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 |
|
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 |
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ファイルパターン | 結果 |
---|---|
other | AC * 50 |
ソースコード
#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_algorithmstd::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;}