結果

問題 No.42 貯金箱の溜息
ユーザー DemystifyDemystify
提出日時 2022-04-24 23:21:23
言語 C++17
(gcc 12.3.0 + boost 1.83.0)
結果
AC  
実行時間 634 ms / 5,000 ms
コード長 10,670 bytes
コンパイル時間 2,729 ms
コンパイル使用メモリ 217,728 KB
実行使用メモリ 5,376 KB
最終ジャッジ日時 2024-06-26 10:14:36
合計ジャッジ時間 4,341 ms
ジャッジサーバーID
（参考情報） 		judge5 / judge2
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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 53 ms
5,248 KB
testcase_01 AC 634 ms
5,376 KB
testcase_02 AC 567 ms
5,376 KB
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ソースコード

diff # 

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
// --------------------------------------------------------
#define FOR(i,l,r) for (ll i = (l); i < (r); ++i)
#define RFOR(i,l,r) for (ll i = (r)-1; (l) <= i; --i)
#define REP(i,n) FOR(i,0,n)
#define RREP(i,n) RFOR(i,0,n)
#define ALL(c) (c).begin(), (c).end()
#define RALL(c) (c).rbegin(), (c).rend()
#define SORT(c) sort(ALL(c))
#define RSORT(c) sort(RALL(c))
#define MIN(c) *min_element(ALL(c))
#define MAX(c) *max_element(ALL(c))
#define SUMLL(c) accumulate(ALL(c), 0LL)
#define COUNT(c,v) count(ALL(c),(v))
#define SZ(c) ((ll)(c).size())
#define BIT(b,i) (((b)>>(i)) & 1)
#define PCNT(b) __builtin_popcountll(b)
#define P0(i) (((i) & 1) == 0)
#define P1(i) (((i) & 1) == 1)
#ifdef _LOCAL
    #define debug_bar cerr << "--------------------\n";
    #define debug(x) cerr << "l." << __LINE__ << " : " << #x << " = " << (x) << '\n'
    #define debug_pair(x) cerr << "l." << __LINE__ << " : " << #x << " = (" << x.first << "," << x.second << ")\n";
    template<class T> void debug_line(const vector<T>& ans, int l, int r, int L = 0) { cerr << "l." << L << " :"; for (int i = l; i < r; i++) { cerr << ' ' << ans[i]; } cerr << '\n'; }
#else
    #define cerr if (false) cerr
    #define debug_bar
    #define debug(x)
    #define debug_pair(x)
    template<class T> void debug_line([[maybe_unused]] const vector<T>& ans, [[maybe_unused]] int l, [[maybe_unused]] int r, [[maybe_unused]] int L = 0) {}
#endif
template<class... T> void input(T&... a) { (cin >> ... >> a); }
void print() { cout << '\n'; }
template<class T> void print(const T& a) { cout << a << '\n'; }
template<class T, class... Ts> void print(const T& a, const Ts&... b) { cout << a; (cout << ... << (cout << ' ', b)); cout << '\n'; }
template<class T> void cout_line(const vector<T>& ans, int l, int r) { for (int i = l; i < r; i++) { if (i != l) { cout << ' '; } cout << ans[i]; } cout << '\n'; }
template<class T> bool chmin(T& a, const T b) { if (b < a) { a = b; return 1; } return 0; }
template<class T> bool chmax(T& a, const T b) { if (a < b) { a = b; return 1; } return 0; }
pair<ll,ll> divmod(ll a, ll b) { assert(a >= 0 && b > 0); return make_pair(a / b, a % b); }
ll mod(ll x, ll m) { assert(m != 0); return (x % m + m) % m; }
ll llceil(ll a, ll b) { if (b < 0) { return llceil(-a, -b); } assert(b > 0); return (a < 0 ? a / b : (a + b - 1) / b); }
ll llfloor(ll a, ll b) { if (b < 0) { return llfloor(-a, -b); } assert(b > 0); return (a > 0 ? a / b : (a - b + 1) / b); }
ll llpow(ll x, ll n) { assert(n >= 0); if (n == 0) { return 1; }; ll res = llpow(x, n>>1); res *= res; if (n & 1) { res *= x; } return res; }
ll bitlen(ll b) { if (b <= 0) { return 0; } return (64LL - __builtin_clzll(b)); }
ll digit_len(ll n) { assert(n >= 0); if (n == 0) { return 1; } ll sum = 0; while (n > 0) { sum++; n /= 10; } return sum; }
ll digit_sum(ll n) { assert(n >= 0); ll sum = 0; while (n > 0) { sum += n % 10; n /= 10; } return sum; }
ll digit_prod(ll n) { assert(n >= 0); if (n == 0) { return 0; } ll prod = 1; while (n > 0) { prod *= n % 10; n /= 10; } return prod; }
ll xor_sum(ll x) { assert(0 <= x); switch (x % 4) { case 0: return x; case 1: return 1; case 2: return x ^ 1; case 3: return 0; } assert(false); }
string toupper(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = toupper(T[i]); } return T; }
string tolower(const string& S) { string T(S); for (int i = 0; i < (int)T.size(); i++) { T[i] = tolower(T[i]); } return T; }
int a2i(const char& c) { assert(islower(c)); return (c - 'a'); }
int A2i(const char& c) { assert(isupper(c)); return (c - 'A'); }
int d2i(const char& d) { assert(isdigit(d)); return (d - '0'); }
char i2a(const int& i) { assert(0 <= i && i < 26); return ('a' + i); }
char i2A(const int& i) { assert(0 <= i && i < 26); return ('A' + i); }
char i2d(const int& i) { assert(0 <= i && i <= 9); return ('0' + i); }
using P = pair<ll,ll>;
using VP = vector<P>;
using VVP = vector<VP>;
using VS = vector<string>;
using VVS = vector<VS>;
using VI = vector<int>;
using VVI = vector<VI>;
using VVVI = vector<VVI>;
using VLL = vector<ll>;
using VVLL = vector<VLL>;
using VVVLL = vector<VVLL>;
using VB = vector<bool>;
using VVB = vector<VB>;
using VVVB = vector<VVB>;
using VD = vector<double>;
using VVD = vector<VD>;
using VVVD = vector<VVD>;
using VLD = vector<ld>;
using VVLD = vector<VLD>;
using VVVLD = vector<VVLD>;
const ld EPS = 1e-10;
const ld PI  = acosl(-1.0);
// constexpr ll MOD = 1000000007;
constexpr ll MOD = 1000000009;
// constexpr ll MOD = 998244353;
constexpr int inf = (1 << 30) - 1;   // 1073741824 - 1
constexpr ll INF = (1LL << 62) - 1;  // 4611686018427387904 - 1
// --------------------------------------------------------
// #include <atcoder/all>
// using namespace atcoder;


// References:
//   mint:
//     <https://github.com/atcoder/live_library/blob/master/mint.cpp>
//     <https://noshi91.hatenablog.com/entry/2019/03/31/174006>
//     <https://ei1333.github.io/luzhiled/snippets/math/mod-int.html>
//     <https://gist.github.com/MiSawa/dc78c3eb3ca16051818759ea069e8ccb>
//     <https://github.com/drken1215/algorithm/blob/master/MathCombinatorics/mod.cpp>
//   combination:
//     <https://github.com/atcoder/live_library/blob/master/comb.cpp>
//     <https://github.com/drken1215/algorithm/blob/master/MathCombinatorics/mod.cpp>

struct mint {
    ll x;
    constexpr mint(ll x = 0) noexcept : x((x % MOD + MOD) % MOD) {}

    constexpr mint& operator+=(const mint& a) noexcept {
        if ((x += a.x) >= MOD) x -= MOD;
        return *this;
    }
    constexpr mint& operator-=(const mint& a) noexcept {
        if ((x += MOD - a.x) >= MOD) x -= MOD;
        return *this;
    }
    constexpr mint& operator*=(const mint& a) noexcept { (x *= a.x) %= MOD; return *this; }
    constexpr mint& operator/=(const mint& a) noexcept { return *this *= a.inv(); }

    constexpr mint operator-() const noexcept { return mint(-x); }
    constexpr mint operator+(const mint& a) const noexcept { return mint(*this) += a; }
    constexpr mint operator-(const mint& a) const noexcept { return mint(*this) -= a; }
    constexpr mint operator*(const mint& a) const noexcept { return mint(*this) *= a; }
    constexpr mint operator/(const mint& a) const noexcept { return mint(*this) /= a; }
    constexpr bool operator==(const mint& a) const noexcept { return x == a.x; }
    constexpr bool operator!=(const mint& a) const noexcept { return x != a.x; }

    constexpr mint pow(ll n) const {
        if (n == 0) return 1;
        mint res = pow(n >> 1);
        res *= res;
        if (n & 1) res *= *this;
        return res;
    }
    constexpr mint inv() const { return pow(MOD - 2); }

    friend istream& operator>>(istream& is, mint& a) noexcept {
        ll v; is >> v;
        a = mint(v);
        return is;
    }
    friend ostream& operator<<(ostream& os, const mint& a) noexcept {
        return os << a.x;
    }
};
using VM = vector<mint>;
using VVM = vector<VM>;
using VVVM = vector<VVM>;
using VVVVM = vector<VVVM>;


struct combination {
    vector<mint> fact_, ifact_, inv_;
    int n_;
    combination() {}
    combination(int n) : fact_(n+1,0), ifact_(n+1,0), inv_(n+1,0) {
        assert(n != 0);
        assert(n < MOD);
        n_ = n;
        fact_[0] = 1; fact_[1] = 1;
        ifact_[0] = 1; ifact_[1] = 1;
        inv_[1] = 1;
        for(int i = 2; i <= n; ++i) {
            fact_[i] = fact_[i-1] * i;
            inv_[i] = -inv_[MOD%i] * (MOD/i);
            ifact_[i] = ifact_[i-1] * inv_[i];
        }
    }

    mint P(const int& n, const int& k) const noexcept {
        if (n < 0 || k < 0 || n < k) return 0;
        assert(n <= n_);
        return fact_[n] * ifact_[n-k];
    }
    mint C(const int& n, const int& k) const noexcept {
        if (n < 0 || k < 0 || n < k) return 0;
        assert(n <= n_);
        return fact_[n] * ifact_[n-k] * ifact_[k];
    }
    mint H(const int& n, const int& k) const noexcept {
        if (n < 0 || k < 0) return 0;
        assert(n + k - 1 <= n_);
        return C(n + k - 1, k);
    }
    mint fact(const int& n) const noexcept {
        assert(n <= n_);
        if (n < 0) return 0;
        return fact_[n];
    }
    mint ifact(const int& n) const noexcept {
        assert(n <= n_);
        if (n < 0) return 0;
        return ifact_[n];
    }
    mint inv(const int& n) const noexcept {
        assert(n <= n_);
        if (n < 0) return 0;
        return inv_[n];
    }
};


/**
 * @brief 行列累乗
 *        d x d の正方行列 A に対して A^n を O(k^3 log n) で求める
 * 
 * @tparam T 行列要素の型  e.g.) mint, ll
 * @param A 正方行列
 * @param n 指数
 * @return vector<vector<T>> A^n の計算結果
 */
template<class T>
vector<vector<T>> mat_exp(vector<vector<T>> A, ll n) {
    int d = A.size();
    vector<vector<T>> B(d, vector<T>(d, 0));
    for (int i = 0; i < d; i++) { B[i][i] = 1; }  // 単位行列で初期化

    auto mat_mul = [&](const vector<vector<T>>& A, const vector<vector<T>>& B) -> vector<vector<T>> {
        vector<vector<T>> C(d, vector<T>(d, 0));
        for (int i = 0; i < d; i++) {
            for (int k = 0; k < d; k++) {
                for (int j = 0; j < d; j++) {
                    C[i][j] += A[i][k] * B[k][j];
                }
            }
        }
        return C;
    };

    // e.g.) n = 11, B = A^(2^3) + A^(2^1) + A^(2^0)  (11 = 2^3 + 2^1 + 2^0)
    while (n > 0) {
        if (n & 1) { B = mat_mul(B, A); }  // 欲しいタイミングで拾う
        A = mat_mul(A, A);
        n >>= 1;
    }
    return B;
};


int main() {
    ios::sync_with_stdio(false);
    cin.tie(nullptr);
    cout << fixed << setprecision(15);

    VI B = {1, 5, 10, 50, 100, 500};
    ll N = 500, K = SZ(B);
    VVVM C(N+1, VVM(K, VM(K, 0)));
    REP(j,K) C[0][j][j] = 1;
    REP(x,N) REP(i,K) REP(j,K) {
        FOR(k,i,K) if (x + B[k] <= N) C[x+B[k]][k][j] += C[x][i][j];
    }

    VVM dp(N+1, VM(K, 0));
    REP(i,K) dp[B[i]][i] = 1;
    FOR(x,1,N) REP(i,K) {
        FOR(k,i,K) if (x + B[k] <= N) dp[x+B[k]][k] += dp[x][i];
    }

    int T; cin >> T;
    while (T--) {
        ll M; cin >> M;

        VVM A(K,VM(K,0));
        REP(i,K) REP(j,K) A[i][j] = C[N][i][j];

        auto [q, r] = divmod(M, 500);
        mint ans = 0;
        if (q == 0) {
            REP(i,K) ans += dp[M][i];
        } else if (r == 0) {
            auto An = mat_exp<mint>(A, q-1);
            REP(i,K) REP(j,K) ans += An[i][j] * dp[N][j];
        } else {
            auto An = mat_exp<mint>(A, q);
            REP(i,K) REP(j,K) ans += An[i][j] * dp[r][j];
        }
        print(ans);
    }

    return 0;
}
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