#723478 (C++17) No.541 3 x N グリッド上のサイクルの個数

• 問題: No.541 3 x N グリッド上のサイクルの個数
• ユーザー: snrnsidy
• 提出日時: 2021-12-11 03:15:08
• 言語: C++17 (gcc 12.3.0 + boost 1.83.0)
• 結果: AC
• 実行時間: 2 ms / 2,000 ms
• コード長: 3,859 bytes
• コンパイル時間: 2,714 ms
• コンパイル使用メモリ: 219,832 KB
• 実行使用メモリ: 4,384 KB
• 最終ジャッジ日時: 2023-09-26 07:25:10
• 合計ジャッジ時間: 5,719 ms
• ジャッジサーバーID （参考情報）: judge15 / judge12

入力	結果	実行時間; 実行使用メモリ
testcase_00	AC	1 ms; 4,380 KB
testcase_01	AC	2 ms; 4,376 KB
testcase_02	AC	1 ms; 4,380 KB
testcase_03	AC	2 ms; 4,380 KB
testcase_04	AC	1 ms; 4,376 KB
testcase_05	AC	2 ms; 4,380 KB
testcase_06	AC	1 ms; 4,380 KB
testcase_07	AC	2 ms; 4,380 KB
testcase_08	AC	1 ms; 4,380 KB
testcase_09	AC	2 ms; 4,380 KB
testcase_10	AC	2 ms; 4,380 KB
testcase_11	AC	1 ms; 4,376 KB
testcase_12	AC	2 ms; 4,380 KB
testcase_13	AC	2 ms; 4,380 KB
testcase_14	AC	1 ms; 4,384 KB
testcase_15	AC	2 ms; 4,380 KB
testcase_16	AC	1 ms; 4,380 KB
testcase_17	AC	1 ms; 4,376 KB
testcase_18	AC	1 ms; 4,376 KB
testcase_19	AC	1 ms; 4,380 KB
testcase_20	AC	1 ms; 4,380 KB
testcase_21	AC	2 ms; 4,384 KB
testcase_22	AC	2 ms; 4,380 KB
testcase_23	AC	1 ms; 4,380 KB
testcase_24	AC	2 ms; 4,376 KB
testcase_25	AC	2 ms; 4,380 KB
testcase_26	AC	2 ms; 4,380 KB
testcase_27	AC	2 ms; 4,380 KB
testcase_28	AC	2 ms; 4,376 KB
testcase_29	AC	2 ms; 4,376 KB
testcase_30	AC	2 ms; 4,376 KB
testcase_31	AC	2 ms; 4,376 KB
testcase_32	AC	2 ms; 4,380 KB
testcase_33	AC	2 ms; 4,376 KB
testcase_34	AC	2 ms; 4,380 KB
testcase_35	AC	2 ms; 4,380 KB
testcase_36	AC	2 ms; 4,380 KB
testcase_37	AC	2 ms; 4,376 KB
testcase_38	AC	1 ms; 4,376 KB
testcase_39	AC	1 ms; 4,380 KB
testcase_40	AC	2 ms; 4,380 KB
testcase_41	AC	2 ms; 4,380 KB
testcase_42	AC	1 ms; 4,380 KB
testcase_43	AC	2 ms; 4,380 KB
testcase_44	AC	1 ms; 4,380 KB
testcase_45	AC	1 ms; 4,376 KB
testcase_46	AC	2 ms; 4,376 KB
testcase_47	AC	2 ms; 4,380 KB
testcase_48	AC	1 ms; 4,376 KB
testcase_49	AC	1 ms; 4,380 KB
testcase_50	AC	2 ms; 4,380 KB
testcase_51	AC	1 ms; 4,376 KB
testcase_52	AC	2 ms; 4,380 KB
testcase_53	AC	2 ms; 4,384 KB
testcase_54	AC	1 ms; 4,380 KB
testcase_55	AC	2 ms; 4,380 KB
testcase_56	AC	2 ms; 4,380 KB
testcase_57	AC	2 ms; 4,380 KB
testcase_58	AC	2 ms; 4,380 KB
testcase_59	AC	2 ms; 4,376 KB
testcase_60	AC	2 ms; 4,376 KB
testcase_61	AC	2 ms; 4,380 KB

コンパイルメッセージ

main.cpp: 関数 ‘std::vector<int> berlekamp_massey(std::vector<int>)’ 内:
main.cpp:32:44: 警告: ‘ld’ may be used uninitialized [-Wmaybe-uninitialized]
   32 |                 lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod;
      |                                        ~~~~^~~~~~~~~~~~~
main.cpp:19:17: 備考: ‘ld’ はここで定義されています
   19 |         int lf, ld;
      |                 ^~
main.cpp:33:32: 警告: ‘lf’ may be used uninitialized [-Wmaybe-uninitialized]
   33 |                 vector<int> c(i-lf-1);
      |                               ~^~~
main.cpp:19:13: 備考: ‘lf’ はここで定義されています
   19 |         int lf, ld;
      |             ^~

ソースコード

#include <bits/stdc++.h>
 
using namespace std;

const long long int MOD = 1e9 + 7;
const long long int mod = 1e9 + 7;
using lint = long long;
lint ipow(lint x, lint p){
	lint ret = 1, piv = x;
	while(p){
		if(p & 1) ret = ret * piv % mod;
		piv = piv * piv % mod;
		p >>= 1;
	}
	return ret;
}
vector<int> berlekamp_massey(vector<int> x){
	vector<int> ls, cur;
	int lf, ld;
	for(int i=0; i<x.size(); i++){
		lint t = 0;
		for(int j=0; j<cur.size(); j++){
			t = (t + 1ll * x[i-j-1] * cur[j]) % mod;
		}
		if((t - x[i]) % mod == 0) continue;
		if(cur.empty()){
			cur.resize(i+1);
			lf = i;
			ld = (t - x[i]) % mod;
			continue;
		}
		lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod;
		vector<int> c(i-lf-1);
		c.push_back(k);
		for(auto &j : ls) c.push_back(-j * k % mod);
		if(c.size() < cur.size()) c.resize(cur.size());
		for(int j=0; j<cur.size(); j++){
			c[j] = (c[j] + cur[j]) % mod;
		}
		if(i-lf+(int)ls.size()>=(int)cur.size()){
			tie(ls, lf, ld) = make_tuple(cur, i, (t - x[i]) % mod);
		}
		cur = c;
	}
	for(auto &i : cur) i = (i % mod + mod) % mod;
	return cur;
}
int get_nth(vector<int> rec, vector<int> dp, lint n){
	int m = rec.size();
	vector<int> s(m), t(m);
	s[0] = 1;
	if(m != 1) t[1] = 1;
	else t[0] = rec[0];
	auto mul = [&rec](vector<int> v, vector<int> w){
		int m = v.size();
		vector<int> t(2 * m);
		for(int j=0; j<m; j++){
			for(int k=0; k<m; k++){
				t[j+k] += 1ll * v[j] * w[k] % mod;
				if(t[j+k] >= mod) t[j+k] -= mod;
			}
		}
		for(int j=2*m-1; j>=m; j--){
			for(int k=1; k<=m; k++){
				t[j-k] += 1ll * t[j] * rec[k-1] % mod;
				if(t[j-k] >= mod) t[j-k] -= mod;
			}
		}
		t.resize(m);
		return t;
	};
	while(n){
		if(n & 1) s = mul(s, t);
		t = mul(t, t);
		n >>= 1;
	}
	lint ret = 0;
	for(int i=0; i<m; i++) ret += 1ll * s[i] * dp[i] % mod;
	return ret % mod;
}
int guess_nth_term(vector<int> x, lint n){
	if(n < x.size()) return x[n];
	vector<int> v = berlekamp_massey(x);
	if(v.empty()) return 0;
	return get_nth(v, x, n);
}
struct elem{int x, y, v;}; // A_(x, y) <- v, 0-based. no duplicate please..
vector<int> get_min_poly(int n, vector<elem> M){
	// smallest poly P such that A^i = sum_{j < i} {A^j \times P_j}
	vector<int> rnd1, rnd2;
	mt19937 rng(0x14004);
	auto randint = [&rng](int lb, int ub){
		return uniform_int_distribution<int>(lb, ub)(rng);
	};
	for(int i=0; i<n; i++){
		rnd1.push_back(randint(1, mod - 1));
		rnd2.push_back(randint(1, mod - 1));
	}
	vector<int> gobs;
	for(int i=0; i<2*n+2; i++){
		int tmp = 0;
		for(int j=0; j<n; j++){
			tmp += 1ll * rnd2[j] * rnd1[j] % mod;
			if(tmp >= mod) tmp -= mod;
		}
		gobs.push_back(tmp);
		vector<int> nxt(n);
		for(auto &i : M){
			nxt[i.x] += 1ll * i.v * rnd1[i.y] % mod;
			if(nxt[i.x] >= mod) nxt[i.x] -= mod;
		}
		rnd1 = nxt;
	}
	auto sol = berlekamp_massey(gobs);
	reverse(sol.begin(), sol.end());
	return sol;
}
lint det(int n, vector<elem> M){
	vector<int> rnd;
	mt19937 rng(0x14004);
	auto randint = [&rng](int lb, int ub){
		return uniform_int_distribution<int>(lb, ub)(rng);
	};
	for(int i=0; i<n; i++) rnd.push_back(randint(1, mod - 1));
	for(auto &i : M){
		i.v = 1ll * i.v * rnd[i.y] % mod;
	}
	auto sol = get_min_poly(n, M)[0];
	if(n % 2 == 0) sol = mod - sol;
	for(auto &i : rnd) sol = 1ll * sol * ipow(i, mod - 2) % mod;
	return sol;
}

vector <int> v;

vector <long long int> dp = {6,40,213,1049,5034,23984,114069};
vector <long long int> c = {9,-27,38,-29,11,1,-2};
int main(void) 
{
  cin.tie(0);
  ios::sync_with_stdio(false);

  long long int n;

  cin >> n;

  for(int i=7;i<=300;i++)
  {
    long long int sum = 0;
    for(int j=0;j<7;j++)
    {
      long long int val = c[j]*dp[i-1-j];
      val%=mod;
      sum += val;
      sum%=mod;
      if(sum < 0) sum += mod;
    }
    dp.push_back(sum);
  }

  for(int i=0;i<dp.size();i++)
  {
    v.push_back(dp[i]);
  }
  
  cout << guess_nth_term(v,n-1) << '\n';

  return 0;
}