結果

問題 No.813 ユキちゃんの冒険
ユーザー ecotteaecottea
提出日時 2023-06-07 22:37:22
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 1,247 ms / 2,000 ms
コード長 15,768 bytes
コンパイル時間 4,372 ms
コンパイル使用メモリ 258,328 KB
最終ジャッジ日時 2025-02-13 23:17:38
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 * 26
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#ifndef HIDDEN_IN_VS //
//
#define _CRT_SECURE_NO_WARNINGS
//
#include <bits/stdc++.h>
using namespace std;
//
using ll = long long; // -2^63 2^63 = 9 * 10^18int -2^31 2^31 = 2 * 10^9
using pii = pair<int, int>; using pll = pair<ll, ll>; using pil = pair<int, ll>; using pli = pair<ll, int>;
using vi = vector<int>; using vvi = vector<vi>; using vvvi = vector<vvi>;
using vl = vector<ll>; using vvl = vector<vl>; using vvvl = vector<vvl>;
using vb = vector<bool>; using vvb = vector<vb>; using vvvb = vector<vvb>;
using vc = vector<char>; using vvc = vector<vc>; using vvvc = vector<vvc>;
using vd = vector<double>; using vvd = vector<vd>; using vvvd = vector<vvd>;
template <class T> using priority_queue_rev = priority_queue<T, vector<T>, greater<T>>;
using Graph = vvi;
//
const double PI = acos(-1);
const vi DX = { 1, 0, -1, 0 }; // 4
const vi DY = { 0, 1, 0, -1 };
int INF = 1001001001; ll INFL = 4004004004004004004LL;
double EPS = 1e-15;
//
struct fast_io { fast_io() { cin.tie(nullptr); ios::sync_with_stdio(false); cout << fixed << setprecision(18); } } fastIOtmp;
//
#define all(a) (a).begin(), (a).end()
#define sz(x) ((int)(x).size())
#define lbpos(a, x) (int)distance((a).begin(), std::lower_bound(all(a), x))
#define ubpos(a, x) (int)distance((a).begin(), std::upper_bound(all(a), x))
#define Yes(b) {cout << ((b) ? "Yes\n" : "No\n");}
#define YES(b) {cout << ((b) ? "YES\n" : "NO\n");}
#define rep(i, n) for(int i = 0, i##_len = int(n); i < i##_len; ++i) // 0 n-1
#define repi(i, s, t) for(int i = int(s), i##_end = int(t); i <= i##_end; ++i) // s t
#define repir(i, s, t) for(int i = int(s), i##_end = int(t); i >= i##_end; --i) // s t
#define repe(v, a) for(const auto& v : (a)) // a
#define repea(v, a) for(auto& v : (a)) // a
#define repb(set, d) for(int set = 0; set < (1 << int(d)); ++set) // d
#define repp(a) sort(all(a)); for(bool a##_perm = true; a##_perm; a##_perm = next_permutation(all(a))) // a
#define smod(n, m) ((((n) % (m)) + (m)) % (m)) // mod
#define uniq(a) {sort(all(a)); (a).erase(unique(all(a)), (a).end());} //
#define EXIT(a) {cout << (a) << endl; exit(0);} //
//
template <class T> inline ll pow(T n, int k) { ll v = 1; rep(i, k) v *= n; return v; }
template <class T> inline bool chmax(T& M, const T& x) { if (M < x) { M = x; return true; } return false; } // true
    
template <class T> inline bool chmin(T& m, const T& x) { if (m > x) { m = x; return true; } return false; } // true
    
template <class T> inline T get(T set, int i) { return (set >> i) & T(1); }
//
template <class T, class U> inline istream& operator>>(istream& is, pair<T, U>& p) { is >> p.first >> p.second; return is; }
template <class T> inline istream& operator>>(istream& is, vector<T>& v) { repea(x, v) is >> x; return is; }
template <class T> inline vector<T>& operator--(vector<T>& v) { repea(x, v) --x; return v; }
template <class T> inline vector<T>& operator++(vector<T>& v) { repea(x, v) ++x; return v; }
#endif //
#if __has_include(<atcoder/all>)
#include <atcoder/all>
using namespace atcoder;
#ifdef _MSC_VER
#include "localACL.hpp"
#endif
using mint = modint1000000007;
//using mint = modint998244353;
//using mint = modint; // mint::set_mod(m);
namespace atcoder {
inline istream& operator>>(istream& is, mint& x) { ll x_; is >> x_; x = x_; return is; }
inline ostream& operator<<(ostream& os, const mint& x) { os << x.val(); return os; }
}
using vm = vector<mint>; using vvm = vector<vm>; using vvvm = vector<vvm>;
#endif
#ifdef _MSC_VER // Visual Studio
#include "local.hpp"
#else // gcc
inline int popcount(int n) { return __builtin_popcount(n); }
inline int popcount(ll n) { return __builtin_popcountll(n); }
inline int lsb(int n) { return n != 0 ? __builtin_ctz(n) : -1; }
inline int lsb(ll n) { return n != 0 ? __builtin_ctzll(n) : -1; }
inline int msb(int n) { return n != 0 ? (31 - __builtin_clz(n)) : -1; }
inline int msb(ll n) { return n != 0 ? (63 - __builtin_clzll(n)) : -1; }
#define gcd __gcd
#define dump(...)
#define dumpel(v)
#define dump_list(v)
#define dump_mat(v)
#define input_from_file(f)
#define output_to_file(f)
#define Assert(b) { if (!(b)) while (1) cout << "OLE"; }
#endif
void WA() {
int n; double p, q;
cin >> n >> p >> q;
double res = 0;
for (int k = 1; k <= 23; k += 2) {
repb(set, k) {
int x = 0, d = 1;
rep(i, k) {
if (get(set, i)) {
d *= -1;
}
else {
x += d;
}
if (x == n || (i != k - 1 && x == 0)) {
x = n;
break;
}
}
double prob = 1;
rep(i, k) prob *= get(set, i) ? p : q;
if (k < 23) {
res += prob * (x == 0);
}
else {
res += prob * (n - x) / n;
}
}
}
cout << res << endl;
}
//
/*
* Matrix<T>(int n, int m) : O(n m)
* n×m
*
* Matrix<T>(int n) : O(n^2)
* n×n
*
* Matrix<T>(vvT a) : O(n m)
* a[0..n)[0..m)
*
* bool empty() : O(1)
*
*
* A + B : O(n m)
* n×m A, B += 使
*
* A - B : O(n m)
* n×m A, B -= 使
*
* c * A A * c : O(n m)
* n×m A c *= 使
*
* A * x : O(n m)
* n×m A n x
*
* x * A : O(n m)
* m x n×m A
*
* A * B : O(n m l)
* n×m A m×l B
*
* Mat pow(ll d) : O(n^3 log d)
* d
*/
template <class T>
struct Matrix {
int n, m; // n m
vector<vector<T>> v; //
// n×m
Matrix(int n, int m) : n(n), m(m), v(n, vector<T>(m)) {}
// n×n
Matrix(int n) : n(n), m(n), v(n, vector<T>(n)) { rep(i, n) v[i][i] = T(1); }
// a[0..n)[0..m)
Matrix(const vector<vector<T>>& a) : n(sz(a)), m(sz(a[0])), v(a) {}
Matrix() : n(0), m(0) {}
//
Matrix(const Matrix&) = default;
Matrix& operator=(const Matrix&) = default;
//
inline vector<T> const& operator[](int i) const { return v[i]; }
inline vector<T>& operator[](int i) {
// verify : https://judge.yosupo.jp/problem/matrix_product
// inline [] v[]
return v[i];
}
//
friend istream& operator>>(istream& is, Matrix& a) {
rep(i, a.n) rep(j, a.m) is >> a.v[i][j];
return is;
}
//
bool empty() { return min(n, m) == 0; }
//
bool operator==(const Matrix& b) const { return n == b.n && m == b.m && v == b.v; }
bool operator!=(const Matrix& b) const { return !(*this == b); }
//
Matrix& operator+=(const Matrix& b) {
rep(i, n) rep(j, m) v[i][j] += b[i][j];
return *this;
}
Matrix& operator-=(const Matrix& b) {
rep(i, n) rep(j, m) v[i][j] -= b[i][j];
return *this;
}
Matrix& operator*=(const T& c) {
rep(i, n) rep(j, m) v[i][j] *= c;
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 T& c) const { return Matrix(*this) *= c; }
friend Matrix operator*(const T& c, const Matrix<T>& a) { return a * c; }
Matrix operator-() const { return Matrix(*this) *= T(-1); }
// : O(m n)
vector<T> operator*(const vector<T>& x) const {
vector<T> y(n);
rep(i, n) rep(j, m) y[i] += v[i][j] * x[j];
return y;
}
// : O(m n)
friend vector<T> operator*(const vector<T>& x, const Matrix& a) {
vector<T> y(a.m);
rep(i, a.n) rep(j, a.m) y[j] += x[i] * a[i][j];
return y;
}
// O(n^3)
Matrix operator*(const Matrix& b) const {
// verify : https://judge.yosupo.jp/problem/matrix_product
Matrix res(n, b.m);
rep(i, res.n) rep(j, res.m) rep(k, m) res[i][j] += v[i][k] * b[k][j];
return res;
}
Matrix& operator*=(const Matrix& b) { *this = *this * b; return *this; }
// O(n^3 log d)
Matrix pow(ll d) const {
Matrix res(n), pow2 = *this;
while (d > 0) {
if (d & 1) res *= pow2;
pow2 *= pow2;
d /= 2;
}
return res;
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Matrix& a) {
rep(i, a.n) {
os << "[";
rep(j, a.m) os << a[i][j] << " ]"[j == a.m - 1];
if (i < a.n - 1) os << "\n";
}
return os;
}
#endif
};
//O(n m min(n, m))
/*
* n×m A n b
* A x = b x0m
* A x = 0 m xs
*/
template <class T>
vector<T> gauss_jordan_elimination(const Matrix<T>& A, const vector<T>& b, vector<vector<T>>* xs = nullptr) {
// verify : https://judge.yosupo.jp/problem/system_of_linear_equations
int n = A.n, m = A.m;
// v : (A | b)
vector<vector<T>> v(n, vector<T>(m + 1));
rep(i, n) rep(j, m) v[i][j] = A[i][j];
rep(i, n) v[i][m] = b[i];
// pivots[i] : i
vi pivots;
//
int pi = -1, pj = -1;
// v[i][j]
int i = 0, j = 0;
while (i < n && j <= m) {
// 0
int i2 = i;
while (i2 < n && v[i2][j] == 0) i2++;
//
if (i2 == n) {
j++;
continue;
}
// i
pi = i; pj = j;
if (i != i2) swap(v[i], v[i2]);
// v[i][j]
pivots.push_back(j);
// v[i][j] 1 i v[i][j]
T vij_inv = T(1) / v[i][j];
repi(j2, j, m) v[i][j2] *= vij_inv;
// i j 0 i
rep(i2, n) {
if (v[i2][j] == T(0) || i2 == i) continue;
T mul = v[i2][j];
repi(j2, j, m) v[i2][j2] -= v[i][j2] * mul;
}
//
i++; j++;
}
// m
if (pivots.back() == m) return vector<T>();
// A x = b x0 0
vector<T> x0(m);
int rnk = sz(pivots);
rep(i, rnk) x0[pivots[i]] = v[i][m];
// A x = 0 {x} 1-hot
if (xs != nullptr) {
xs->clear();
int i = 0;
rep(j, m) {
if (i < rnk && j == pivots[i]) {
i++;
continue;
}
vector<T> x(m, T(0));
x[j] = 1;
rep(i2, i) x[pivots[i2]] = -v[i2][j];
xs->emplace_back(move(x));
}
}
return x0;
}
//
/*
* Random_walk<T>(int n) : O(1)
* n 0
*
* add_edge(int s, int t, T prob) : O(1)
* s→t prob
* s Σs→t p[s][t] = 1
*
* vT arrive_probability_to(int GL) : O(n^3)
* GL
*
* vT expected_turn_to(int GL) : O(n^3)
* GL
* GL
*
* vT stationary_distribution() : O(n^3)
*
*
*
*
*/
template <class T>
class Random_walk {
int n;
// p[i][j] : i j
vector<vector<T>> p;
public:
// n 0
Random_walk(int n) : n(n), p(n, vector<T>(n)) {
}
Random_walk() : n(0) {}
// s→t prob
void add_edge(int s, int t, T prob) {
p[s][t] += prob;
}
// GL
vector<T> arrive_probability_to(int GL) {
//
// s GL x[s]
// x[s] = Σs→t p[s][t] x[t] (s ≠ GL)
// x[GL] = 1
//
// (1 - p[s][s])x[s] - Σs→t,t≠s p[s][t] x[t] = 0
// x[GL] = 1
//
Matrix<T> mat(n); vector<T> vec(n);
rep(i, n) rep(j, n) if (i != GL) mat[i][j] -= p[i][j];
vec[GL] = 1;
return gauss_jordan_elimination(mat, vec);
}
// GL
vector<T> expected_turn_to(int GL) {
//
// s→GL e[s]
// e[s] = 1 + Σs→t p[s][t] e[t] (s ≠ GL)
// e[GL] = 0
//
// (1 - p[s][s])e[s] - Σs→t,t≠s p[s][t] e[t] = 1
// e[GL] = 0
//
Matrix<T> mat(n); vector<T> vec(n, 1);
rep(i, n) rep(j, n) if (i != GL) mat[i][j] -= p[i][j];
vec[GL] = 0;
return gauss_jordan_elimination(mat, vec);
}
//
vector<T> stationary_distribution() {
//
// π[0..n)
// π[t] = Σs→t p[s][t] π[s]
// Σπ[0..n) = 1
//
// (1 - p[t][t])π[t] - Σs→t,t≠s p[s][t] π[s] = 0
// Σπ[0..n) = 1
//
Matrix<T> mat(n); vector<T> vec(n);
rep(i, n - 1) rep(j, n) mat[i][j] -= p[j][i];
rep(j, n) mat[n - 1][j] = 1;
vec[n - 1] = 1;
return gauss_jordan_elimination(mat, vec);
}
#ifdef _MSC_VER
friend ostream& operator<<(ostream& os, const Random_walk& rw) {
rep(i, rw.n) {
rep(j, rw.n) os << rw.p[i][j] << " ";
os << endl;
}
return os;
}
#endif
};
void check_Random_walk() {
Random_walk<double> RW(4);
RW.add_edge(0, 1, 0.5);
RW.add_edge(0, 0, 0.5);
RW.add_edge(1, 2, 1);
RW.add_edge(2, 3, 1);
RW.add_edge(3, 0, 1);
dump(RW.expected_turn_to(3)); // 4 2 1 0
dump(RW.arrive_probability_to(3)); // 1 1 1 1
dump(RW.stationary_distribution()); // 0.4 0.2 0.2 0.2
exit(0);
}
int main() {
// input_from_file("input.txt");
// output_to_file("output.txt");
// check_Random_walk();
int n; double p, q;
cin >> n >> p >> q;
int DEATH = 2 * (n + 1);
Random_walk<double> g(DEATH + 1);
repi(i, 0, n - 1) {
g.add_edge(2 * i + 0, 2 * i + 1, p);
g.add_edge(2 * i + 0, 2 * (i + 1) + 0, q);
g.add_edge(2 * i + 0, DEATH, 1 - p - q);
}
g.add_edge(2 * n + 0, DEATH, 1);
repi(i, 1, n) {
g.add_edge(2 * i + 1, 2 * i + 0, p);
g.add_edge(2 * i + 1, 2 * (i - 1) + 1, q);
g.add_edge(2 * i + 1, DEATH, 1 - p - q);
}
g.add_edge(2 * 0 + 1, DEATH, 1);
g.add_edge(DEATH, DEATH, 1);
// dump(g);
auto res = g.arrive_probability_to(2 * 0 + 1);
dump(res);
cout << res[2 * 0 + 0] << endl;
}
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