結果

問題 No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率
ユーザー ningenMeningenMe
提出日時 2021-06-11 23:51:21
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 246 ms / 2,000 ms
コード長 9,401 bytes
コンパイル時間 2,560 ms
コンパイル使用メモリ 205,924 KB
最終ジャッジ日時 2025-01-22 07:17:05
ジャッジサーバーID
（参考情報） 		judge2 / 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
other AC * 36
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; 
using int128  = __int128_t; 
using int64   = long long; 
using int32   = int; 
using uint128 = __uint128_t; 
using uint64  = unsigned long long; 
using uint32  = unsigned int; 

#define ALL(obj) (obj).begin(),(obj).end() 
template<class T> using priority_queue_reverse = priority_queue<T,vector<T>,greater<T>>; 

constexpr int64 MOD = 1'000'000'000LL + 7; //' 
constexpr int64 MOD2 = 998244353; 
constexpr int64 HIGHINF = 1'000'000'000'000'000'000LL; 
constexpr int64 LOWINF = 1'000'000'000'000'000LL; //' 
constexpr long double PI = 3.1415926535897932384626433L; 

template <class T> vector<T> multivector(size_t N,T init){return vector<T>(N,init);} 
template <class... T> auto multivector(size_t N,T... t){return vector<decltype(multivector(t...))>(N,multivector(t...));} 
template <class T> void corner(bool flg, T hoge) {if (flg) {cout << hoge << endl; exit(0);}} 
template <class T, class U>ostream &operator<<(ostream &o, const map<T, U>&obj) {o << "{"; for (auto &x : obj) o << " {" << x.first << " : " << x.second << "}" << ","; o << " }"; return o;} 
template <class T>ostream &operator<<(ostream &o, const set<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const multiset<T>&obj) {o << "{"; for (auto itr = obj.begin(); itr != obj.end(); ++itr) o << (itr != obj.begin() ? ", " : "") << *itr; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const vector<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} 
template <class T>ostream &operator<<(ostream &o, const deque<T>&obj) {o << "{"; for (int i = 0; i < (int)obj.size(); ++i)o << (i > 0 ? ", " : "") << obj[i]; o << "}"; return o;} 
template <class T, class U>ostream &operator<<(ostream &o, const pair<T, U>&obj) {o << "{" << obj.first << ", " << obj.second << "}"; return o;} 
void print(void) {cout << endl;} 
template <class Head> void print(Head&& head) {cout << head;print();} 
template <class Head, class... Tail> void print(Head&& head, Tail&&... tail) {cout << head << " ";print(forward<Tail>(tail)...);} 
template <class T> void chmax(T& a, const T b){a=max(a,b);} 
template <class T> void chmin(T& a, const T b){a=min(a,b);} 
vector<string> split(const string &str, const char delemiter) {vector<string> res;stringstream ss(str);string buffer; while( getline(ss, buffer, delemiter) ) res.push_back(buffer); return res;} 
inline constexpr int msb(int x) {return x?31-__builtin_clz(x):-1;} 
inline constexpr int64 ceil_div(const int64 a,const int64 b) {return (a+(b-1))/b;}// return ceil(a/b) 
void YN(bool flg) {cout << (flg ? "YES" : "NO") << endl;} 
void Yn(bool flg) {cout << (flg ? "Yes" : "No") << endl;} 
void yn(bool flg) {cout << (flg ? "yes" : "no") << endl;} 

/*
 * @title ModInt
 * @docs md/util/ModInt.md
 */
template<long long mod> class ModInt {
public:
    long long x;
    constexpr ModInt():x(0) {}
    constexpr 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 long long y) {ModInt p(y);if((x += p.x) >= mod) x -= mod;return *this;}
    ModInt &operator+=(const int y) {ModInt p(y);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 long long y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
    ModInt &operator-=(const int y) {ModInt p(y);if((x += mod - p.x) >= mod) x -= mod;return *this;}
    ModInt &operator*=(const ModInt &p) {x = (x * p.x % mod);return *this;}
    ModInt &operator*=(const long long y) {ModInt p(y);x = (x * p.x % mod);return *this;}
    ModInt &operator*=(const int y) {ModInt p(y);x = (x * p.x % mod);return *this;}
    ModInt &operator^=(const ModInt &p) {x = (x ^ p.x) % mod;return *this;}
    ModInt &operator^=(const long long y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
    ModInt &operator^=(const int y) {ModInt p(y);x = (x ^ p.x) % mod;return *this;}
    ModInt &operator/=(const ModInt &p) {*this *= p.inv();return *this;}
    ModInt &operator/=(const long long y) {ModInt p(y);*this *= p.inv();return *this;}
    ModInt &operator/=(const int y) {ModInt p(y);*this *= p.inv();return *this;}
    ModInt operator=(const int y) {ModInt p(y);*this = p;return *this;}
    ModInt operator=(const long long y) {ModInt p(y);*this = p;return *this;}
    ModInt operator-() const {return ModInt(-x); }
    ModInt operator++() {x++;if(x>=mod) x-=mod;return *this;}
    ModInt operator--() {x--;if(x<0) x+=mod;return *this;}
    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; }
    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 inv() 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);for(;n > 0;mul *= mul,n >>= 1) if(n & 1) ret *= mul;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);}
};
using modint = ModInt<MOD2>;

/*
 * @title Matrix - 行列演算
 * @docs md/math/Matrix.md
 */
template <class T, int H, int W = H> class Matrix {
public:
	int h,w;
	array<array<T,W>,H> a;
	Matrix():h(H),w(W){
		// do nothing
	}
	Matrix(const vector<vector<T>>& vec):h(H),w(W) {
		assert(vec.size()==H && vec.front().size()==W);
		for(int i = 0; i < H; ++i) for(int j = 0; j < W; ++j) a[i][j]=vec[i][j];
	}
	static Matrix E() {
		assert(H==W);
		Matrix res = Matrix();
		for(int i = 0; i < H; ++i) res[i][i]=1;
		return res;
	}
	Matrix &operator+=(const Matrix &r) {
		assert(H==r.h&&W==r.w);
		for(int i = 0; i < H; ++i) for(int j = 0; j < W; ++j) a[i][j]+=r[i][j];
		return *this;
	}
	Matrix &operator-=(const Matrix &r) {
		assert(H==r.h&&W==r.w);
		for(int i = 0; i < H; ++i) for(int j = 0; j < W; ++j) a[i][j]-=r[i][j];
		return *this;
	}
	Matrix &operator*=(const Matrix &r) {
		assert(W==r.h);
		Matrix res = Matrix();
		for(int i = 0; i < H; ++i) for(int j = 0; j < r.w; ++j) for(int k = 0; k < W; ++k) res[i][j]+=(a[i][k])*(r[k][j]);
		a.swap(res.a);
		return *this;
	}
	Matrix operator+(const Matrix& r) const {
		return Matrix(*this) += r;
	}
	Matrix operator-(const Matrix& r) const {
		return Matrix(*this) -= r;
	}
	Matrix operator*(const Matrix& r) const {
		return Matrix(*this) *= r;
	}
	inline array<T,W> &operator[](int i) { 
		return a[i];
	}
	inline const array<T,W> &operator[](int i) const { 
		return a[i];
	}
	Matrix pow(long long K) const {
		assert(H == W);
		Matrix x(*this);
		Matrix res = this->E();
		for (; K > 0; K /= 2) {
			if (K & 1) res *= x;
			x *= x;
		}
		return res;
	}
	T determinant(void) const {
		assert(H==W);
		Matrix x(*this);
		T res = 1;
		for(int i = 0; i < H; i++) {
			int idx = -1;
			for(int j = i; j < W; j++) if(x[j][i] != 0) idx = j;
			if(idx == -1) return 0;
			if(i != idx) {
				res *= -1;
				swap(x[i], x[idx]);
			}
			res *= x[i][i];
			T tmp = x[i][i];
			for(int j = 0; j < W; ++j) x[i][j] /= tmp;
			for(int j = i + 1; j < H; j++) {
				tmp = x[j][i];
				for(int k = 0; k < W; k++) x[j][k] -= x[i][k]*tmp;
			}
		}
		return res;
	}
};

constexpr int M = 120;
using matrix = Matrix<modint,M,M>;
/** 
 * @url  
 * @est 
 */  
int main() { 
    cin.tie(0);ios::sync_with_stdio(false);
    modint ma,na;int s; cin >> ma >> na >> s;
    modint mb,nb;int t; cin >> mb >> nb >> t;
    modint pa = ma/na, qa = (na-ma)/na;
    modint pb = mb/nb, qb = (nb-mb)/nb;
    modint aaa = 0, bbb = 0;
    matrix mta,mtb;
    int K; cin >> K;
    {
        mta[M-1][M-1]=1;
        mta[M-2][M-2]=1;
        mta[M-2][0]=1;
        for(int j=s+t-1; 0<j;--j) {
            mta[s+t][j] = pa.pow(s+t-j);
        }
    }
    for(int i=s+t-1;0<=i;--i) {
        for(int j=i; 0<j;--j) {
            mta[i][j] = pa.pow(abs(i-j))*qa;
        }
    }
    {
        mtb[M-1][M-1]=1;
        mtb[M-1][s+t]=1;
        mtb[M-2][M-2]=1;
        for(int j=1; j<s+t;++j) {
            mtb[0][j] = pb.pow(j);
        }
    }
    for(int i=1;i<s+t;++i) {
        for(int j=i; j<s+t;++j) {
            mtb[i][j] = pb.pow(abs(i-j))*qb;
        }
    }

    // for(int i=0;i<M; ++i) {
    //     for(int j=0;j<M;++j) {
    //         cout << mta[i][j] << " ";
    //     }
    //     cout << endl;
    // }
    // print();
    // for(int i=0;i<M; ++i) {
    //     for(int j=0;j<M;++j) {
    //         cout << mtb[i][j] << " ";
    //     }
    //     cout << endl;
    // }
    // print();

    auto mtc = (mtb * mta).pow(K-1);

    auto mtac = (mta * mtc);
    aaa = mtac[M-1][t] + mtac[s+t][t];
    auto mtbc = (mtb * mtac);
    bbb = mtbc[M-2][t] + mtbc[0][t];
    cout << aaa << "\n" << bbb << "\n";

    return 0; 
}
0