結果

問題 No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率
ユーザー FF256grhyFF256grhy
提出日時 2021-06-12 00:00:02
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
WA  
実行時間 -
コード長 8,929 bytes
コンパイル時間 2,809 ms
コンパイル使用メモリ 218,364 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-05-08 20:42:53
合計ジャッジ時間 13,287 ms
ジャッジサーバーID
（参考情報） 		judge1 / judge2
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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 WA -
testcase_01 WA -
testcase_02 WA -
testcase_03 WA -
testcase_04 RE -
testcase_05 RE -
testcase_06 WA -
testcase_07 WA -
testcase_08 WA -
testcase_09 RE -
testcase_10 WA -
testcase_11 RE -
testcase_12 WA -
testcase_13 RE -
testcase_14 RE -
testcase_15 WA -
testcase_16 WA -
testcase_17 WA -
testcase_18 WA -
testcase_19 RE -
testcase_20 WA -
testcase_21 RE -
testcase_22 WA -
testcase_23 RE -
testcase_24 RE -
testcase_25 RE -
testcase_26 RE -
testcase_27 RE -
testcase_28 RE -
testcase_29 RE -
testcase_30 RE -
testcase_31 RE -
testcase_32 RE -
testcase_33 RE -
testcase_34 RE -
testcase_35 RE -
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 LL = long long int;
#define incII(i, l, r) for(LL i = (l)    ; i <= (r); i++)
#define incIX(i, l, r) for(LL i = (l)    ; i <  (r); i++)
#define incXI(i, l, r) for(LL i = (l) + 1; i <= (r); i++)
#define incXX(i, l, r) for(LL i = (l) + 1; i <  (r); i++)
#define decII(i, l, r) for(LL i = (r)    ; i >= (l); i--)
#define decIX(i, l, r) for(LL i = (r) - 1; i >= (l); i--)
#define decXI(i, l, r) for(LL i = (r)    ; i >  (l); i--)
#define decXX(i, l, r) for(LL i = (r) - 1; i >  (l); i--)
#define inc(i, n)  incIX(i, 0, n)
#define dec(i, n)  decIX(i, 0, n)
#define inc1(i, n) incII(i, 1, n)
#define dec1(i, n) decII(i, 1, n)
auto inII = [](auto x, auto l, auto r) { return (l <= x && x <= r); };
auto inIX = [](auto x, auto l, auto r) { return (l <= x && x <  r); };
auto inXI = [](auto x, auto l, auto r) { return (l <  x && x <= r); };
auto inXX = [](auto x, auto l, auto r) { return (l <  x && x <  r); };
auto setmin   = [](auto & a, auto b) { return (b <  a ? a = b, true : false); };
auto setmax   = [](auto & a, auto b) { return (b >  a ? a = b, true : false); };
auto setmineq = [](auto & a, auto b) { return (b <= a ? a = b, true : false); };
auto setmaxeq = [](auto & a, auto b) { return (b >= a ? a = b, true : false); };
#define PB push_back
#define EB emplace_back
#define MP make_pair
#define MT make_tuple
#define FI first
#define SE second
#define FR front()
#define BA back()
#define ALL(c) c.begin(), c.end()
#define RALL(c) c.rbegin(), c.rend()
#define RV(c) reverse(ALL(c))
#define SC static_cast
#define SI(c) SC<int>(c.size())
#define SL(c) SC<LL >(c.size())
#define RF(e, c) for(auto & e: c)
#define SF(c, ...) for(auto & [__VA_ARGS__]: c)
#define until(e) while(! (e))
#define if_not(e) if(! (e))
#define ef else if
#define UR assert(false)
auto * IS = & cin;
auto * OS = & cout;
array<string, 3> SEQ = { "", " ", "" };
// input
template<typename T> T in() { T a; (* IS) >> a; return a; }
// input: tuple
template<int I, typename U> void tin_(istream & is, U & t) {
	if constexpr(I < tuple_size<U>::value) { is >> get<I>(t); tin_<I + 1>(is, t); }
}
template<typename ... T> istream & operator>>(istream & is, tuple<T ...> & t) { tin_<0>(is, t); return is; }
template<typename ... T> auto tin() { return in<tuple<T ...>>(); }
// input: array
template<typename T, size_t N> istream & operator>>(istream & is, array<T, N> & a) { RF(e, a) { is >> e; } return is; }
template<typename T, size_t N> auto ain() { return in<array<T, N>>(); }
// input: multi-dimensional vector
template<typename T> T vin() { T v; (* IS) >> v; return v; }
template<typename T, typename N, typename ... M> auto vin(N n, M ... m) {
	vector<decltype(vin<T, M ...>(m ...))> v(n); inc(i, n) { v[i] = vin<T, M ...>(m ...); } return v;
}
// input: multi-column (tuple<vector>)
template<typename U, int I> void colin_([[maybe_unused]] U & t) { }
template<typename U, int I, typename A, typename ... B> void colin_(U & t) {
	get<I>(t).PB(in<A>()); colin_<U, I + 1, B ...>(t);
}
template<typename ... T> auto colin(int n) {
	tuple<vector<T> ...> t; inc(i, n) { colin_<tuple<vector<T> ...>, 0, T ...>(t); } return t;
}
// output
void out_([[maybe_unused]] string s) { }
template<typename A> void out_([[maybe_unused]] string s, A && a) { (* OS) << a; }
template<typename A, typename ... B> void out_(string s, A && a, B && ... b) { (* OS) << a << s; out_(s, b ...); }
auto outF = [](auto x, auto y, auto z, auto ... a) { (* OS) << x; out_(y, a ...); (* OS) << z << flush; };
auto out  = [](auto ... a) { outF("", " " , "\n", a ...); };
auto outS = [](auto ... a) { outF("", " " , " " , a ...); };
auto outL = [](auto ... a) { outF("", "\n", "\n", a ...); };
auto outN = [](auto ... a) { outF("", ""  , ""  , a ...); };
// output: multi-dimensional vector
template<typename T> ostream & operator<<(ostream & os, vector<T> const & v) {
	os << SEQ[0]; inc(i, SI(v)) { os << (i == 0 ? "" : SEQ[1]) << v[i]; } return (os << SEQ[2]);
}
template<typename T> void vout_(T && v) { (* OS) << v; }
template<typename T, typename A, typename ... B> void vout_(T && v, A a, B ... b) {
	inc(i, SI(v)) { (* OS) << (i == 0 ? "" : a); vout_(v[i], b ...); }
}
template<typename T, typename A, typename ... B> void vout (T && v, A a, B ... b) { vout_(v, a, b ...); (* OS) << a << flush; }
template<typename T, typename A, typename ... B> void voutN(T && v, A a, B ... b) { vout_(v, a, b ...); (* OS)      << flush; }

// ---- ----

template<typename T, T(* PLUS)(T, T), T(* MULT)(T, T), T(* ZERO)(), T(* UNIT)()> struct Matrix_ {
	int h, w;
	vector<vector<T>> v;
	explicit Matrix_(int h = 1):    h(h), w(h), v(h, vector<T>(w, ZERO())) { }
	explicit Matrix_(int h, int w): h(h), w(w), v(h, vector<T>(w, ZERO())) { }
	Matrix_(vector<vector<T>> const & v): h(SI(v)), w(SI(v[0])), v(v) {
		inc(i, h) { assert(SI(v[i]) == w); }
	}
	vector<T> const & operator[](int i) const { return v.at(i); }
	vector<T>       & operator[](int i)       { return v.at(i); }
	static Matrix_ unit(int n) {
		Matrix_ a(n);
		inc(i, n) { a[i][i] = UNIT(); }
		return a;
	}
	friend Matrix_ operator*(Matrix_ const & a, Matrix_ const & b) {
		assert(a.w == b.h);
		Matrix_ c(a.h, b.w);
		inc(i, a.h) {
		inc(j, b.w) {
		inc(k, a.w) {
			c[i][j] = PLUS(c[i][j], MULT(a[i][k], b[k][j]));
		}
		}
		}
		return c;
	}
	friend Matrix_ operator^(Matrix_ a, LL b) {
		assert(a.h == a.w);
		assert(b >= 0);
		auto p = Matrix_::unit(a.h);
		while(b) {
			if(b & 1) { p *= a; }
			a *= a;
			b >>= 1;
		}
		return p;
	}
	friend Matrix_ & operator*=(Matrix_ & a, Matrix_ const & b) { return (a = a * b); }
	friend Matrix_ & operator^=(Matrix_ & a, LL              b) { return (a = a ^ b); }
	friend Matrix_ & operator*=(Matrix_ & a, T b) {
		inc(i, a.h) {
		inc(j, a.w) {
			a[i][j] = MULT(a[i][j], b);
		}
		}
		return a;
	}
	friend Matrix_ operator*(Matrix_ a, T b) { return (a *= b); }
	friend Matrix_ operator*(T b, Matrix_ a) { return (a *= b); }
	friend ostream & operator<<(ostream & s, Matrix_ const & a) {
		inc(i, a.h) { s << a[i] << endl; }
		return s;
	}
};
template<typename T> T PLUS(T a, T b) { return a + b; };
template<typename T> T MULT(T a, T b) { return a * b; };
template<typename T> T ZERO() { return 0; };
template<typename T> T UNIT() { return 1; };
template<typename T> using Matrix = Matrix_<T, PLUS<T>, MULT<T>, ZERO<T>, UNIT<T>>;

// ----

template<LL M> class ModInt {
private:
	LL v;
	pair<LL, LL> ext_gcd(LL a, LL b) {
		if(b == 0) { assert(a == 1); return { 1, 0 }; }
		auto p = ext_gcd(b, a % b);
		return { p.SE, p.FI - (a / b) * p.SE };
	}
public:
	ModInt(LL vv = 0) { v = vv; if(abs(v) >= M) { v %= M; } if(v < 0) { v += M; } }
	LL val() { return v; }
	static LL mod() { return M; }
	ModInt inv() { return ext_gcd(M, v).SE; }
	ModInt exp(LL b) {
		ModInt p = 1, a = v; if(b < 0) { a = a.inv(); b = -b; }
		while(b) { if(b & 1) { p *= a; } a *= a; b >>= 1; }
		return p;
	}
	friend bool      operator< (ModInt    a, ModInt   b) { return (a.v <  b.v); }
	friend bool      operator> (ModInt    a, ModInt   b) { return (a.v >  b.v); }
	friend bool      operator<=(ModInt    a, ModInt   b) { return (a.v <= b.v); }
	friend bool      operator>=(ModInt    a, ModInt   b) { return (a.v >= b.v); }
	friend bool      operator==(ModInt    a, ModInt   b) { return (a.v == b.v); }
	friend bool      operator!=(ModInt    a, ModInt   b) { return (a.v != b.v); }
	friend ModInt    operator+ (ModInt    a            ) { return ModInt(+a.v); }
	friend ModInt    operator- (ModInt    a            ) { return ModInt(-a.v); }
	friend ModInt    operator+ (ModInt    a, ModInt   b) { return ModInt(a.v + b.v); }
	friend ModInt    operator- (ModInt    a, ModInt   b) { return ModInt(a.v - b.v); }
	friend ModInt    operator* (ModInt    a, ModInt   b) { return ModInt(a.v * b.v); }
	friend ModInt    operator/ (ModInt    a, ModInt   b) { return a * b.inv(); }
	friend ModInt    operator^ (ModInt    a, LL       b) { return a.exp(b); }
	friend ModInt  & operator+=(ModInt  & a, ModInt   b) { return (a = a + b); }
	friend ModInt  & operator-=(ModInt  & a, ModInt   b) { return (a = a - b); }
	friend ModInt  & operator*=(ModInt  & a, ModInt   b) { return (a = a * b); }
	friend ModInt  & operator/=(ModInt  & a, ModInt   b) { return (a = a / b); }
	friend ModInt  & operator^=(ModInt  & a, LL       b) { return (a = a ^ b); }
	friend istream & operator>>(istream & s, ModInt & b) { s >> b.v; b = ModInt(b.v); return s; }
	friend ostream & operator<<(ostream & s, ModInt   b) { return (s << b.v); }
};

// ----

using MI = ModInt<998244353>;

int main() {
	auto [ma, na, s, mb, nb, t, k] = tin<MI, MI, int, MI, MI, int, int>();
	MI pa = ma / na;
	MI pb = mb / nb;
	
	Matrix<MI> A(t + 1 + s), B = A;
	incII(i, 1, t + s) {
		A[i][i] = 1 - pa;
		A[i][i + 1] = pa;
	}
	A[t + s][t + s] = 1;
	incII(i, 1, t + s) {
		B[i][i] = 1 - pb;
		B[i][i - 1] = pb;
	}
	B[0][0] = 1;
	outL(A, B, A * B);
	
	auto ans = (A * B) ^ k;
	outL(ans[t][0], ans[t][t + s]);
}
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