結果
| 問題 | No.301 サイコロで確率問題 (1) |
| コンテスト | |
| ユーザー |
 iiljj
|
| 提出日時 | 2020-05-22 02:46:40 |
| 言語 | C++17(gcc12) (gcc 12.4.0 + boost 1.89.0) |
| 結果 |
TLE
|
| 実行時間 | - |
| コード長 | 9,437 bytes |
| 記録 | |
| コンパイル時間 | 1,947 ms |
| コンパイル使用メモリ | 231,580 KB |
| 実行使用メモリ | 15,232 KB |
| 最終ジャッジ日時 | 2026-06-10 05:33:31 |
| 合計ジャッジ時間 | 4,317 ms |
|
ジャッジサーバーID （参考情報） |
judge1_1 / judge2_1 |
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| ファイルパターン | 結果 |
|---|---|
| other | AC * 1 TLE * 1 |
ソースコード
/* #region Head */
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using pll = pair<ll, ll>;
template <class T> using vc = vector<T>;
template <class T> using vvc = vc<vc<T>>;
using vll = vc<ll>;
using vvll = vvc<ll>;
using vld = vc<ld>;
using vvld = vvc<ld>;
using vs = vc<string>;
using vvs = vvc<string>;
template <class T, class U> using um = unordered_map<T, U>;
template <class T> using pq = priority_queue<T>;
template <class T> using pqa = priority_queue<T, vc<T>, greater<T>>;
template <class T> using us = unordered_set<T>;
#define REP(i, m, n) for (ll i = (m), i##_len = (ll)(n); i < i##_len; ++(i))
#define REPM(i, m, n) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; ++(i))
#define REPR(i, m, n) for (ll i = (m), i##_min = (ll)(n); i >= i##_min; --(i))
#define REPD(i, m, n, d) for (ll i = (m), i##_len = (ll)(n); i < i##_len; i += (d))
#define REPMD(i, m, n, d) for (ll i = (m), i##_max = (ll)(n); i <= i##_max; i += (d))
#define REPI(itr, ds) for (auto itr = ds.begin(); itr != ds.end(); itr++)
#define ALL(x) begin(x), end(x)
#define SIZE(x) ((ll)(x).size())
#define PERM(c) \
sort(ALL(c)); \
for (bool c##p = 1; c##p; c##p = next_permutation(ALL(c)))
#define UNIQ(v) v.erase(unique(ALL(v)), v.end());
#define endl '\n'
#define sqrt sqrtl
#define floor floorl
#define log2 log2l
constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ld EPS = 1e-12;
constexpr ld PI = 3.14159265358979323846;
template <typename T> istream &operator>>(istream &is, vc<T> &vec) { // vector 入力
for (T &x : vec) is >> x;
return is;
}
template <typename T> ostream &operator<<(ostream &os, vc<T> &vec) { // vector 出力 (for dump)
os << "{";
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "" : ", ");
os << "}";
return os;
}
template <typename T> ostream &operator>>(ostream &os, vc<T> &vec) { // vector 出力 (inline)
REP(i, 0, SIZE(vec)) os << vec[i] << (i == i_len - 1 ? "\n" : " ");
return os;
}
template <typename T, typename U> istream &operator>>(istream &is, pair<T, U> &pair_var) { // pair 入力
is >> pair_var.first >> pair_var.second;
return is;
}
template <typename T, typename U> ostream &operator<<(ostream &os, pair<T, U> &pair_var) { // pair 出力
os << "(" << pair_var.first << ", " << pair_var.second << ")";
return os;
}
// map, um, set, us 出力
template <class T> ostream &out_iter(ostream &os, T &map_var) {
os << "{";
REPI(itr, map_var) {
os << *itr;
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
return os << "}";
}
template <typename T, typename U> ostream &operator<<(ostream &os, map<T, U> &map_var) { return out_iter(os, map_var); }
template <typename T, typename U> ostream &operator<<(ostream &os, um<T, U> &map_var) {
os << "{";
REPI(itr, map_var) {
auto [key, value] = *itr;
os << "(" << key << ", " << value << ")";
auto itrcp = itr;
if (++itrcp != map_var.end()) os << ", ";
}
os << "}";
return os;
}
template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, pq<T> &pq_var) {
pq<T> pq_cp(pq_var);
os << "{";
if (!pq_cp.empty()) {
os << pq_cp.top(), pq_cp.pop();
while (!pq_cp.empty()) os << ", " << pq_cp.top(), pq_cp.pop();
}
return os << "}";
}
// dump
#define DUMPOUT cerr
void dump_func() { DUMPOUT << endl; }
template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) {
DUMPOUT << head;
if (sizeof...(Tail) > 0) DUMPOUT << ", ";
dump_func(move(tail)...);
}
// chmax (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmax(T &xmax, const U &x, Comp comp = {}) {
if (comp(xmax, x)) {
xmax = x;
return true;
}
return false;
}
// chmin (更新「される」かもしれない値が前)
template <typename T, typename U, typename Comp = less<>> bool chmin(T &xmin, const U &x, Comp comp = {}) {
if (comp(x, xmin)) {
xmin = x;
return true;
}
return false;
}
// ローカル用
#define DEBUG_
#ifdef DEBUG_
#define DEB
#define dump(...) \
DUMPOUT << " " << string(#__VA_ARGS__) << ": " \
<< "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \
<< " ", \
dump_func(__VA_ARGS__)
#else
#define DEB if (false)
#define dump(...)
#endif
struct AtCoderInitialize {
static constexpr int IOS_PREC = 15;
static constexpr bool AUTOFLUSH = false;
AtCoderInitialize() {
ios_base::sync_with_stdio(false), cin.tie(nullptr), cout.tie(nullptr);
cout << fixed << setprecision(IOS_PREC);
if (AUTOFLUSH) cout << unitbuf;
}
} ATCODER_INITIALIZE;
string yes = "Yes", no = "No";
// string yes = "YES", no = "NO";
void yn(bool p) { cout << (p ? yes : no) << endl; }
/* #endregion */
/* #region Mat */
// 行列，==, !=, [] あたりは vector と一緒
template <class Num> class Mat : public vc<vc<Num>> {
public:
// using vc<vc<Num>>::vector;
ll h, w;
// コンストラクタ
Mat<Num>() : vc<vc<Num>>(0), h(0), w(0) {}
Mat<Num>(const ll h, ll w) : vc<vc<Num>>(h, vc<Num>(w, 0)), h(h), w(w) {}
Mat<Num>(const Mat<Num> &mt) : vc<vc<Num>>(mt), h(mt.h), w(mt.w) {}
// 行列に別の行列を足す
Mat &operator+=(const Mat &another) {
assert(this->h == another.h && this->w == another.w);
REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] += another[i][j];
return *this;
}
// 行列から別の行列を引く
Mat &operator-=(const Mat &another) {
assert(this->h == another.h && this->w == another.w);
REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] -= another[i][j];
return *this;
}
// 行列に別の行列を右から掛ける
Mat &operator*=(const Mat &another) {
assert(w == another.h);
Mat<Num> ret(this->h, another.w);
REP(i, 0, this->h) REP(j, 0, another.w) REP(k, 0, this->w) ret[i][j] += (*this)[i][k] * another[k][j];
*this = ret;
return *this;
}
// 行列に別の行列を足す
Mat operator+(const Mat &another) const {
Mat<Num> ret(*this);
return ret += another;
}
// 行列から別の行列を引く
Mat operator-(const Mat &another) const {
Mat<Num> ret(*this);
return ret -= another;
}
// 行列に別の行列を右から掛ける
Mat operator*(const Mat &another) const {
Mat<Num> ret(*this);
return ret *= another;
}
// 行列の n 乗を計算する
Mat pow(ll n) const {
assert(this->h == this->w);
Mat<Num> ret(this->h, this->w);
Mat<Num> a(*this);
REP(i, 0, this->h) ret[i][i] = 1;
while (n) {
if (n & 1) ret = a * ret;
a = a * a, n >>= 1;
}
return ret;
}
template <class... T> Mat assign(T... nums) {
vc<Num> num_list = vc<Num>{nums...};
assert(SIZE(num_list) == this->h * this->w);
REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num_list[this->w * i + j];
return *this;
}
void fill(Num num) { REP(i, 0, this->h) REP(j, 0, this->w)(*this)[i][j] = num; }
};
/* #endregion */
// Problem
void solve() {
ll t;
cin >> t;
vll n(t);
cin >> n;
// REP(i, 0, t) sub(n[i]);
vll n_asc = n;
sort(ALL(n_asc));
UNIQ(n_asc);
using mat = Mat<ld>;
mat te(7, 7);
REP(i, 0, 5) te[1 + i][i] = 1;
te[0][6] = te[6][6] = 1;
auto m = [&te](ll ii) -> mat {
mat ret = te;
REP(j, 0, ii) ret[0][j] = 1.0L / 6.0L;
if (ii <= 4) ret[0][ii] = ((5.0L - ii) / 6.0L);
return ret;
};
um<ll, mat> mp;
mat m6 = m(6);
REP(i, 0, t) {
ll k = n_asc[i];
if (i == 0 || n_asc[i - 1] <= 6) {
mat coef(7, 7);
REP(i, 0, 7) coef[i][i] = 1;
ll ptr = k;
while (ptr > 0) {
ll idx = k - ptr;
if (idx >= 6) {
coef = m6.pow(ptr) * coef;
break;
}
coef = m(idx) * coef;
// dump(idx, m(idx));
ptr--;
}
mp[k] = coef;
} else {
ll dif = k - n_asc[i - 1];
mp[k] = m6.pow(dif) * mp[n_asc[i - 1]];
}
}
REP(i, 0, t) {
mat coef = mp[n[i]];
cout << (coef[0][6] / (1.0L - coef[0][0])) << endl;
}
}
// entry point
int main() {
solve();
return 0;
}