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 |
![]() |
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 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
other | AC * 2 |
ソースコード
#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 0x3f3f3f3f3f3f3f3fLLusing 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 + 1int 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;}//naivePolynomial 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 divisionpair<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;}