結果
問題 | No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率 |
ユーザー |
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提出日時 | 2021-06-11 23:53:25 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 217 ms / 2,000 ms |
コード長 | 7,915 bytes |
コンパイル時間 | 2,151 ms |
コンパイル使用メモリ | 208,316 KB |
最終ジャッジ日時 | 2025-01-22 07:19:55 |
ジャッジサーバーID (参考情報) |
judge2 / judge5 |
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ファイルパターン | 結果 |
---|---|
other | AC * 36 |
ソースコード
#include <bits/stdc++.h>using namespace std;typedef long long i64;typedef unsigned long long ui64;typedef vector<i64> vi;typedef vector<vi> vvi;typedef pair<i64, i64> pi;#define pb push_back#define sz(a) i64((a).size())#define all(c) (c).begin(), (c).end()#define REP(s, e, i) for(i=(s); i < (e); ++i)inline void RI(i64 &i) {scanf("%lld", &(i));}inline void RVI(vi &v) { for(i64 i=0;i<sz(v);++i) { RI(v[i]); } }inline void RVVI(vvi &vv) { for(i64 i=0;i<sz(vv);++i) { RVI(vv[i]); } }inline void WI(const i64 &i) {printf("%lld\n", i);}inline void WVI(const vi &v, char sep=' ') { for(i64 i=0;i<sz(v);++i) { if(i != 0){ printf("%c", sep); } printf("%lld", v[i]);} printf("\n"); }inline void WS(const string &s) { printf("%s\n", s.c_str()); }inline void WB(bool b, const string &yes, const string &no) { if(b){ WS(yes);} else { WS(no);} }inline void YESNO(bool b) { WB(b, "YES", "NO"); }inline void YesNo(bool b) { WB(b, "Yes", "No"); }#define BUF_LENGTH 1000000inline void RS(string &s) {static char buf[BUF_LENGTH]; scanf("%s", buf); s = buf;}template<typename T> inline bool IN(T &S, const typename T::key_type &key) {return S.find(key) != S.end();}template<typename T> inline bool ON(const T &b, i64 idx) {return ((T(1) << idx) & b) != 0;}template<long long M, typename T=long long>struct modint {modint(T v=T(0)) : val((v >= 0 ? v : (M - ((-v) % M))) % M) {}using this_type = modint<M, T>;T val;this_type operator++(int) {this_type ret = *this;val++; val %= M;return ret;}this_type operator--(int) {this_type ret = *this;val += M-1; val %= M;return ret;}this_type &operator++() {val++; val %= M;return *this;}this_type &operator--() {val += M-1; val %= M;return *this;}this_type operator+() const { return *this; }this_type operator-() const { return this_type(M-val); };friend this_type operator+(const this_type &lhs, const this_type &rhs) {return this_type(lhs) += rhs;}friend this_type operator-(const this_type &lhs, const this_type &rhs) {return this_type(lhs) -= rhs;}friend this_type operator*(const this_type &lhs, const this_type &rhs) {return this_type(lhs) *= rhs;}friend this_type operator/(const this_type &lhs, const this_type &rhs) {return this_type(lhs) /= rhs;}this_type pow(long long b) const {this_type ret = 1, a = *this;while(b != 0) {if(b % 2 != 0) {ret *= a;}b /= 2;a = a * a;}return ret;}this_type inv() const {return pow(M-2);}this_type& operator+=(const this_type &rhs) {val += rhs.val; val %= M; return *this;}this_type& operator-=(const this_type &rhs) {val += M - rhs.val; val %= M; return *this;}this_type& operator*=(const this_type &rhs) {val *= rhs.val; val %= M; return *this;}this_type& operator/=(const this_type &rhs) {*this *= rhs.inv(); return *this;}friend bool operator==(const this_type &lhs, const this_type &rhs) {return lhs.val == rhs.val;}friend bool operator!=(const this_type &lhs, const this_type &rhs) {return lhs.val != rhs.val;}T mod() const {return M;}};using mi = modint<998244353>;//using mi = modint<1000000007>;using vmi = vector<mi>;using vvmi = vector<vmi>;// row initializerstemplate<typename T>vector<T> init_row(size_t cols) {return vector<T>(cols, 0);}template<typename T, typename R = vector<T>>class matrix_ {public:using this_type = matrix_<T>;matrix_(size_t rows, size_t cols) {assert(rows > 0 && cols > 0);data.resize(rows, init_row<T>(cols));}matrix_(const vector<R> &values) {assert(!values.empty());data = values;}T& operator()(size_t r, size_t c) {assert(0 <= r && r < rows());assert(0 <= c && c < cols());return data[r][c];}const T& operator()(size_t r, size_t c) const {assert(0 <= r && r < rows());assert(0 <= c && c < cols());return data[r][c];}/////// matrix-matrix operationsthis_type &operator+=(const this_type &rhs) {assert(rows() == rhs.rows() && cols() == rhs.cols());for(size_t r=0;r<rows;++r) { for(size_t c=0;c<cols;++c) {(*this)(r, c) += rhs(r, c);}}return *this;}this_type &operator-=(const this_type &rhs) {assert(rows() == rhs.rows() && cols() == rhs.cols());for(size_t r=0;r<rows;++r) { for(size_t c=0;c<cols;++c) {(*this)(r, c) -= rhs(r, c);}}return *this;}this_type operator*=(const this_type &rhs) {assert(cols() == rhs.rows());this_type res(rows(), rhs.cols());for(size_t r=0;r<rows();++r) { for(size_t c=0;c<rhs.cols(); ++c) {for(size_t i=0;i<cols();++i) {res(r, c) += (*this)(r, i) * rhs(i, c);}}}(*this).swap(res);return *this;}friend this_type operator+(const this_type &lhs, const this_type &rhs) {return this_type(lhs) += rhs;}friend this_type operator-(const this_type &lhs, const this_type &rhs) {return this_type(lhs) -= rhs;}friend this_type operator*(const this_type &lhs, const this_type &rhs) {return this_type(lhs) *= rhs;}/////// matrix-scalar operationsthis_type operator+=(const T &rhs) {for(size_t r=0;r<rows();++r) { for(size_t c=0;c<cols(); ++c) {(*this)(r, c) += rhs;} }return *this;}this_type operator-=(const T &rhs) {(*this) += (-rhs);return *this;}this_type operator*=(const T &rhs) {for(size_t r=0;r<rows();++r) { for(size_t c=0;c<cols(); ++c) {(*this)(r, c) *= rhs;} }return *this;}this_type operator+() const {return *this; }this_type operator-() const {this_type res(data); res *= -1; return res; };size_t rows() const { return data.size(); }size_t cols() const { return data[0].size(); }void swap(this_type &rhs) {data.swap(rhs.data);}private:vector<R> data;};using matrix = matrix_<mi>;matrix matpow(const matrix &a, i64 p) {matrix res(a.rows(), a.cols());for(i64 i=0;i<res.rows();++i) { // set identityres(i, i) = 1;}matrix aa = a;while(p != 0) {if(p % 2 == 1) {res = res * aa;}aa = aa * aa;p /= 2;}return res;}int main(int argc, char *argv[]) {i64 i, j, k;i64 MA, NA, S; cin >> MA >> NA >> S;i64 MB, NB, T; cin >> MB >> NB >> T;i64 K; cin >> K;i64 SIZE = S + T + 1;matrix XA(SIZE, SIZE), XB(SIZE, SIZE);// X = idx - Tauto v2i = [&](i64 v) {return v + T;};// make XAXA(0, 0) = XA(S+T, S+T) = 1;mi PA = mi(MA) * mi(NA).inv();mi RA = 1 - PA;for(i64 v=-T+1;v<S;++v) {XA(v2i(v), v2i(v)) = RA;mi PS = RA;for(i64 u=v+1;u<S;++u) {XA(v2i(u), v2i(v)) = XA(v2i(u-1), v2i(v)) * PA;PS += XA(v2i(u), v2i(v));}XA(v2i(S), v2i(v)) = 1 - PS;}// make XBXB(0, 0) = XB(S+T, S+T) = 1;mi PB = mi(MB) * mi(NB).inv();mi RB = 1 - PB;for(i64 v=-T+1;v<S;++v) {XB(v2i(v), v2i(v)) = RB;mi PS = RB;for(i64 u=v-1;u>-T;--u) {XB(v2i(u), v2i(v)) = XB(v2i(u+1), v2i(v)) * PB;PS += XB(v2i(u), v2i(v));}XB(v2i(-T), v2i(v)) = 1 - PS;}#if 0REP(0, SIZE, i) {REP(0, SIZE, j) {cerr << XA(i,j).val << " ";}cerr << endl;}REP(0, SIZE, i) {REP(0, SIZE, j) {cerr << XB(i,j).val << " ";}cerr << endl;}#endifmatrix X = XB * XA;#if 0REP(0, SIZE, i) {REP(0, SIZE, j) {cerr << X(i,j).val << " ";}cerr << endl;}#endifmatrix XP = matpow(X, K);matrix U(SIZE, 1);U(v2i(0), 0) = 1;matrix V = XP * U;#if 0REP(0, SIZE, i) {cerr << U(i,0).val << " ";}cerr << endl;REP(0, SIZE, i) {cerr << V(i,0).val << " ";}cerr << endl;#endifWI(V(v2i(S), 0).val);WI(V(v2i(-T), 0).val);return 0;}