結果

問題 No.75 回数の期待値の問題
ユーザー iiljjiiljj
提出日時 2020-05-22 00:52:37
言語 C++17(1z)
(gcc 10.2.0 + boost 1.73.0)
結果
AC  
実行時間 3 ms / 5,000 ms
コード長 8,828 Byte
コンパイル時間 2,185 ms
使用メモリ 8,940 KB
最終ジャッジ日時 2020-08-09 01:30:22
このコードへのチャレンジ(β)

テストケース

テストケース表示
入力 結果 実行時間
使用メモリ
testcase_00 AC 2 ms
8,940 KB
testcase_01 AC 2 ms
6,896 KB
testcase_02 AC 2 ms
8,936 KB
testcase_03 AC 2 ms
8,940 KB
testcase_04 AC 3 ms
6,896 KB
testcase_05 AC 3 ms
6,892 KB
testcase_06 AC 2 ms
8,940 KB
testcase_07 AC 2 ms
6,892 KB
testcase_08 AC 2 ms
6,896 KB
testcase_09 AC 2 ms
6,896 KB
testcase_10 AC 2 ms
8,940 KB
testcase_11 AC 2 ms
6,896 KB
testcase_12 AC 2 ms
8,940 KB
testcase_13 AC 3 ms
6,896 KB
testcase_14 AC 2 ms
6,896 KB
testcase_15 AC 2 ms
8,940 KB
testcase_16 AC 3 ms
8,936 KB
testcase_17 AC 3 ms
8,900 KB
testcase_18 AC 3 ms
6,892 KB
testcase_19 AC 2 ms
6,900 KB
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 #

/* #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>(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 k;
    cin >> k;

    using mat = Mat<ld>;
    mat t(7, 7);
    REP(i, 0, 5) t[1 + i][i] = 1;
    t[0][6] = t[6][6] = 1;

    auto m = [&t](ll ii) -> mat {
        mat ret = t;
        REP(j, 0, ii) ret[0][j] = 1.0L / 6.0L;
        if (ii <= 4) ret[0][ii] = ((5.0L - ii) / 6.0L);
        return ret;
    };
    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 = m(6).pow(ptr) * coef;
            break;
        }
        coef = m(idx) * coef;
        // dump(idx, m(idx));
        ptr--;
    }
    cout << (coef[0][6] / (1.0L - coef[0][0])) << endl;
}

// entry point
int main() {
    solve();
    return 0;
}
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