結果

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 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 20 ms / 2,000 ms
コード長 3,859 bytes
コンパイル時間 2,419 ms
コンパイル使用メモリ 215,712 KB
最終ジャッジ日時 2025-01-26 07:41:39
ジャッジサーバーID
（参考情報） 		judge4 / judge2
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ファイルパターン 結果
other AC * 62
権限があれば一括ダウンロードができます
コンパイルメッセージ
main.cpp: In function ‘std::vector<int> berlekamp_massey(std::vector<int>)’:
main.cpp:33:32: warning: ‘lf’ may be used uninitialized [-Wmaybe-uninitialized]
   33 |                 vector<int> c(i-lf-1);
      |                               ~^~~
main.cpp:19:13: note: ‘lf’ was declared here
   19 |         int lf, ld;
      |             ^~
main.cpp:32:44: warning: ‘ld’ may be used uninitialized [-Wmaybe-uninitialized]
   32 |                 lint k = -(x[i] - t) * ipow(ld, mod - 2) % mod;
      |                                        ~~~~^~~~~~~~~~~~~
main.cpp:19:17: note: ‘ld’ was declared here
   19 |         int lf, ld;
      |                 ^~

ソースコード

diff #
プレゼンテーションモードにする

#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;
}
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