結果
問題 | No.75 回数の期待値の問題 |
ユーザー |
|
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 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 4 |
other | AC * 16 |
ソースコード
#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)#endiftemplate <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} を加えると \texttt{debug(...)} による出力が有効となる#undef NOTE#line 3 "src/math/ExtGCD.hpp"#define CUTconstexpr 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}`.// 一般解は `(x,y)=(x_0+k\cdot\dfrac{b}{g}, y_0-k\cdot\dfrac{a}{g})\;(k\in\mathbb{Z})` なので、`(x_0,y_0)` は `x` が非負の下で最小の解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 CUTtemplate <class T>struct GaussianElimination {vector<T> sol;vector<vector<T>> bases;// 解が一つも存在しないかどうか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;// 浮動小数点数型のときT max_val = 0;rep(i, k, n) {const auto& v = Ab[i];// 浮動小数点数型のとき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;// 浮動小数点数型のとき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;}