testcase_14 AC 221 ms
97,280 KB
testcase_15 AC 221 ms
97,192 KB
testcase_16 AC 222 ms
97,280 KB
testcase_17 AC 227 ms
98,176 KB
testcase_18 AC 231 ms
97,664 KB
testcase_19 AC 231 ms
97,536 KB
testcase_20 AC 220 ms
97,152 KB
testcase_21 AC 221 ms
97,252 KB
testcase_22 AC 224 ms
97,348 KB
testcase_23 AC 225 ms
97,168 KB
testcase_24 AC 223 ms
97,220 KB
testcase_25 AC 218 ms
97,232 KB
testcase_26 AC 225 ms
97,536 KB
testcase_27 AC 224 ms
97,408 KB
testcase_28 AC 234 ms
98,604 KB
testcase_29 AC 240 ms
98,608 KB
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 # 

#include<bits/stdc++.h>
using namespace std;
#define ALL(x) begin(x),end(x)
#define rep(i,n) for(int i=0;i<(n);i++)
#define debug(v) cout<<#v<<":";for(auto x:v){cout<<x<<' ';}cout<<endl;
#define mod 1000000007
using ll=long long;
const int INF=1000000000;
const ll LINF=1001002003004005006ll;
int dx[]={1,0,-1,0},dy[]={0,1,0,-1};
template<class T>bool chmax(T &a,const T &b){if(a<b){a=b;return true;}return false;}
template<class T>bool chmin(T &a,const T &b){if(b<a){a=b;return true;}return false;}

struct IOSetup{
    IOSetup(){
        cin.tie(0);
        ios::sync_with_stdio(0);
        cout<<fixed<<setprecision(12);
    }
} iosetup;
 
template<typename T>
ostream &operator<<(ostream &os,const vector<T>&v){
    for(int i=0;i<(int)v.size();i++) os<<v[i]<<(i+1==(int)v.size()?"":" ");
    return os;
}
template<typename T>
istream &operator>>(istream &is,vector<T>&v){
    for(T &x:v)is>>x;
    return is;
}

template<ll Mod>
struct ModInt{
    long long x;
    ModInt():x(0){}
    ModInt(long long y):x(y>=0?y%Mod:(Mod-(-y)%Mod)%Mod){}
    ModInt &operator+=(const ModInt &p){
        if((x+=p.x)>=Mod) x-=Mod;
        return *this;
    }
    ModInt &operator-=(const ModInt &p){
        if((x+=Mod-p.x)>=Mod)x-=Mod;
        return *this;
    }
    ModInt &operator*=(const ModInt &p){
        x=(int)(1ll*x*p.x%Mod);
        return *this;
    }
    ModInt &operator/=(const ModInt &p){
        (*this)*=p.inverse();
        return *this;
    }
    ModInt operator-()const{return ModInt(-x);}
    ModInt operator+(const ModInt &p)const{return ModInt(*this)+=p;}
    ModInt operator-(const ModInt &p)const{return ModInt(*this)-=p;}
    ModInt operator*(const ModInt &p)const{return ModInt(*this)*=p;}
    ModInt operator/(const ModInt &p)const{return ModInt(*this)/=p;}
    bool operator==(const ModInt &p)const{return x==p.x;}
    bool operator!=(const ModInt &p)const{return x!=p.x;}
    ModInt inverse()const{
        int a=x,b=Mod,u=1,v=0,t;
        while(b>0){
            t=a/b;
            swap(a-=t*b,b);swap(u-=t*v,v);
        }
        return ModInt(u);
    }
    ModInt pow(long long n)const{
        ModInt ret(1),mul(x);
        while(n>0){
            if(n&1) ret*=mul;
            mul*=mul;n>>=1;
        }
        return ret;
    }
    friend ostream &operator<<(ostream &os,const ModInt &p){return os<<p.x;}
    friend istream &operator>>(istream &is,ModInt &a){long long t;is>>t;a=ModInt<Mod>(t);return (is);}
    static int get_mod(){return Mod;}
};
using mint=ModInt<mod>;
 
 
template<int MAX>
struct comcalc{
    vector<mint> fact,finv,inv;
    comcalc():fact(MAX),finv(MAX),inv(MAX){
        fact[0]=mint(1),fact[1]=mint(1),finv[0]=mint(1),finv[1]=mint(1),inv[1]=mint(1);
        for(int i=2;i<MAX;i++){
            fact[i]=fact[i-1]*mint(i);
            inv[i]=mint(0)-inv[mod%i]*(mint(mod/i));
            finv[i]=finv[i-1]*inv[i];
        }
    }
    mint com(int n,int k){
        if(n<k) return mint(0);
        if(n<0 or k<0) return mint(0);
        return fact[n]*(finv[k]*finv[n-k]);
    }
    mint fac(int n){
        return fact[n];
    }
    // 重複組み合わせ:n種類の物から重複を許し，k個選ぶ
    mint nHk(int n,int k){
        return com(n+k-1,k);
    }
    // 玉n区別，箱k区別，各箱1個以上O(k)
    mint F12_dis_dis_one(int n,int k){
        if(n<k)return mint(0);
        mint ret=0;
        for(int i=0;i<=k;i++){
            mint add=com(k,i)*(mint(i).pow(n));
            if((k-i)%2) ret-=add;
            else        ret+=add;
        }
        return ret;
    }
    /* sum combination(n+x, x), x=l to r
       https://www.wolframalpha.com/input/?i=sum+combination%28n%2Bx+%2Cx%29%2C+x%3Dl+to+r&lang=ja 
       check n+x < [COM_PRECALC_MAX]    */
    mint sum_of_comb(int n,int l,int r){
        if(l>r)return mint(0);
        mint ret=mint(r+1)*com(n+r+1,r+1)-mint(l)*com(l+n,l);
        ret/=mint(n+1);
        return ret;
    }
};
mint pow_mod(mint x,ll n){
    return x.pow(n);
}
mint inv_mod(mint x){
    return x.inverse();
}
// O(n)
mint fact_mod(ll n){
    mint ret=1;
    for(int i=2;i<=n;i++) ret*=mint(i);
    return ret;
}
// O(r)
mint comb_mod(ll n,ll r){
    if(r>n-r) r=n-r;
    if(r==0) return 1;
    mint a=1,b=mint(fact_mod(r)).inverse();
    for(int i=0;i<r;i++)a*=mint(n-i);
    return a*b;
}
 
const int MAX=4010000;
using cominit=comcalc<MAX>;

template<typename T>
struct FormalPowerSeries:vector<T>{
    using vector<T>::vector;
    using P=FormalPowerSeries;
    using MULT=function<P(P,P)>;
 
    static MULT &get_mult(){static MULT mult=nullptr;return mult;}
    static void set_mult(MULT f){get_mult()=f;}
    void shrink(){while(this->size() and this->back()==T(0)) this->pop_back();}
    P pre(int sz)const{return P(begin(*this),begin(*this)+min((int)this->size(),sz));}
    P operator+(const P &rhs)const{return P(*this)+=rhs;}
    P operator+(const T &rhs)const{return P(*this)+=rhs;}
    P operator-(const P &rhs)const{return P(*this)-=rhs;}
    P operator-(const T &rhs)const{return P(*this)-=rhs;}
    P operator*(const P &rhs)const{return P(*this)*=rhs;}
    P operator*(const T &rhs)const{return P(*this)*=rhs;}
    P operator/(const P &rhs)const{return P(*this)/=rhs;}
    P operator%(const P &rhs)const{return P(*this)%=rhs;}
    P &operator+=(const P &rhs){
        if(rhs.size()>this->size()) this->resize(rhs.size());
        for(int i=0;i<(int)rhs.size();i++) (*this)[i]+=rhs[i];
        return (*this);
    }
    P &operator+=(const T &rhs){
        if(this->empty()) this->resize(1);
        (*this)[0]+=rhs;
        return (*this);
    }
    P &operator-=(const P &rhs){
        if(rhs.size()>this->size()) this->resize(rhs.size());
        for(int i=0;i<(int)rhs.size();i++) (*this)[i]-=rhs[i];
        shrink();
        return (*this);
    }
    P &operator-=(const T &rhs){
        if(this->empty()) this->resize(1);
        (*this)[0]-=rhs;
        shrink();
        return (*this);
    }
    P &operator*=(const T &rhs){
        const int n=(int)this->size();
        for(int i=0;i<n;i++) (*this)[i]*=rhs;
        return (*this);
    }
    P &operator*=(const P &rhs){
        if(this->empty() or rhs.empty()){
            this->clear();
            return (*this);
        }
        assert(get_mult()!=nullptr);
        return (*this)=get_mult()(*this,rhs);
    }
    P &operator%=(const P &rhs){return (*this)-=(*this)/rhs*rhs;}
    P operator-()const{
        P ret(this->size());
        for(int i=0;i<(int)this->size();i++) ret[i]=-(*this)[i];
        return ret;
    }
    P &operator/=(const P &rhs){
        if(this->size()<rhs.size()){
            this->clear();
            return (*this);
        }
        int n=(int)this->size()-rhs.size()+1;
        return (*this)=(rev().pre(n)*rhs.rev().inv(n));
    }
    P operator>>(int sz)const{
        if((int)this->size()<=sz) return {};
        P ret(*this);
        ret.erase(ret.begin(),ret.begin()+sz);
        return ret;
    }
    P operator<<(int sz)const{
        P ret(*this);
        ret.insert(ret.begin(),sz,T(0));
        return ret;
    }
    P rev(int deg=-1)const{
        P ret(*this);
        if(deg!=-1) ret.resize(deg,T(0));
        reverse(begin(ret),end(ret));
        return ret;
    }
    // 微分
    P diff()const{
        const int n=(int)this->size();
        P ret(max(0,n-1));
        for(int i=1;i<n;i++) ret[i-1]=(*this)[i]*T(i);
        return ret;
    }
    // 積分
    P integral()const{
        const int n=(int)this->size();
        P ret(n+1);
        ret[0]=T(0);
        for(int i=0;i<n;i++) ret[i+1]=(*this)[i]/T(i+1);
        return ret;
    }
    // ref : https://qiita.com/hotman78/items/f0e6d2265badd84d429a
    P inv(int deg=-1)const{
        assert(((*this)[0])!=T(0));
        const int n=(int)this->size();
        if(deg==-1) deg=n;
        P ret({T(1)/(*this)[0]});
        for(int i=1;i<deg;i<<=1) ret=(ret+ret-ret*ret*pre(i<<1)).pre(i<<1);
        return ret.pre(deg);
    }
    // ?
    P log(int deg=-1)const{
        assert((*this)[0]==1);
        const int n=(int)this->size();
        if(deg==-1) deg=n;
        return (this->diff()*this->inv(deg)).pre(deg-1).integral();
    }
    // ?
    P exp(int deg=-1)const{
        assert((*this)[0]==T(0));
        const int n=(int)this->size();
        if(deg==-1) deg=n;
        P ret({T(1)});
        for(int i=1;i<deg;i<<=1) ret=(ret*(pre(i<<1)+T(1)-ret.log(i<<1))).pre(i<<1);
        return ret.pre(deg);
    }
    // O(nlogn) with NTT
    // 
    P pow_fast(long long k,int deg=-1){
        int n=(int)this->size();
        if(deg==-1) deg=n;
        for(int i=0;i<n;i++){
            if((*this)[i]!=T(0)){
                T rev=T(1)/(*this)[i];
                P ret=(((*this*rev)>>i).log()*k).exp()*((*this)[i].pow(k));
                if(i*k>deg) return P(deg,T(0));
                ret=(ret<<(i*k)).pre(deg);
                if((int)ret.size()<deg) ret.resize(deg,T(0));
                return ret;
            }
        }
        return *this;
    }
    // O(Mult * log k)
    // resize not verified
    P pow(ll k,int deg=-1){
        if(deg==-1) deg=1000000000;
        P ret=P{1};
        P b(*this);
        while(k){
            if(k&1) ret*=b;
            b=b*b;
            k>>=1;
            if((int)ret.size()>deg) ret.resize(deg);
            if((int)b.size()>deg) b.resize(deg);
        }
        return ret;
    }
    // [l,r) k個飛び
    P slice(int l,int r,int k=1){
        P ret;
        for(int i=l;i<r;i+=k) ret.push_back((*this)[i]);
        return ret;
    }
    /*
    ref : https://atcoder.jp/contests/aising2020/submissions/15300636
          http://q.c.titech.ac.jp/docs/progs/polynomial_division.html
 
    order :      
        O(M(d)log(k))  (M(d) -> d次元，multiplyの計算量)
 
    return :
        [x^k] (*this) / q
    */
    T nth_term(P q,ll k){
        if(k==0) return (*this)[0]/q[0];
        P p(*this),q_=q;
        for(int i=1;i<(int)q_.size();i+=2) q_[i]*=-1;
        q*=q_;p*=q_;// qは奇数項が消える
        return p.slice(k%2,p.size(),2).nth_term(q.slice(0,q.size(),2),k/2);
    }
};
using FPS=FormalPowerSeries<mint>;
 
auto multiply_naive(const FPS::P &lhs,const FPS::P &rhs){
    assert(!lhs.empty() and !rhs.empty());
    auto ret=FPS(int(lhs.size())+int(rhs.size())-1);
    rep(i,(int)lhs.size())rep(j,(int)rhs.size()) ret[i+j]+=lhs[i]*rhs[j];
    return ret;
}


signed main(){
    FPS::set_mult(multiply_naive);
    cominit F;

    int n,k;cin>>n>>k;
    rep(i,n){int a;cin>>a;}
    
    FPS P{1};
    rep(i,n) P-=(P<<(i+1));

    mint res=0;
    rep(i,k+1){
        res+=P[i]*F.com(k+n-i,n);
    }
    cout<<res<<endl;
    return 0;
}
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