結果

問題 No.213 素数サイコロと合成数サイコロ (3-Easy)
ユーザー antaanta
提出日時 2015-05-23 00:13:06
言語 C++11
(gcc 13.3.0)
結果
AC  
実行時間 7 ms / 3,000 ms
コード長 7,302 bytes
コンパイル時間 986 ms
コンパイル使用メモリ 96,104 KB
実行使用メモリ 6,944 KB
最終ジャッジ日時 2024-07-06 05:44:14
合計ジャッジ時間 1,396 ms
ジャッジサーバーID
(参考情報)
judge2 / judge1
このコードへのチャレンジ
(要ログイン)
ファイルパターン 結果
other AC * 2
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 #
プレゼンテーションモードにする

#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 <functional>
#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;
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 {
signed a = x, b = MOD, u = 1, v = 0;
while(b) {
signed t = a / b;
a -= t * b; std::swap(a, b);
u -= t * v; std::swap(u, v);
}
if(u < 0) u += Mod;
ModInt res; res.x = (unsigned)u;
return res;
}
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<1000000007> mint;
vector<mint> doDP(const int a[6], int n) {
int maxX = a[5] * n;
vector<vector<mint> > dp(n+1, vector<mint>(maxX+1));
dp[0][0] = 1;
rep(k, 6) {
int t = a[k];
for(int i = n; i >= 0; -- i) {
int maxx = k == 0 ? 0 : i * a[k-1];
rer(j, 0, maxx) {
mint x = dp[i][j];
if(x.get() == 0) continue;
rer(l, 1, n-i)
dp[i+l][j + l * t] += x;
}
}
}
return dp[n];
}
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;
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; }
};
Polynomial powmod(Polynomial a, Polynomial m, unsigned long long k) {
Polynomial r = Polynomial::One();
while(k) {
if(k & 1) r = r * a % m;
a = a * a % m;
k >>= 1;
}
return r;
}
vector<mint> solveSmall(int N, const vector<mint> &ways) {
vector<mint> dp(N+1);
dp[0] = 1;
int X = (int)ways.size() - 1;
rep(i, N) {
mint x = dp[i];
if(x.get() == 0) continue;
rer(j, 1, X)
dp[min(N, i + j)] += x * ways[j];
}
return dp;
}
int main() {
long long N;
int P, C;
while(~scanf("%lld%d%d", &N, &P, &C)) {
const int primes[6] = { 2, 3, 5, 7, 11, 13 };
const int composites[6] = { 4, 6, 8, 9, 10, 12 };
vector<mint> cntP = doDP(primes, P);
vector<mint> cntC = doDP(composites, C);
int X = P * primes[5] + C * composites[5];
vector<mint> ways(X+1);
rep(i, cntP.size()) rep(j, cntC.size())
ways[i + j] += cntP[i] * cntC[j];
// rer(i, 0, 100)
// cerr << "ans " << i << " = " << solveSmall(i, ways)[i].get() << endl;
if(N <= X * 2) {
vector<mint> v = solveSmall((int)N, ways);
mint ans = v[(int)N];
printf("%d\n", ans.get());
continue;
}
vector<mint> firstX = solveSmall(X, ways);
Polynomial f(X+1);
f.coef[X] = 1;
rer(i, 1, X) f.coef[X - i] = -ways[i];
Polynomial x(2); x.coef[1] = 1;
/*
{ Polynomial d = Polynomial::One();
rep(k, 30) {
mint sum;
rer(j, 0, X)
sum += d[j] * firstX[j];
cerr << "a " << k << ": " << sum.get() << endl;
d = d * x;
d = d % f;
}
}*/
vector<mint> lastX(X);
/*
vector<mint> v = solveSmall(N + 2, ways);
rep(i, X)
lastX[i] = v[N - X + i];
*/
// /*
Polynomial d = powmod(x, f, N - X);
rep(i, X) {
mint sum;
rer(j, 0, X)
sum += d[j] * firstX[j];
lastX[i] = sum;
// cerr << N - X + i << ": " << sum.get() << endl;
d = d * x;
d = d % f;
}
// */
mint ans;
rep(i, X) {
mint x = lastX[i];
rer(j, X - i, X)
ans += x * ways[j];
}
printf("%d\n", ans.get());
}
return 0;
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX
0