結果

問題 No.578 3 x N グリッド上のサイクルのサイズ(easy)
ユーザー pekempey
提出日時 2017-10-14 00:32:46
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 10 ms / 2,000 ms
コード長 4,347 bytes
コンパイル時間 1,139 ms
コンパイル使用メモリ 87,096 KB
実行使用メモリ 6,820 KB
最終ジャッジ日時 2024-11-17 11:58:09
合計ジャッジ時間 2,908 ms
ジャッジサーバーID
(参考情報)
judge1 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
other AC * 50
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 <iostream>
#include <algorithm>
#include <vector>
using namespace std;
constexpr int mod = 1e9 + 7;
struct Modint {
int n;
Modint(int n = 0) : n(n) {}
};
Modint operator+(Modint a, Modint b) { return Modint((a.n += b.n) >= mod ? a.n - mod : a.n); }
Modint operator-(Modint a, Modint b) { return Modint((a.n -= b.n) < 0 ? a.n + mod : a.n); }
Modint operator*(Modint a, Modint b) { return Modint(1LL * a.n * b.n % mod); }
Modint &operator+=(Modint &a, Modint b) { return a = a + b; }
Modint &operator-=(Modint &a, Modint b) { return a = a - b; }
Modint &operator*=(Modint &a, Modint b) { return a = a * b; }
Modint modinv(Modint n) {
if (n.n == 1) return 1;
return modinv(mod % n.n) * (mod - mod / n.n);
}
Modint operator/(Modint a, Modint b) { return a * modinv(b); }
// ref: https://en.wikipedia.org/wiki/Berlekamp%E2%80%93Massey_algorithm
std::vector<Modint> berlekamp_massey(std::vector<Modint> s) {
using K = Modint;
const int N = s.size();
std::vector<K> C(N);
std::vector<K> B(N);
C[0] = 1;
B[0] = 1;
int L = 0;
int m = 1;
K b = 1;
for (int n = 0; n < N; n++) {
K d = s[n];
for (int i = 1; i <= L; i++) d += C[i] * s[n - i];
if (d.n == 0) {
m++;
} else if (2 * L <= n) {
auto T = C;
for (int i = 0; i + m < N; i++) C[i + m] -= B[i] * (d / b);
L = n + 1 - L;
B = T;
b = d;
m = 1;
} else {
for (int i = 0; i + m < N; i++) C[i + m] -= B[i] * (d / b);
m++;
}
}
C.resize(L + 1);
reverse(C.begin(), C.end());
return C;
}
vector<Modint> poly_mod(vector<Modint> a, const vector<Modint> &m) {
const int n = m.size();
for (int i = a.size() - 1; i >= m.size(); i--) {
for (int j = 0; j < m.size(); j++) {
a[i - n + j] += a[i] * m[j];
}
}
a.resize(m.size());
return a;
}
// a*b mod m(x)
vector<Modint> poly_mul(const vector<Modint> &a, const vector<Modint> &b, const vector<Modint> &m) {
vector<Modint> ret(a.size() + b.size() - 1);
for (int i = 0; i < a.size(); i++) {
for (int j = 0; j < b.size(); j++) {
ret[i + j] += a[i] * b[j];
}
}
return poly_mod(ret, m);
}
// x^n mod m(x)
vector<Modint> nth_power(long long n, const vector<Modint> &m) {
vector<Modint> ret(1);
vector<Modint> x(2);
ret[0] = x[1] = 1;
while (n > 0) {
if (n & 1) ret = poly_mul(ret, x, m);
x = poly_mul(x, x, m);
n /= 2;
}
return poly_mod(ret, m);
}
int main() {
int c[10] = {0, 4, 4, 4, 6, 8, 8, 6, 8, 0};
vector<vector<int>> g = {
/* 0 */ {0, 1, 2, 3, 4, 5, 7, 8},
/* 0 */ {0, 0, 0, 0, 0, 0, 0, 0},
/* 1 */ {1, 4, 5, 8, 9},
/* 1 */ {1, 1, 1, 1, 0},
/* 2 */ {2, 4, 7, 8, 9},
/* 2 */ {1, 1, 1, 1, 0},
/* 3 */ {3, 5, 7, 8, 9},
/* 3 */ {1, 1, 1, 1, 0},
/* 4 */ {1, 2, 4, 7, 8, 9},
/* 4 */ {1, 1, 2, 1, 2, 0},
/* 5 */ {5, 8},
/* 5 */ {2, 2},
/* 6 */ {1, 3, 6, 9},
/* 6 */ {1, 1, 2, 0},
/* 7 */ {2, 3, 4, 7, 8, 9},
/* 7 */ {1, 1, 1, 2, 2, 0},
/* 8 */ {1, 2, 3, 4, 6, 7, 8, 9},
/* 8 */ {1, 1, 1, 2, 2, 2, 3, 0},
/* 9 */ {9},
/* 9 */ {0},
};
// std::vector<std::string> s = {" ", "o ", " o ", " o", "oo ", "o o", "o o", " oo", "ooo", " "};
// for (int i = 0; i < 10; i++) {
// for (int j = 0; j < g[i * 2].size(); j++) {
// int ii = g[i * 2][j];
// std::cout << s[i] << std::endl;
// std::cout << s[ii] << std::endl;
// std::cout << g[i * 2 + 1][j] << std::endl;
// std::cout << std::endl;
// }
// }
static Modint dp[55][10][1000];
dp[0][0][0] = 1;
for (int i = 0; i < 50; i++) {
for (int j = 0; j < 10; j++) {
for (int k = 0; k < 950; k++) {
for (int l = 0; l < g[j * 2].size(); l++) {
int jj = g[j * 2][l];
dp[i + 1][jj][k + c[jj] - 2 * g[j * 2 + 1][l]] += dp[i][j][k];
}
}
}
}
std::vector<Modint> a;
for (int i = 1; i <= 50; i++) {
Modint ret;
for (int j = 0; j < 1000; j++) {
ret += dp[i][9][j] * j;
}
a.push_back(ret);
cerr << ret.n << endl;
}
vector<Modint> m = berlekamp_massey(a);
m.pop_back();
for (int i = 0; i < m.size(); i++) {
m[i] *= mod - 1;
}
long long n;
cin >> n;
auto x = nth_power(n, m);
Modint ans;
for (int i = 0; i < x.size(); i++) {
ans += x[i] * a[i];
}
cout << ans.n << endl;
}
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