【Codeforces】450 B(div2)

题目链接：http://codeforces.com/problemset/problem/450/B

题意：

求这个的第n项。

题解：$f_{i+1} = f_i - f_{i-1} $

\begin{pmatrix} 1 & 1\\ -1 & 0 \end{pmatrix} *

\begin{pmatrix} f(n)& f(n-1) \end{pmatrix} =

\begin{pmatrix} f(n) - f(n-1) & f(n) \end{pmatrix}=

\begin{pmatrix} f(n+1) & f(n) \end{pmatrix}

代入前两项即可。

代码：

 #include<iostream>
 #include<cstdio>
 #include<cstring>
 using namespace std;
 #define ll long long
 const int maxn = ;
 const ll mod = 1e9+;

 ll n,p;

 struct Matrix{
     ll a[maxn][maxn];
     void init(){
         memset(a, , sizeof(a));
         for(int i = ; i <= maxn;i++){
             a[i][i] = ;
         }
     }
 };

 //矩阵乘法
 Matrix mul(Matrix a, Matrix b){
     Matrix ans;
     for(int i = ;i <= ;++i){
         for(int j = ;j <= ;++j){
             ans.a[i][j] = ;
             for(int k = ;k <= ;++k){
                 ans.a[i][j] = ans.a[i][j] % mod + a.a[i][k] * b.a[k][j] % mod;
                 ans.a[i][j] %= mod;
             }
         }
     }
     return ans;
 }

 //矩阵快速幂
 Matrix qpow(Matrix a,ll b){
     Matrix ans;
     ans.init();
     while(b){
         if(b & )
             ans = mul(ans,a);
         a = mul(a,a);
         b >>= ;
     }
     return ans;
 }

 void print(Matrix a){
     for(int i = ; i <= n;++i){
         for(int j = ;j <= n;++j){
             cout << a.a[i][j]%mod<< " ";
         }
         cout << endl;
     }
 }

 int main(){
     Matrix base;
     Matrix ans;
     int x,y,n;
     cin>>x>>y>>n;
     if(n == ){
         cout<<(mod + x) % mod<<endl;
         return ;
     }
     if( n == ){
         cout<<(mod + y) % mod<<endl;
         return ;
     }

     ans.a[][] = y;ans.a[][] = x;
     base.a[][] = ;base.a[][] = ;
     base.a[][] = -;base.a[][] = ;

     ans = mul(ans,qpow(base,n-));
     ll res = (mod + ans.a[][]) % mod;
     cout<<res<<endl;
     return ;
 }