洛谷 P1962 斐波那契数列

题目链接：https://www.luogu.org/problemnew/show/P1962

题目链接：https://www.nowcoder.com/practice/376282a6682a4005973cde7b3df69584?tpId=101&tqId=33251&tPage=1&rp=1&ru=/ta/programmer-code-interview-guide&qru=/ta/programmer-code-interview-guide/question-ranking

题目链接：https://www.nowcoder.com/practice/fd66768dc08748f2be6626f07a02e466?tpId=101&tqId=33252&tPage=1&rp=1&ru=/ta/programmer-code-interview-guide&qru=/ta/programmer-code-interview-guide/question-ranking

题目大意：

　　略

分析：

　　由于数据规模很大，需要用矩阵快速幂来解。

代码如下：

 #include <bits/stdc++.h>
 using namespace std;
 
 #define INIT() ios::sync_with_stdio(false);cin.tie(0);cout.tie(0);
 #define Rep(i,n) for (int i = 0; i < (int)(n); ++i)
 #define For(i,s,t) for (int i = (int)(s); i <= (int)(t); ++i)
 #define rFor(i,t,s) for (int i = (int)(t); i >= (int)(s); --i)
 #define ForLL(i, s, t) for (LL i = LL(s); i <= LL(t); ++i)
 #define rForLL(i, t, s) for (LL i = LL(t); i >= LL(s); --i)
 #define foreach(i,c) for (__typeof(c.begin()) i = c.begin(); i != c.end(); ++i)
 #define rforeach(i,c) for (__typeof(c.rbegin()) i = c.rbegin(); i != c.rend(); ++i)
 
 #define pr(x) cout << #x << " = " << x << "  "
 #define prln(x) cout << #x << " = " << x << endl
 
 #define LOWBIT(x) ((x)&(-x))
 
 #define ALL(x) x.begin(),x.end()
 #define INS(x) inserter(x,x.begin())
 #define UNIQUE(x) x.erase(unique(x.begin(), x.end()), x.end())
 #define REMOVE(x, c) x.erase(remove(x.begin(), x.end(), c), x.end()); // 删去 x 中所有 c
 #define TOLOWER(x) transform(x.begin(), x.end(), x.begin(),::tolower);
 #define TOUPPER(x) transform(x.begin(), x.end(), x.begin(),::toupper);
 
 #define ms0(a) memset(a,0,sizeof(a))
 #define msI(a) memset(a,0x3f,sizeof(a))
 #define msM(a) memset(a,-1,sizeof(a))
 
 #define MP make_pair
 #define PB push_back
 #define ft first
 #define sd second
 
 template<typename T1, typename T2>
 istream &operator>>(istream &in, pair<T1, T2> &p) {
     in >> p.first >> p.second;
     return in;
 }
 
 template<typename T>
 istream &operator>>(istream &in, vector<T> &v) {
     for (auto &x: v)
         in >> x;
     return in;
 }
 
 template<typename T>
 ostream &operator<<(ostream &out, vector<T> &v) {
     Rep(i, v.size()) out << v[i] << " \n"[i == v.size() - ];
     return out;
 }
 
 template<typename T1, typename T2>
 ostream &operator<<(ostream &out, const std::pair<T1, T2> &p) {
     out << "[" << p.first << ", " << p.second << "]" << "\n";
     return out;
 }
 
 inline int gc(){
     static const int BUF = 1e7;
     static char buf[BUF], *bg = buf + BUF, *ed = bg;
 
     if(bg == ed) fread(bg = buf, , BUF, stdin);
     return *bg++;
 } 
 
 inline int ri(){
     int x = , f = , c = gc();
     for(; c<||c>; f = c=='-'?-:f, c=gc());
     for(; c>&&c<; x = x* + c - , c=gc());
     return x*f;
 }
 
 template<class T>
 inline string toString(T x) {
     ostringstream sout;
     sout << x;
     return sout.str();
 }
 
 inline int toInt(string s) {
     int v;
     istringstream sin(s);
     sin >> v;
     return v;
 }
 
 //min <= aim <= max
 template<typename T>
 inline bool BETWEEN(const T aim, const T min, const T max) {
     return min <= aim && aim <= max;
 }
 
 typedef unsigned int uI;
 typedef long long LL;
 typedef unsigned long long uLL;
 typedef vector< int > VI;
 typedef vector< bool > VB;
 typedef vector< char > VC;
 typedef vector< double > VD;
 typedef vector< string > VS;
 typedef vector< LL > VL;
 typedef vector< VI > VVI;
 typedef vector< VB > VVB;
 typedef vector< VS > VVS;
 typedef vector< VL > VVL;
 typedef vector< VVI > VVVI;
 typedef vector< VVL > VVVL;
 typedef pair< int, int > PII;
 typedef pair< LL, LL > PLL;
 typedef pair< int, string > PIS;
 typedef pair< string, int > PSI;
 typedef pair< string, string > PSS;
 typedef pair< double, double > PDD;
 typedef vector< PII > VPII;
 typedef vector< PLL > VPLL;
 typedef vector< VPII > VVPII;
 typedef vector< VPLL > VVPLL;
 typedef vector< VS > VVS;
 typedef map< int, int > MII;
 typedef unordered_map< int, int > uMII;
 typedef map< LL, LL > MLL;
 typedef map< string, int > MSI;
 typedef map< int, string > MIS;
 typedef set< int > SI;
 typedef stack< int > SKI;
 typedef deque< int > DQI;
 typedef queue< int > QI;
 typedef priority_queue< int > PQIMax;
 typedef priority_queue< int, VI, greater< int > > PQIMin;
 const double EPS = 1e-;
 const LL inf = 0x7fffffff;
 const LL infLL = 0x7fffffffffffffffLL;
 const LL mod = 1e9 + ;
 const int maxN = 1e6 + ;
 const LL ONE = ;
 const LL evenBits = 0xaaaaaaaaaaaaaaaa;
 const LL oddBits = 0x5555555555555555;
 
 struct Matrix{
     int row, col;
     LL MOD;
     VVL mat;
 
     Matrix(int r, int c, LL p = mod) : row(r), col(c), MOD(p) {
         mat.assign(r, VL(c, ));
     }
     Matrix(const Matrix &x, LL p = mod) : MOD(p){
         mat = x.mat;
         row = x.row;
         col = x.col;
     }
     Matrix(const VVL &A, LL p = mod) : MOD(p){
         mat = A;
         row = A.size();
         col = A[].size();
     }
 
     // x * 单位阵
     inline void E(int x = ) {
         assert(row == col);
         Rep(i, row) mat[i][i] = x;
     }
 
     inline VL& operator[] (int x) {
         assert(x >=  && x < row);
         return mat[x];
     }
 
     inline Matrix operator= (const VVL &x) {
         row = x.size();
         col = x[].size();
         mat = x;
         return *this;
     }
 
     inline Matrix operator+ (const Matrix &x) {
         assert(row == x.row && col == x.col);
         Matrix ret(row, col);
         Rep(i, row) {
             Rep(j, col) {
                 ret.mat[i][j] = mat[i][j] + x.mat[i][j];
                 ret.mat[i][j] %= MOD;
             }
         }
         return ret;
     }
 
     inline Matrix operator* (const Matrix &x) {
         assert(col == x.row);
         Matrix ret(row, x.col);
         Rep(k, x.col) {
             Rep(i, row) {
                 if(mat[i][k] == ) continue;
                 Rep(j, x.col) {
                     ret.mat[i][j] += mat[i][k] * x.mat[k][j];
                     ret.mat[i][j] %= MOD;
                 }
             }
         }
         return ret;
     }
 
     inline Matrix operator*= (const Matrix &x) { return *this = *this * x; }
     inline Matrix operator+= (const Matrix &x) { return *this = *this + x; }
 };
 
 // 矩阵快速幂，计算x^y
 inline Matrix mat_pow_mod(Matrix x, LL y) {
     Matrix ret(x.row, x.col);
     ret.E();
     while(y){
         if(y & ) ret *= x;
         x *= x;
         y >>= ;
     }
     return ret;
 }
 
 LL N;
 Matrix ans(VVL({{, }, {, }}));
 
 int main(){
     //freopen("MyOutput.txt","w",stdout);
     //freopen("input.txt","r",stdin);
     //INIT();
     scanf("%lld", &N);
     ans = mat_pow_mod(ans, N);
     printf("%lld\n", ans.mat[][]);
     return ;
 }