#665953 (C++17) No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率

提出ソース

結果

問題	No.1547 [Cherry 2nd Tune *] 偶然の勝利の確率
ユーザー	iiljj
提出日時	2021-06-11 23:16:45
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	128 ms / 2,000 ms
コード長	14,548 bytes
コンパイル時間	1,867 ms
コンパイル使用メモリ	150,116 KB
実行使用メモリ	5,376 KB
最終ジャッジ日時	2024-05-08 19:38:47
合計ジャッジ時間	4,513 ms
ジャッジサーバーID （参考情報）	judge1 / judge4

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	2 ms 5,248 KB
testcase_01	AC	1 ms 5,376 KB
testcase_02	AC	6 ms 5,376 KB
testcase_03	AC	2 ms 5,376 KB
testcase_04	AC	2 ms 5,376 KB
testcase_05	AC	2 ms 5,376 KB
testcase_06	AC	2 ms 5,376 KB
testcase_07	AC	2 ms 5,376 KB
testcase_08	AC	2 ms 5,376 KB
testcase_09	AC	2 ms 5,376 KB
testcase_10	AC	2 ms 5,376 KB
testcase_11	AC	2 ms 5,376 KB
testcase_12	AC	2 ms 5,376 KB
testcase_13	AC	23 ms 5,376 KB
testcase_14	AC	16 ms 5,376 KB
testcase_15	AC	7 ms 5,376 KB
testcase_16	AC	11 ms 5,376 KB
testcase_17	AC	11 ms 5,376 KB
testcase_18	AC	10 ms 5,376 KB
testcase_19	AC	5 ms 5,376 KB
testcase_20	AC	69 ms 5,376 KB
testcase_21	AC	7 ms 5,376 KB
testcase_22	AC	2 ms 5,376 KB
testcase_23	AC	123 ms 5,376 KB
testcase_24	AC	121 ms 5,376 KB
testcase_25	AC	124 ms 5,376 KB
testcase_26	AC	124 ms 5,376 KB
testcase_27	AC	126 ms 5,376 KB
testcase_28	AC	128 ms 5,376 KB
testcase_29	AC	125 ms 5,376 KB
testcase_30	AC	124 ms 5,376 KB
testcase_31	AC	124 ms 5,376 KB
testcase_32	AC	127 ms 5,376 KB
testcase_33	AC	123 ms 5,376 KB
testcase_34	AC	11 ms 5,376 KB
testcase_35	AC	10 ms 5,376 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

raw source code

/* #region Head */

// #include <bits/stdc++.h>
#include <algorithm>
#include <array>
#include <bitset>
#include <cassert> // assert.h
#include <cmath>   // math.h
#include <cstring>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <list>
#include <map>
#include <memory>
#include <numeric>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <vector>
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 TREP(T, i, m, n) for (T i = (m), i##_len = (T)(n); i < i##_len; ++(i))
#define TREPM(T, i, m, n) for (T i = (m), i##_max = (T)(n); i <= i##_max; ++(i))
#define TREPR(T, i, m, n) for (T i = (m), i##_min = (T)(n); i >= i##_min; --(i))
#define TREPD(T, i, m, n, d) for (T i = (m), i##_len = (T)(n); i < i##_len; i += (d))
#define TREPMD(T, i, m, n, d) for (T i = (m), i##_max = (T)(n); i <= i##_max; i += (d))

#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 REPIR(itr, ds) for (auto itr = ds.rbegin(); itr != ds.rend(); 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 CEIL(a, b) (((a) + (b)-1) / (b))

#define endl '\n'

constexpr ll INF = 1'010'000'000'000'000'017LL;
constexpr int IINF = 1'000'000'007LL;
// constexpr ll MOD = 1'000'000'007LL; // 1e9 + 7
constexpr ll MOD = 998244353;
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, const 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, const 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, size_t _Nm> istream &operator>>(istream &is, array<T, _Nm> &arr) { // array 入力
    REP(i, 0, SIZE(arr)) is >> arr[i];
    return is;
}
template <typename T, size_t _Nm> ostream &operator<<(ostream &os, const array<T, _Nm> &arr) { // array 出力 (for dump)
    os << "{";
    REP(i, 0, SIZE(arr)) os << arr[i] << (i == i_len - 1 ? "" : ", ");
    os << "}";
    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, const 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, const 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, const map<T, U> &map_var) {
    return out_iter(os, map_var);
}
template <typename T, typename U> ostream &operator<<(ostream &os, const 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, const set<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const us<T> &set_var) { return out_iter(os, set_var); }
template <typename T> ostream &operator<<(ostream &os, const 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 << "}";
}

void pprint() { cout << endl; }
template <class Head, class... Tail> void pprint(Head &&head, Tail &&...tail) {
    cout << head;
    if (sizeof...(Tail) > 0) cout << ' ';
    pprint(move(tail)...);
}

// 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
#ifndef ONLINE_JUDGE
#define DEBUG_
#endif

#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

#define VAR(type, ...)                                                                                                 \
    type __VA_ARGS__;                                                                                                  \
    cin >> __VA_ARGS__;

template <typename T> istream &operator,(istream &is, T &rhs) { return is >> rhs; }
template <typename T> ostream &operator,(ostream &os, const T &rhs) { return os << ' ' << rhs; }

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;

void Yn(bool p) { cout << (p ? "Yes" : "No") << endl; }
void YN(bool p) { cout << (p ? "YES" : "NO") << endl; }

/* #endregion */

// #include <atcoder/all>
// using namespace atcoder;

/* #region mint */

// 自動で MOD を取る整数
struct mint {
    ll x;
    mint(ll x = 0) : x((x % MOD + MOD) % MOD) {}
    mint &operator+=(const mint a) {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint &operator-=(const mint a) {
        if ((x += MOD - a.x) >= MOD) x -= MOD;
        return *this;
    }
    mint &operator*=(const mint a) {
        (x *= a.x) %= MOD;
        return *this;
    }
    mint operator+(const mint a) const {
        mint res(*this);
        return res += a;
    }
    mint operator-(const mint a) const {
        mint res(*this);
        return res -= a;
    }
    mint operator*(const mint a) const {
        mint res(*this);
        return res *= a;
    }
    // O(log(t))
    mint pow_rec(ll t) const {
        if (!t) return 1;
        mint a = pow(t >> 1); // ⌊t/2⌋ 乗
        a *= a;               // ⌊t/2⌋*2 乗
        if (t & 1)            // ⌊t/2⌋*2 == t-1 のとき
            a *= *this;       // ⌊t/2⌋*2+1 乗 => t 乗
        return a;
    }

    mint pow(ll t) const {
        mint a(*this);
        mint res = 1;
        while (t) {
            if (t & 1) res *= a;
            t >>= 1, a *= a;
        }
        return res;
    }

    // for prime mod
    mint inv_prime() const {
        return pow(MOD - 2); // オイラーの定理から， x^(-1) ≡ x^(p-2)
    }
    mint inv() const {
        ll a = this->x, b = MOD, u = 1, v = 0, t;
        mint res;
        while (b) {
            t = a / b;
            a -= t * b;
            swap(a, b);
            u -= t * v;
            swap(u, v);
        }
        if (u < 0) u += MOD;
        res = u;
        return res;
    }
    mint &operator/=(const mint a) { return (*this) *= a.inv(); }
    mint operator/(const mint a) const {
        mint res(*this);
        return res /= a;
    }
    bool operator==(const mint a) const { return this->x == a.x; }
    bool operator==(const ll a) const { return this->x == a; }
    bool operator!=(const mint a) const { return this->x != a.x; }
    bool operator!=(const ll a) const { return this->x != a; }

    // mint 入力
    friend istream &operator>>(istream &is, mint &x) {
        is >> x.x;
        return is;
    }

    // mint 出力
    friend ostream &operator<<(ostream &os, const mint x) {
        os << x.x;
        return os;
    }
};

/* #endregion */

/* #region Mat */

template <typename T> constexpr bool false_v = false;

// 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;
    size_t h, w;

    // コンストラクタ
    Mat<Num>(const size_t h, size_t 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) {}
    Mat<Num>(std::initializer_list<vc<Num>> init) : vc<vc<Num>>() {
        for (auto iter = init.begin(); iter != init.end(); ++iter) this->emplace_back(*iter);
        h = this->size(), w = (*this)[0].size();
    }

    // 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(num_list.size() == 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; }

    void print() { REP(i, 0, h) REP(j, 0, w) cout << (*this)[i][j] << (j == (ll)w - 1 ? '\n' : ' '); }
};

/* #endregion */

// Problem
void solve() {
    VAR(ll, ma, na, s);
    VAR(ll, mb, nb, t);
    VAR(ll, k);

    mint pa = mint(ma) / na;
    mint pb = mint(mb) / nb;
    mint pa2 = (mint(1) - pa);
    mint pb2 = (mint(1) - pb);

    // s, t が小さいので行列累乗っぽい．
    // 位置 -t, ..., 0, ..., s について，k 周したあとに各状態にいる確率を求める．
    ll sz = s + t + 1;
    auto idx = [&](ll x) -> ll { return x + t; };
    using mat = Mat<mint>;

    mat A(sz, sz), B(sz, sz);
    A.fill(0), B.fill(0);
    A[idx(-t)][idx(-t)] = 1, B[idx(-t)][idx(-t)] = 1;
    A[idx(s)][idx(s)] = 1, B[idx(s)][idx(s)] = 1;
    REPM(from, -t + 1, s - 1) {
        A[idx(from)][idx(from)] = pa2;
        REPM(to, from + 1, s) {
            ll cnt_front = to - from;
            if (to == s)
                A[idx(to)][idx(from)] = pa.pow(cnt_front);
            else
                A[idx(to)][idx(from)] = pa.pow(cnt_front) * pa2;
        }
        B[idx(from)][idx(from)] = pb2;
        REPR(to, from - 1, -t) {
            ll cnt_front = from - to;
            if (to == -t)
                B[idx(to)][idx(from)] = pb.pow(cnt_front);
            else
                B[idx(to)][idx(from)] = pb.pow(cnt_front) * pb2;
        }
    }
    mat M = B * A;
    M = M.pow(k);

    mat P(sz, 1);
    P.fill(0);
    P[idx(0)][0] = 1;

    mat ans = M * P;
    pprint(ans[idx(s)][0]);
    pprint(ans[idx(-t)][0]);
}

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

yukicoder

結果

テストケース

ソースコード