結果

問題 No.75 回数の期待値の問題
ユーザー suisen
提出日時 2022-12-12 03:51:34
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 3 ms / 5,000 ms
コード長 7,484 bytes
コンパイル時間 2,460 ms
コンパイル使用メモリ 209,772 KB
最終ジャッジ日時 2025-02-09 09:57:35
ジャッジサーバーID
(参考情報)
judge5 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 16
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 #
プレゼンテーションモードにする

#line 1 "test/matrix/gaussian_elimination/yuki129.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/system_of_linear_equations"
#line 2 "src/math/Modint.hpp"
#define CUT
#line 2 "src/Template.hpp"
#define CUT
#include <bits/stdc++.h>
using namespace std;
#define rep(i, l, r) for (int i = (l); i < (r); ++i)
#define rrep(i, l, r) for (int i = (r); i --> (l);)
#define all(c) begin(c), end(c)
#ifdef LOCAL
#define debug(...) debug_impl(#__VA_ARGS__, __VA_ARGS__)
template <class H, class... Ts> void debug_impl(string s, H&& h, Ts&&... ts) {
cerr << '(' << s << "): (" << forward<H>(h);
((cerr << ", " << forward<Ts>(ts)), ..., (cerr << ")\n"));
}
#else
#define debug(...) void(0)
#endif
template <class T> bool chmax(T& a, const T& b) { return b > a ? (a = b, true) : false; }
template <class T> bool chmin(T& a, const T& b) { return b < a ? (a = b, true) : false; }
template <class T> istream& operator>>(istream& in, vector<T>& v) {
for (auto& e : v) in >> e;
return in;
}
template <class ...Args> void read(Args&... args) {
(cin >> ... >> args);
}
template <class T> ostream& operator<<(ostream& out, const vector<T>& v) {
int n = v.size();
rep(i, 0, n) {
out << v[i];
if (i + 1 != n) out << ' ';
}
return out;
}
template <class H, class ...Ts> void print(H&& h, Ts &&... ts) {
cout << h, ((cout << ' ' << forward<Ts>(ts)), ..., (cout << '\n'));
}
struct io_setup_ {
io_setup_() {
ios::sync_with_stdio(false), cin.tie(nullptr);
cout << fixed << setprecision(10);
}
} io_setup{};
#undef CUT
#define NOTE compile command: \texttt{g++ -std=gnu++17 -Wall -Wextra -g -fsanitize=address -fsanitize=undefined \$\{file\} -o \$\{fileDirname\}
    /\$\{fileBasenameNoExtension\}}
#undef NOTE
#define NOTE \texttt{-DLOCAL} \texttt{debug(...)}
#undef NOTE
#line 3 "src/math/ExtGCD.hpp"
#define CUT
constexpr long safe_mod(long long x, long long m) {
return (x %= m) < 0 ? x + m : x;
}
// Returns `(x,g)` s.t. `g=\gcd(a,b)`, `xa\equiv g \pmod{b}`, and `0\leq x< \frac{b}{g}`
constexpr pair<long long, long long> inv_gcd(long long a, long long b) {
assert(b > 0);
a = safe_mod(a, b);
if (a == 0) return { 0, b };
long long s = b, t = a, x = 0, y = 1, tmp = 0;
while (t) {
long long u = s / t;
s -= t * u;
x -= y * u;
tmp = s, s = t, t = tmp;
tmp = x, x = y, y = tmp;
}
if (x < 0) x += b / s;
return { x, s };
}
// Returns `x` s.t. `xa\equiv 1 \pmod{m}`.
// Requirement: `\gcd(a, m) = 1`.
constexpr long long inv_mod(long long a, long long m) {
auto [x, g] = inv_gcd(a, m);
assert(g == 1);
return x;
}
// Returns `(x_0,y_0,g)` s.t. `g=\gcd(a,b)`, `ax_0 + by_0 = g`, and `0\leq x_0<\frac{b}{g}`.
// `(x,y)=(x_0+k\cdot\dfrac{b}{g}, y_0-k\cdot\dfrac{a}{g})\;(k\in\mathbb{Z})` `(x_0,y_0)` `x`
constexpr tuple<long long, long long, long long> ext_gcd(long long a, long long b) {
auto [x, g] = inv_gcd(a, b);
return { x, (g - x * a) / b, g };
}
#undef CUT
#line 4 "src/math/Modint.hpp"
constexpr long long pow_mod(long long x, long long b, int m) {
long long p = safe_mod(x, m), r = 1;
for (; b; b >>= 1) {
if (b & 1) (r *= p) %= m;
(p *= p) %= m;
}
return r;
}
template <int mod> struct modint {
unsigned x;
modint(): x(0) {}
modint(long long v): x(safe_mod(v, mod)) {}
int val() const { return x; }
static modint raw(unsigned v) {
modint res;
res.x = v;
return v;
}
modint operator-() const {
return raw(x ? mod - x : 0);
}
modint& operator+=(modint t) {
if ((x += t.x) >= mod) x -= mod;
return *this;
}
modint& operator-=(modint t) {
if ((x += mod - t.x) >= mod) x -= mod;
return *this;
}
modint& operator*=(modint t) {
x = (unsigned long long) x * t.x % mod;
return *this;
}
modint& operator/=(modint t) { return *this *= t.inv(); }
friend modint operator+(modint x, modint y) { return x += y; }
friend modint operator-(modint x, modint y) { return x -= y; }
friend modint operator*(modint x, modint y) { return x *= y; }
friend modint operator/(modint x, modint y) { return x /= y; }
friend bool operator==(modint x, modint y) { return x.x == y.x; }
friend bool operator!=(modint x, modint y) { return x.x != y.x; }
modint inv() const { return inv_mod(x, mod); }
modint pow(long long b) const {
assert(b >= 0);
return pow_mod(x, b, mod);
}
};
#undef CUT
#line 3 "src/matrix/GaussianElimination.hpp"
#define CUT
template <class T>
struct GaussianElimination {
vector<T> sol;
vector<vector<T>> bases;
//
bool empty = false;
GaussianElimination(vector<vector<T>> A, const vector<T>& b) {
int n = A.size();
for (int i = 0; i < n; ++i) A[i].push_back(b[i]);
solve(A);
}
private:
static constexpr bool is_fp = is_floating_point_v<T>;
static bool is_zero(T x) {
if constexpr (is_fp) {
return abs(x) < 1e-9;
} else {
return x == 0;
}
}
void solve(vector<vector<T>>& Ab) {
const int n = Ab.size(), m = Ab[0].size() - 1;
auto pivoting = [&](int l, int k) {
int pos = m, res = n;
//
T max_val = 0;
rep(i, k, n) {
const auto& v = Ab[i];
//
if constexpr (is_fp) {
if (pos < m and abs(v[pos]) > max_val) {
res = i, max_val = abs(v[pos]);
}
}
rep(j, l, pos) {
if (not is_zero(Ab[k][j])) {
pos = j, res = i;
//
if constexpr (is_fp) {
max_val = abs(Ab[i][j]);
}
break;
}
}
}
return pair{ pos, res };
};
int l = 0;
rep(i, 0, n) {
auto [mse, k] = pivoting(l, i);
l = mse + 1;
if (k == n) break;
Ab[i].swap(Ab[k]);
T cinv = T{ 1 } / Ab[i][mse];
rep(row, i + 1, n) if (not is_zero(Ab[row][mse])) {
T c = Ab[row][mse] * cinv;
rep(col, mse, m + 1) Ab[row][col] -= c * Ab[i][col];
}
}
int basis_num = m;
vector<int8_t> down(m);
sol.assign(m, T{0});
rrep(i, 0, n) {
int mse = m + 1;
rep(col, 0, m + 1) if (not is_zero(Ab[i][col])) {
mse = col;
break;
}
if (mse < m) {
T cinv = T{ 1 } / Ab[i][mse];
rep(row, 0, i) if (not is_zero(Ab[row][mse])) {
T c = Ab[row][mse] * cinv;
rep(col, mse, m + 1) Ab[row][col] -= c * Ab[i][col];
}
rep(col, mse, m + 1) Ab[i][col] *= cinv;
sol[mse] = Ab[i][m];
down[mse] = true;
--basis_num;
} else if (mse == m) {
empty = true;
return;
}
}
bases.assign(basis_num, vector<T>(m));
int id = 0;
rep(j, 0, m) if (not down[j]) {
int i = 0;
rep(j2, 0, m) bases[id][j2] = down[j2] ? Ab[i++][j] : 0;
bases[id++][j] = -1;
}
}
};
#undef CUT
#line 5 "test/matrix/gaussian_elimination/yuki129.test.cpp"
int main() {
int k;
read(k);
vector A(k, vector<double>(k));
vector<double> b(k, 1);
rep(i, 0, k) {
rep(v, 1, 7) {
if (i + v == k) {
} else {
int j = i + v;
if (j > k) j = 0;
A[i][j] -= 1. / 6.;
}
}
A[i][i] += 1;
}
GaussianElimination<double> gauss(A, b);
print(gauss.sol[0]);
return 0;
}
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