#696737 (C++17) No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率

• 問題: No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率
• ユーザー: suzuken_w
• 提出日時: 2021-09-05 14:42:44
• 言語: C++17 (gcc 13.3.0 + boost 1.87.0)
• 結果: AC
• 実行時間: 138 ms / 2,000 ms
• コード長: 6,429 bytes
• コンパイル時間: 2,649 ms
• コンパイル使用メモリ: 224,600 KB
• 最終ジャッジ日時: 2025-01-24 08:20:02
• ジャッジサーバーID （参考情報）: judge3 / judge4

ファイルパターン	結果
other	AC * 36

ソースコード

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#pragma GCC optimize("O3")
#include<bits/stdc++.h> 
using namespace std;
using ll=long long;
using P=pair<ll,ll>;
template<class T> using V=vector<T>; 
#define fi first
#define se second
#define all(v) (v).begin(),(v).end()
const ll inf=(1e18);
const ll mod=998244353;
//const ll mod=1000000007;
const vector<int> dy={-1,0,1,0},dx={0,-1,0,1};
ll GCD(ll a,ll b) {return b ? GCD(b,a%b):a;}
ll LCM(ll c,ll d){return c/GCD(c,d)*d;}
struct __INIT{__INIT(){cin.tie(0);ios::sync_with_stdio(false);cout<<fixed<<setprecision(20);}} __init;
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; }
template<class T>void debag(const vector<T> &a){cerr<<"debag :";for(auto v:a)cerr<<v<<" ";cerr<<"\n";}
template<class T>void print(const vector<T> &a){for(auto v:a)cout<<v<<" ";cout<<"\n";}
struct mint{
    using ull=unsigned long long int;
    ull v;
    mint(ll vv=0){s(vv%mod+mod);}
    mint& s(ull vv){
        v=vv<mod?vv:vv-mod;
        return *this;
    }
    //オーバーロード
    mint operator-()const{return mint()-*this;}//mint型にキャスト
    mint&operator+=(const mint&val){return s(v+val.v);}
    mint&operator-=(const mint&val){return s(v+mod-val.v);}
    mint&operator*=(const mint&val){
        v=ull(v)*val.v%mod;
        return *this;
    }
    mint&operator/=(const mint&val){return *this*=val.inv();}
    mint operator+(const mint&val){return mint(*this)+=val;}
    mint operator-(const mint&val){return mint(*this)-=val;}
    mint operator*(const mint&val){return mint(*this)*=val;}
    mint operator/(const mint&val){return mint(*this)/=val;}
    mint pow(ll n)const{
        mint res(1),x(*this);
        while(n){
            if(n&1)res*=x;
            x*=x;
            n>>=1ll;
        }
        return res;
    }
    mint inv()const{return pow(mod-2);}
    //拡張ユークリッドの互除法
    /* mint inv()const{
        int x,y;
        int g=extgcd(v,mod,x,y);
        assert(g==1);
        if(x<0)x+=mod;
        return mint(x);
    }*/
    friend ostream& operator<<(ostream&os,const mint&val){
        return os<<val.v;
    }//出力
    bool operator<(const mint&val)const{return v<val.v;}
    bool operator==(const mint&val)const{return v==val.v;}
    bool operator>(const mint&val)const{return v>val.v;}
};
template<class T> struct Matrix{
    vector<vector<T>> A;
    Matrix() {}
    Matrix(int n,int m):A(n,vector<T>(m,0)) {}
    Matrix(int n):A(n,vector<T>(n,0)) {}
    int height() const{return (A.size());}
    int width() const{return (A[0].size());}
    inline const vector<T> &operator[](int k)const{return (A.at(k));}
    inline vector<T> &operator[](int k){return (A.at(k));}
   //単位行列
    static Matrix I(int n){
        Matrix mat(n);
        for(int i=0;i<n;i++)mat[i][i]=(T)(1);
        return mat;
    }
    Matrix &operator+=(const Matrix &B){
        int n=height(),m=width();
        assert(n==B.height()&&m==B.width());
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                (*this)[i][j]+=B[i][j];
            }
        }
        return (*this);
    }
    Matrix &operator-=(const Matrix &B){
        int n=height(),m=width();
        assert(n==B.height()&&m==B.width());
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                (*this)[i][j]-=B[i][j];
            }
        }
        return (*this);
    }
    Matrix &operator*=(const Matrix &B){
        int n=height(),m=B.width(),w=height();
        assert(w==B.height());
        vector<vector<T>> C(n,vector<T>(m,0));
        for(int i=0;i<n;i++){
            for(int j=0;j<m;j++){
                for(int k=0;k<w;k++){
                    C[i][j]+=(*this)[i][k]*B[k][j];
                }
            }
        }
        A.swap(C);
        return (*this);
    }
    //累乗計算
    Matrix &operator^=(long long k){
        Matrix B=Matrix::I(height());
        while(k>0){
            if(k&1){
                B*=(*this);
            }
            (*this)*=(*this);
            k>>=1ll;
        }
        A.swap(B.A);
        return (*this);
    }
    Matrix operator+(const Matrix &B)const{return (Matrix(*this)+=B);}
    Matrix operator-(const Matrix &B)const{return (Matrix(*this)-=B);}
    Matrix operator*(const Matrix &B)const{return (Matrix(*this)*=B);}
    Matrix operator^(const long long k)const{return (Matrix(*this)^=k);}
    friend ostream &operator<<(ostream &os,Matrix &mat){
        int n=mat.height(),m=mat.width();
        for(int i=0;i<n;i++){
            os<<"[";
            for(int j=0;j<m;j++){
                os<<mat[i][j]<<(j+1==m?"]\n":",");
            }
        }
        return (os);
    }
    //行列式
    T det(){
        Matrix B(*this);
        assert(height()==width());
        T ret=(T)(1);
        for(int i=0;i<width();i++){
            int idx=-1;
            for(int j=i;j<width();j++){
                if(!(B[j][i]==(T)(0)))idx=j;
            }
            if(idx==-1)return (T)(0);
            if(i!=idx){
                ret*=(T)(-1);
                swap(B[i],B[idx]);
            }
            ret*=B[i][i];
            T v=B[i][i];
            for(int j=0;j<width();j++){
                B[i][j]/=v;
            }
            for(int j=i+1;j<width();j++){
                T a=B[j][i];
                for(int k=0;k<width();k++){
                    B[j][k]-=B[i][k]*a;
                }
            }
        }
        return (ret);
    }
};
int main(){
      ll a,b,s,c,d,t;
      cin>>a>>b>>s>>c>>d>>t;
      ll k;
      cin>>k;
      int n=(s+t+1);
      Matrix<mint> mat(n,n),res(n,1);
      mint p=mint(a)/mint(b),q=mint(c)/mint(d);
      mat[0][0]=mint(1);
      mat[n-1][n-1]=mint(1);
      res[s][0]=mint(1);
      for(int i=0;i<n-1;i++){
            for(int j=1;j<n-1;j++){
                  mint val=mint(0);
                  for(int k=(i!=0);k<=min(j,i);k++){
                        val+=p.pow(j-k)*q.pow(i-k);
                  }
                  if(i!=0)val*=(mint(1)-p)*(mint(1)-q);
                  mat[i][j]=val;
            }
      }
      for(int i=1;i<n-1;i++){
            mint val=mint(0);
            for(int j=1;j<=i;j++){
                  val+=p.pow(i-j)*q.pow(n-1-j);
            }
            val*=(mint(1)-p);
            mat[n-1][i]=val;
      }
      mat^=(k);
      mat*=res;
      cout<<mat[0][0]<<"\n";
      cout<<mat[n-1][0]<<"\n";
}
 
 
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