#519 (C++11（廃止可能性あり）) No.42 貯金箱の溜息

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問題	No.42 貯金箱の溜息
コンテスト
ユーザー	anta
提出日時	2014-10-17 00:27:02
言語	C++11（廃止可能性あり） (gcc 13.3.0)
結果	WA
実行時間	-
コード長	6,854 bytes
コンパイル時間	1,027 ms
コンパイル使用メモリ	94,632 KB
実行使用メモリ	7,552 KB
最終ジャッジ日時	2024-12-30 09:23:59
合計ジャッジ時間	1,981 ms
ジャッジサーバーID （参考情報）	judge2 / judge5

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ファイルパターン	結果
other	AC * 1 WA * 2

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コンパイルメッセージ

main.cpp: In function ‘int main()’:
main.cpp:182:14: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  182 |         scanf("%d", &T);
      |         ~~~~~^~~~~~~~~~
main.cpp:213:22: warning: ignoring return value of ‘int scanf(const char*, ...)’ declared with attribute ‘warn_unused_result’ [-Wunused-result]
  213 |                 scanf("%lld", &M);
      |                 ~~~~~^~~~~~~~~~~~

ソースコード

raw source code

#define _CRT_SECURE_NO_WARNINGS
#include <string>
#include <vector>
#include <algorithm>
#include <numeric>
#include <set>
#include <map>
#include <queue>
#include <iostream>
#include <sstream>
#include <cstdio>
#include <cmath>
#include <ctime>
#include <cstring>
#include <cctype>
#include <cassert>
#include <limits>
#include <unordered_set>
#define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i))
#define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i))
#define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i))
#if defined(_MSC_VER) || __cplusplus > 199711L
#define aut(r,v) auto r = (v)
#else
#define aut(r,v) typeof(v) r = (v)
#endif
#define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it)
#define all(o) (o).begin(), (o).end()
#define pb(x) push_back(x)
#define mp(x,y) make_pair((x),(y))
#define mset(m,v) memset(m,v,sizeof(m))
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
using namespace std;
typedef vector<int> vi; typedef pair<int,int> pii; typedef vector<pair<int,int> > vpii;
typedef long long ll; typedef vector<long long> vl; typedef pair<long long,long long> pll; typedef vector<pair<long long,long long> > vpll;
typedef vector<string> vs; typedef long double ld;
template<typename T, typename U> inline void amin(T &x, U y) { if(y < x) x = y; }
template<typename T, typename U> inline void amax(T &x, U y) { if(x < y) x = y; }

template<int MOD>
struct ModInt {
	static const int Mod = MOD;
	unsigned x;
	ModInt(): x(0) { }
	ModInt(signed sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; }
	ModInt(signed long long sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; }
	int get() const { return (int)x; }
	
	ModInt &operator+=(ModInt that) { if((x += that.x) >= MOD) x -= MOD; return *this; }
	ModInt &operator-=(ModInt that) { if((x += MOD - that.x) >= MOD) x -= MOD; return *this; }
	ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; }
	ModInt &operator/=(ModInt that) { return *this *= that.inverse(); }
	
	ModInt operator+(ModInt that) const { return ModInt(*this) += that; }
	ModInt operator-(ModInt that) const { return ModInt(*this) -= that; }
	ModInt operator*(ModInt that) const { return ModInt(*this) *= that; }
	ModInt operator/(ModInt that) const { return ModInt(*this) /= that; }
	
	ModInt inverse() const {
		long long a = x, b = MOD, u = 1, v = 0;
		while(b) {
			long long t = a / b;
			a -= t * b; std::swap(a, b);
			u -= t * v; std::swap(u, v);
		}
		return ModInt(u);
	}
	
	bool operator==(ModInt that) const { return x == that.x; }
	bool operator!=(ModInt that) const { return x != that.x; }
	ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; }
};
typedef ModInt<1000000009> mint;

struct Polynomial {
	typedef mint Coef; typedef Coef Val;
	vector<Coef> coef;	//... + coef[2] x^2 + coef[1] x + coef[0]
	Polynomial() {}
	explicit Polynomial(int n): coef(n) {}
	static Polynomial One() {
		Polynomial r(1);
		r.coef[0] = 1;
		return r;
	}
	bool iszero() const { return coef.empty(); }
	int degree1() const { return coef.size(); }	//degree + 1
	int resize(int d) { if(degree1() < d) coef.resize(d); return d; }
	const Coef operator[](int i) const {
		return i >= degree1() ? Coef() : coef[i];
	}
	void canonicalize() {
		int i = coef.size();
		while(i > 0 && coef[i-1] == Coef()) i --;
		coef.resize(i);
	}
	Val evalute(Val x) const {
		int d = degree1();
		Val t = 0, y = 1;
		rep(i, d) {
			t += y * coef[i];
			y *= x;
		}
		return t;
	}
	Polynomial &operator+=(const Polynomial &that) {
		int d = resize(that.degree1());
		for(int i = 0; i < d; i ++) coef[i] += that[i];
		canonicalize();
		return *this;
	}
	Polynomial operator+(const Polynomial &that) const { return Polynomial(*this) += that; }
	Polynomial &operator-=(const Polynomial &that) {
		int d = resize(that.degree1());
		for(int i = 0; i < d; i ++) coef[i] -= that[i];
		canonicalize();
		return *this;
	}
	Polynomial operator-(const Polynomial &that) const { return Polynomial(*this) -= that; }
	Polynomial operator-() const {
		int d = degree1();
		Polynomial res(d);
		for(int i = 0; i < d; i ++) res.coef[i] = - coef[i];
		return res;
	}
	//naive
	Polynomial operator*(const Polynomial &that) const {
		if(iszero() || that.iszero()) return Polynomial();
		int x = degree1(), y = that.degree1(), d = x + y - 1;
		Polynomial res(d);
		rep(i, x) rep(j, y)
			res.coef[i+j] += coef[i] * that.coef[j];
		res.canonicalize();
		return res;
	}
	//long division
	pair<Polynomial, Polynomial> divmod(const Polynomial &that) const {
		int x = degree1() - 1, y = that.degree1() - 1;
		int d = max(0, x - y);
		Polynomial q(d + 1), r = *this;
		for(int i = x; i >= y; i --) {
			Coef t = r.coef[i] / that.coef[y];
			q.coef[i - y] = t;
			assert(t * that.coef[y] == r.coef[i]);
			r.coef[i] = 0;
			if(t == 0) continue;
			for(int j = 0; j < y; j ++)
				r.coef[i - y + j] -= t * that.coef[j];
		}
		q.canonicalize(); r.canonicalize();
		return make_pair(q, r);
	}
	Polynomial operator/(const Polynomial &that) const { return divmod(that).first; }
	Polynomial operator%(const Polynomial &that) const { return divmod(that).second; }

	static Polynomial interpolate(const vector<pair<Coef,Val> > &points) {
		int n = points.size();
		vector<Coef> dp(n+1);
		dp[0] = 1;
		rep(i, n) for(int j = i; j >= 0; j --) {
			dp[j+1] += dp[j];
			dp[j] *= -points[i].first;
		}
		Polynomial r(n);
		rep(i, n) {
			Coef den = 1;
			rep(j, n) if(i != j)
				den *= points[i].first - points[j].first;
			Coef iden = (Coef)1 / den, minus = 0;
			for(int j = n-1; j >= 0; j --) {
				minus = dp[j+1] + minus * points[i].first;
				r.coef[j] += minus * iden * points[i].second;
			}
		}
		r.canonicalize();
		return r;
	}
};

int main() {
	int T;
	scanf("%d", &T);
	const int N = 6;
	const int xs[N] = { 1, 5, 10, 50, 100, 500 };
	const int X = 1000000, Y = 500, Z = 500 * 500, D = 100;
	vector<mint> dp(X+1);
	dp[0] = 1;
	rep(i, N) {
		int x = xs[i];
		rer(j, 0, X-x)
			dp[j + x] += dp[j];
	}
	vector<Polynomial> polynomials(Y);
	rep(c, Y) {
//		cerr << c << "..." << endl;
		vector<pair<mint,mint> > points(D);
		rep(i, D) {
			int z = Z + i * Y;
			points[i] = mp(z, dp[z]);
		}
		polynomials[c] = Polynomial::interpolate(points);
/*
		rep(i, D + 100) {
			int z = Z + i * Y;
			mint a = polynomials[c].evalute(z);
			mint b = dp[z];
			if(a.get() != b.get()) cerr << c << ", " << z << ": " << a.get() << ", " << b.get() << endl;
		}
//		*/
	}
	rep(ii, T) {
		long long M;
		scanf("%lld", &M);
		mint ans;
		if(M <= X)
			ans = dp[(int)M];
		else
			ans = polynomials[M % Y].evalute(M);
		printf("%d\n", ans.get());
	}
	return 0;
}

yukicoder

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