結果

問題 No.720 行列のできるフィボナッチ数列道場 (2)
ユーザー saksak
提出日時 2020-07-23 15:02:48
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 4 ms / 2,000 ms
コード長 2,911 bytes
コンパイル時間 2,574 ms
コンパイル使用メモリ 209,372 KB
最終ジャッジ日時 2025-01-12 04:13:52
ジャッジサーバーID
(参考情報)
judge3 / judge2
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ファイルパターン 結果
sample AC * 3
other AC * 20
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 #

#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
typedef pair<ll, ll> p_ll;

template<class T>
void debug(T itr1, T itr2) { auto now = itr1; while(now<itr2) { cout << *now << " "; now++; } cout << endl; }
#define repr(i,from,to) for (int i=(int)from; i<(int)to; i++)
#define all(vec) vec.begin(), vec.end()
#define rep(i,N) repr(i,0,N)
#define per(i,N) for (int i=(int)N-1; i>=0; i--)

const ll MOD = pow(10,9)+7;
const ll LLINF = pow(2,61)-1;
const int INF = pow(2,30)-1;

vector<ll> fac;
void c_fac(int x=pow(10,6)+10) { fac.resize(x,true); rep(i,x) fac[i] = i ? (fac[i-1]*i)%MOD : 1; }
ll inv(ll a, ll m=MOD) { ll b = m, x = 1, y = 0; while (b!=0) { int d = a/b; a -= b*d; swap(a,b); x -= y*d; swap(x,y); } return (x+m)%m; }
ll nck(ll n, ll k) { return fac[n]*inv(fac[k]*fac[n-k]%MOD)%MOD; }
ll gcd(ll a, ll b) { if (a<b) swap(a,b); return b==0 ? a : gcd(b, a%b); }
ll lcm(ll a, ll b) { return a/gcd(a,b)*b; }

// ----------------------------------------------------------------------
// ----------------------------------------------------------------------

vector<vector<ll>> matdot(vector<vector<ll>> A, vector<vector<ll>> B) {
  if (A[0].size()!=B.size()) return {{}};
  ll h = A.size(), w = B[0].size(), x = A[0].size();
  vector<vector<ll>> result(h,vector<ll>(w,0));
  rep(i,h) rep(j,w) rep(k,x) result[i][j] = (result[i][j] + A[i][k]*B[k][j])%MOD;
  return result;
}

vector<vector<ll>> matpow(vector<vector<ll>> A, ll n) {
  if (A.size()!=A[0].size()) return {{}};
  int N = A.size();
  vector<vector<ll>> result(N,vector<ll>(N,0)), now;
  copy(all(A),back_inserter(now));
  rep(i,N) result[i][i] = 1;
  ll p2 = 1; 
  while (n>=p2) {
    if (n&p2) result = matdot(result,now);
    now = matdot(now,now); p2 *= 2;
  }
  return result;
}

// ----------------------------------------------------------------------
// ----------------------------------------------------------------------

int main() {
  ll N, M; cin >> N >> M;
  vector<vector<ll>> mat = {{0,1}, {1,1}};
  vector<vector<ll>> matm = matpow(mat,M);
  // rep(i,2) debug(all(matm[i]));

  vector<vector<ll>> matme = {{(matm[0][0]-1+MOD)%MOD, matm[0][1]}, {matm[1][0], (matm[1][1]-1+MOD)%MOD}};
  vector<vector<ll>> invme = {{matme[1][1], (MOD-matme[0][1])%MOD}, {(MOD-matme[1][0])%MOD, matme[0][0]}};
  ll adbc = (MOD+(matme[0][0]*matme[1][1] - matme[0][1]*matme[1][0])%MOD)%MOD;
  rep(i,2) rep(j,2) invme[i][j] = invme[i][j]*inv(adbc) % MOD;
  // rep(i,2) debug(all(invme[i]));
  // cout << adbc << endl;

  vector<vector<ll>> matmn = matpow(matm, N);
  vector<vector<ll>> matmne = {{(matmn[0][0]-1+MOD)%MOD, matmn[0][1]}, {matmn[1][0], (matmn[1][1]-1+MOD)%MOD}};
  // rep(i,2) debug(all(matmne[i]));

  vector<vector<ll>> matres = {{1,0},{0,1}};
  matres = matdot(matres, matm);
  matres = matdot(matres, matmne);
  matres = matdot(matres, invme);

  ll result = matres[0][1];
  cout << result << endl;
  return 0;
}
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