結果

問題 No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率
ユーザー midri1784
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
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ソースコード

diff #
プレゼンテーションモードにする

#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 1000000
inline 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 initializers
template<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 operations
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(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 operations
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 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 identity
res(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 - T
auto v2i = [&](i64 v) {
return v + T;
};
// make XA
XA(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 XB
XB(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 0
REP(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;
}
#endif
matrix X = XB * XA;
#if 0
REP(0, SIZE, i) {
REP(0, SIZE, j) {
cerr << X(i,j).val << " ";
}
cerr << endl;
}
#endif
matrix XP = matpow(X, K);
matrix U(SIZE, 1);
U(v2i(0), 0) = 1;
matrix V = XP * U;
#if 0
REP(0, SIZE, i) {
cerr << U(i,0).val << " ";
}
cerr << endl;
REP(0, SIZE, i) {
cerr << V(i,0).val << " ";
}
cerr << endl;
#endif
WI(V(v2i(S), 0).val);
WI(V(v2i(-T), 0).val);
return 0;
}
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