結果
問題 | No.194 フィボナッチ数列の理解(1) |
ユーザー | fumiphys |
提出日時 | 2019-06-10 22:27:02 |
言語 | C++14 (gcc 12.3.0 + boost 1.83.0) |
結果 |
AC
|
実行時間 | 20 ms / 5,000 ms |
コード長 | 7,338 bytes |
コンパイル時間 | 2,055 ms |
コンパイル使用メモリ | 179,728 KB |
実行使用メモリ | 11,136 KB |
最終ジャッジ日時 | 2024-10-06 00:59:31 |
合計ジャッジ時間 | 3,661 ms |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
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テストケース
テストケース表示入力 | 結果 | 実行時間 実行使用メモリ |
---|---|---|
testcase_00 | AC | 2 ms
5,248 KB |
testcase_01 | AC | 2 ms
5,248 KB |
testcase_02 | AC | 18 ms
5,248 KB |
testcase_03 | AC | 3 ms
5,248 KB |
testcase_04 | AC | 8 ms
5,248 KB |
testcase_05 | AC | 7 ms
5,248 KB |
testcase_06 | AC | 8 ms
5,248 KB |
testcase_07 | AC | 12 ms
5,248 KB |
testcase_08 | AC | 3 ms
5,248 KB |
testcase_09 | AC | 9 ms
5,248 KB |
testcase_10 | AC | 4 ms
5,248 KB |
testcase_11 | AC | 4 ms
5,248 KB |
testcase_12 | AC | 6 ms
5,248 KB |
testcase_13 | AC | 3 ms
5,248 KB |
testcase_14 | AC | 2 ms
5,248 KB |
testcase_15 | AC | 14 ms
5,248 KB |
testcase_16 | AC | 13 ms
5,248 KB |
testcase_17 | AC | 5 ms
5,248 KB |
testcase_18 | AC | 13 ms
5,248 KB |
testcase_19 | AC | 17 ms
5,248 KB |
testcase_20 | AC | 2 ms
5,248 KB |
testcase_21 | AC | 20 ms
11,136 KB |
testcase_22 | AC | 2 ms
5,248 KB |
testcase_23 | AC | 3 ms
5,248 KB |
testcase_24 | AC | 11 ms
6,912 KB |
testcase_25 | AC | 9 ms
6,656 KB |
testcase_26 | AC | 9 ms
6,400 KB |
testcase_27 | AC | 11 ms
7,296 KB |
testcase_28 | AC | 4 ms
5,248 KB |
testcase_29 | AC | 17 ms
10,368 KB |
testcase_30 | AC | 18 ms
5,248 KB |
testcase_31 | AC | 2 ms
5,248 KB |
testcase_32 | AC | 7 ms
5,248 KB |
testcase_33 | AC | 9 ms
5,248 KB |
testcase_34 | AC | 7 ms
5,248 KB |
testcase_35 | AC | 6 ms
5,248 KB |
testcase_36 | AC | 14 ms
5,248 KB |
testcase_37 | AC | 3 ms
5,248 KB |
testcase_38 | AC | 16 ms
5,248 KB |
testcase_39 | AC | 7 ms
5,248 KB |
ソースコード
// includes #include <bits/stdc++.h> // macros #define ll long long int #define pb emplace_back #define mk make_pair #define pq priority_queue #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define rep(i, n) FOR(i, 0, n) #define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--) #define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr) #define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr) #define vrep(v, i) for(int i = 0; i < (v).size(); i++) #define all(x) (x).begin(),(x).end() #define sz(x) ((int)(x).size()) #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end()) #define FI first #define SE second #define dump(a, n) for(int i = 0; i < n; i++)cout << a[i] << "\n "[i + 1 != n]; #define dump2(a, n, m) for(int i = 0; i < n; i++)for(int j = 0; j < m; j++)cout << a[i][j] << "\n "[j + 1 != m]; #define bit(n) (1LL<<(n)) #define INT(n) int n; cin >> n; #define LL(n) ll n; cin >> n; #define DOUBLE(n) double n; cin >> n; using namespace std; // types typedef pair<int, int> P; typedef pair<ll, int> Pl; typedef pair<ll, ll> Pll; typedef pair<double, double> Pd; typedef complex<double> cd; // constants const int inf = 1e9; const ll linf = 1LL << 50; const double EPS = 1e-10; const int mod = 1e9 + 7; const int dx[4] = {-1, 0, 1, 0}; const int dy[4] = {0, -1, 0, 1}; // solve template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;} template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;} template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;} template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} template<typename T> T extgcd(T a, T b, T &x, T &y){ T d = a; if(b != 0){ d = extgcd(b, a % b, y, x); y -= (a / b) * x; }else{ x = 1, y = 0; } return d; } template <typename T> T modinv(T a, T m){ long long x = 0, y = 0; extgcd<long long>(a, m, x, y); x %= m; if(x < 0)x += m; return x; } template <int MOD = int(1e9+7)> struct LMatrix{ vector<vector<long long>> v; int n, m; LMatrix(int n_, int m_ = -1): n(n_), m(m_){ if(m < 0)m = n; v.resize(n); for(int i = 0; i < n; i++)v[i].resize(m, 0); } void identity(){ assert(n == m); for(int i = 0; i < n; i++){ for(int j = 0; j < n; j++){ v[i][j] = (i == j ? 1: 0); } } } vector<long long> &operator[](size_t i){ return v[i]; } const vector<long long> &operator[](size_t i) const{ return v[i]; } LMatrix operator*(const LMatrix &r) const{ assert(m == r.n); int l = r.m; LMatrix res(n, l); for(int i = 0; i < n; i++){ for(int j = 0; j < l; j++){ res.v[i][j] = 0; for(int k = 0; k < m; k++){ res.v[i][j] = (res.v[i][j] + v[i][k] * r.v[k][j] % MOD) % MOD; } } } return res; } LMatrix operator+(const LMatrix &r) const{ assert(n == r.n); assert(m == r.m); LMatrix res(n, m); for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res[i][j] = (v[i][j] + r[i][j]) % MOD; } } return res; } LMatrix operator-(const LMatrix &r) const{ assert(n == r.n); assert(m == r.m); LMatrix res(n, m); for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res[i][j] = (v[i][j] - r[i][j]) % MOD; if(res[i][j] < 0)res[i][j] += MOD; } } return res; } template <typename T> LMatrix operator*(T a) const{ LMatrix res = *this; for(int i = 0; i < n; i++){ for(int j = 0; j < n; j++){ res[i][j] = a * res[i][j] % MOD; } } return res; } LMatrix inv2() const{ assert(n == 2 && m == 2); long long det = v[0][0] * v[1][1] % MOD - v[0][1] * v[1][0] % MOD; if(det < 0)det += MOD; assert(det != 0); LMatrix res(2, 2); long long inv = modinv(det, (long long)MOD); res[0][0] = v[1][1]; res[1][1] = v[0][0]; res[1][0] = - v[1][0]; res[0][1] = - v[0][1]; for(int i = 0; i < n; i++){ for(int j = 0; j < m; j++){ res[i][j] %= MOD; res[i][j] = res[i][j] * inv % MOD; if(res[i][j] < 0)res[i][j] += MOD; } } return res; } }; template <typename T, int MOD = int(1e9+7)> LMatrix<MOD> operator*(T a, const LMatrix<MOD> b){ return b * a; } template <int MOD = int(1e9+7)> LMatrix<MOD> powerm(LMatrix<MOD> &a, long long n){ long long tmp = n; LMatrix<MOD> curr = a; LMatrix<MOD> res(a.n); res.identity(); while(tmp){ if(tmp % 2 == 1){ res = res * curr; } curr = curr * curr; tmp /= 2; } return res; } int main(int argc, char const* argv[]) { ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20); INT(n); LL(k); vector<ll> a(n); cin >> a; if(n > 30){ vector<ll> ans(k, 0); ll res = 0; rep(i, n)ans[i] = a[i]; rep(i, n)res += a[i]; ans[n] = res; res += ans[n]; FOR(i, n + 1, k){ ans[i] = (ans[i-1] * 2 % mod - ans[i-n-1]) % mod; if(ans[i] < 0)ans[i] += mod; res = (res + ans[i]) % mod; } cout << ans[k-1] << " " << res << endl; }else{ LMatrix<> l(n, n); rep(i, n)l[0][i] = 1; FOR(i, 1, n)l[i][i-1] = 1; auto LP = powerm(l, k - n); ll res = 0; rep(i, n)res = (res + LP[0][i] * a[n-1-i] % mod) % mod; LMatrix<> ls(n + 1, n + 1); ls[0][0] = 2, ls[0][n] = -1; FOR(i, 1, n + 1)ls[i][i-1] = 1; auto LSP = powerm(ls, k - n); ll res2 = 0; vector<ll> asum(n, 0); rep(i, n)asum[i] = a[i] + (i > 0 ? asum[i-1]: 0); rep(i, n)res2 = (res2 + LSP[0][i] * asum[n-1-i] % mod) % mod; if(res2 < 0)res2 += mod; cout << res << " " << res2 << endl; } return 0; }