#540543 (C++14) No.42 貯金箱の溜息

提出ソース
結果

問題	No.42 貯金箱の溜息
ユーザー	satanic
提出日時	2020-08-26 15:10:15
言語	C++14 (gcc 13.2.0 + boost 1.83.0)
結果	AC
実行時間	21 ms / 5,000 ms
コード長	12,290 bytes
コンパイル時間	1,259 ms
コンパイル使用メモリ	128,308 KB
実行使用メモリ	11,396 KB
最終ジャッジ日時	2023-08-07 06:56:42
合計ジャッジ時間	1,865 ms
ジャッジサーバーID （参考情報）	judge13 / judge14
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	実行時間実行使用メモリ
testcase_00	AC	20 ms 11,268 KB
testcase_01	AC	21 ms 11,396 KB
testcase_02	AC	21 ms 11,224 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
//
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//
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//       ?77WMMMYB""!                                                                        _7"WWMMMY"7=     

// need
#include <iostream>
#include <algorithm>
// data structure
#include <bitset>
#include <map>
#include <queue>
#include <set>
#include <stack>
#include <string>
#include <utility>
#include <vector>
#include <complex>
//#include <deque>
#include <valarray>
#include <unordered_map>
#include <unordered_set>
#include <array>
// etc
#include <cassert>
#include <cmath>
#include <functional>
#include <iomanip>
#include <chrono>
#include <random>
#include <numeric>
#include <fstream>

//std::ifstream ifs("b.in");
//auto& scan_in = ifs;
auto& scan_in = std::cin;

// input
#define INIT std::ios::sync_with_stdio(false);std::cin.tie(0);
#define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__);
template<typename T> void MACRO_VAR_Scan(T& t) { scan_in >> t; }
template<typename First, typename...Rest>void MACRO_VAR_Scan(First& first, Rest& ...rest) { scan_in >> first; MACRO_VAR_Scan(rest...); }
#define VEC_ROW(type, n, ...)std::vector<type> __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w_=0; w_<n; ++w_){MACRO_VEC_ROW_Scan(w_, __VA_ARGS__);}
template<typename T> void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Init(int n, First& first, Rest& ...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); }
template<typename T> void MACRO_VEC_ROW_Scan(int p, T& t) { scan_in >> t[p]; }
template<typename First, typename...Rest>void MACRO_VEC_ROW_Scan(int p, First& first, Rest& ...rest) { scan_in >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); }
#define VEC(type, c, n) std::vector<type> c(n);for(auto& i:c)scan_in>>i;
#define MAT(type, c, m, n) std::vector<std::vector<type>> c(m, std::vector<type>(n));for(auto& R:c)for(auto& w:R)scan_in>>w;
// output
template<typename T>void MACRO_OUT(const T t) { std::cout << t; }
template<typename First, typename...Rest>void MACRO_OUT(const First first, const Rest...rest) { std::cout << first << " "; MACRO_OUT(rest...); }
#define OUT(...) MACRO_OUT(__VA_ARGS__);
#define FOUT(n, dist) std::cout<<std::fixed<<std::setprecision(n)<<(dist);
#define SOUT(n, c, dist) std::cout<<std::setw(n)<<std::setfill(c)<<(dist);
#define VOUT(v) for(size_t i = 0; i < v.size(); ++i) {OUT(v[i]);if(i+1<v.size()){SP}}
#define EOUT(...) do{ OUT(__VA_ARGS__)BR; exit(0); }while(0);
#define SP std::cout<<" ";
#define TAB std::cout<<"\t";
#define BR std::cout<<"\n";
#define SPBR(w, n) std::cout<<(w + 1 == n ? '\n' : ' ');
#define ENDL std::cout<<std::endl;
#define FLUSH std::cout<<std::flush;
#define SHOW(dist) {std::cerr << #dist << "\t: " << (dist) << "\n";}
// utility
#define ALL(a) (a).begin(),(a).end()
#define FOR(w, a, n) for(int w=(a);w<(n);++w)
#define REP(w, n) FOR(w, 0, n)
#define RFOR(w, a, n) for(int w=(n)-1;w>=(a);--w)
#define RREP(w, n) RFOR(w, 0, n)
template<class S, class T, class U> bool IN(S a, T x, U b) { return a <= x && x < b; }
template<class T> inline T CHMAX(T& a, const T b) { return a = (a < b) ? b : a; }
template<class T> inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; }
// test
template<class T> using V = std::vector<T>;
template<class T> using VV = V<V<T>>;

template<typename S, typename T>
std::ostream& operator<<(std::ostream& os, const std::pair<S, T>& p) {
	os << "(" << p.first << ", " << p.second << ")"; return os;
}
template<typename T>
std::ostream& operator<<(std::ostream& os, const std::vector<T>& v) {
	os << "{";
	for (size_t i = 0; i < v.size(); ++i) os << v[i] << ((i + 1 < v.size()) ? ", " : ""); os << "}";
	return os;
}
template<typename T>
std::ostream & operator<<(std::ostream & os, const std::set<T> & v) {
	os << "{";
	for (auto it = v.cbegin();;) {
		os << *it; ++it;
		if (it == v.cend()) { os << "}"; break; }
		else { os << ", "; }
	}
	return os;
}
template<typename S, typename T>
std::ostream& operator<<(std::ostream & os, const std::map<S, T> & m) {
	os << "{";
	for (auto it = m.cbegin(); it != m.cend();) { os << it->first << ":" << it->second; ++it; os << (it == m.cend() ? "" : ", "); } os << "}";
	return os;
}
template<typename T>
std::ostream& operator<<(std::ostream & os, std::queue<T> q) {
	os << "<";
	while (!q.empty()) { os << q.front(); q.pop(); os << (q.empty() ? "<" : ", "); }
	return os;
}
template<typename T>
std::ostream& operator<<(std::ostream & os, std::stack<T> q) {
	os << ">";
	while (!q.empty()) { os << q.top(); q.pop(); os << (q.empty() ? "]" : ", "); }
	return os;
}
namespace std {
	template<typename S, typename T> class numeric_limits<pair<S, T>> {
	public:
		static constexpr pair<S, T> max() noexcept { return { numeric_limits<S>::max(), numeric_limits<T>::max() }; }
		static constexpr pair<S, T> lowest() noexcept { return { numeric_limits<S>::lowest(), numeric_limits<T>::lowest() }; }
	};
}

// type/const
using i64 = std::int_fast64_t;
using u64 = std::uint_fast64_t;
using ll = long long;
using ull = unsigned long long;
using ld = long double;
using PAIR = std::pair<int, int>;
using PAIRLL = std::pair<ll, ll>;
constexpr int INFINT = (1 << 30) - 1;                    // 1.07x10^ 9
constexpr int INFINT_LIM = (1LL << 31) - 1;              // 2.15x10^ 9
constexpr ll INFLL = 1LL << 60;                          // 1.15x10^18
constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62);  // 9.22x10^18
constexpr double EPS = 1e-6;
constexpr i64 MOD = 1000000009;
constexpr double PI = 3.141592653589793238462643383279;
template<class T, size_t N> void FILL(T(&a)[N], const T & val) { for (auto& x : a) x = val; }
template<class ARY, size_t N, size_t M, class T> void FILL(ARY(&a)[N][M], const T & val) { for (auto& b : a) FILL(b, val); }
template<class T> void FILL(std::vector<T> & a, const T & val) { for (auto& x : a) x = val; }
template<class ARY, class T> void FILL(std::vector<std::vector<ARY>> & a, const T & val) { for (auto& b : a) FILL(b, val); }
// ------------>8---------

ll powMod(ll n, ll p, ll mod) {
	ll res = 1;
	while (p) {
		if (p & 1) (res *= n) %= mod;
		(n *= n) %= mod;
		p >>= 1;
	}
	return res;
}
ll invMod(ll n, ll mod) {
	return powMod(n, MOD - 2, MOD);
}

const signed FACT_MAX_N = 1000006;
signed fact[FACT_MAX_N];
signed factInv[FACT_MAX_N];
struct INIT_FACT {
	INIT_FACT() {
		fact[0] = 1;
		for (int i = 1; i < FACT_MAX_N; ++i) fact[i] = (long long)i * fact[i - 1] % MOD;
		factInv[FACT_MAX_N - 1] = powMod(fact[FACT_MAX_N - 1], MOD - 2, MOD);
		for (int i = FACT_MAX_N - 2; i >= 0; --i) factInv[i] = (long long)(i + 1) * factInv[i + 1] % MOD;
	}
} init_fact;

ll Combination(ll n, ll r) {
	if (n < r) return 0;
	if (n < 2 * r) r = n - r;
	ll ans = factInv[r];
	n %= MOD;
	for (int i = 1; i <= r; ++i) (ans *= n - i + 1) %= MOD;
	if (ans < 0) ans += MOD;
	return ans;
}

class Polynomial {
	std::vector<int> coef;
public:
	Polynomial(int N) : coef(N + 1, 0) {}
	Polynomial(std::initializer_list<int> a) : coef(a) {}
	Polynomial& operator+=(const Polynomial& r) {
		if (coef.size() < r.coef.size()) coef.resize(r.coef.size());
		for (size_t i = 0; i < r.coef.size(); ++i) (coef[i] += r.coef[i]) %= MOD;
		return *this;
	}
	Polynomial & operator*=(const Polynomial & r) { // O(N^2)
		std::vector<int> c(this->coef.size() + r.coef.size() - 1);
		REP(i, this->coef.size()) REP(j, r.coef.size()) c[i + j] += this->coef[i] * r.coef[j];
		coef = c;
		return *this;
	}
	/*Polynomial& operator*=(const Polynomial & r) { // O(NlogN)
		auto c = NTT::mul(this->coef, r.coef, MOD);
		coef = c;
		return *this;
	}*/
	Polynomial& operator^=(long long p) {
		Polynomial x(*this);
		*this = Polynomial(0);
		coef[0] = 1;
		while (p) {
			if (p & 1) (*this) *= x;
			x *= x;
			p >>= 1;
		}
		return *this;
	}
	int& operator[](size_t i) { return coef[i]; }
	std::vector<int> getCoef() const { return coef; }
};

signed main() {
	INIT;

	Polynomial P(0); P[0] = 1;
	{
		{
			Polynomial t(4); REP(k, 5) t[k] = 1;
			P *= t;
		}
		{
			Polynomial t(5); t[0] = t[5] = 1;
			REP(_, 2) P *= t;
		}
		{
			Polynomial t(40); REP(k, 5) t[k * 10] = 1;
			REP(_, 3) P *= t;
		}
		{
			Polynomial t(50); t[0] = t[50] = 1;
			REP(_, 4) P *= t;
		}
		{
			Polynomial t(400); REP(k, 5) t[k * 100] = 1;
			REP(_, 5) P *= t;
		}
	}

	auto Q = [&](i64 m) {
		if (m < 0 || m % 500) return 0ll;
		return Combination(m / 500 + 5, 5);
	};

	VAR(int, T);
	REP(_, T) {
		VAR(i64, m);
		i64 ans = 0;
		for (i64 k = m / 500 * 500; k >= std::max((i64)0, m - 2334); k -= 500) 
			(ans += P[m - k] * Q(k)) %= MOD;
		OUT(ans)BR;
	}

	return 0;
}
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結果

テストケース

ソースコード
