2018年湘潭大学程序设计竞赛 G- 又见斐波那契

推一推矩阵直接快速幂。

 #include<bits/stdc++.h>
 #define LL long long
 #define pii pair<int,int>
 #define mk make_pair
 #define fi first
 #define se second
 using namespace std;

 const int N=1e5+;
 const int M=1e5+;
 const int inf=0x3f3f3f3f;
 const LL INF=0x3f3f3f3f3f3f3f3f;
 const int mod=1e9+;

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

     Matrix operator * (const Matrix &B) const {
         Matrix C;
         for(int i = ; i < ; i++) {
             for(int j = ; j < ; j++) {
                 for(int k = ; k < ; k++) {
                     C.a[i][j] = (C.a[i][j] + a[i][k] * B.a[k][j]) % mod;
                 }
             }
         }
         return C;
     }

     Matrix operator ^ (const LL &p) const {
         Matrix A =  *this, res;
         res.init();
         LL t = p;
         while(t) {
             if(t & ) res = res * A;
             A = A * A; t >>= ;
         }
         return res;
     }
 }A;

 int main() {

     int a[][] = {
         {, , , , , },
         {, , , , , },
         {, , , , , },
         {, , , , , },
         {, , , , , },
         {, , , , , }
     };

     for(int i = ; i < ; i++)
         for(int j = ; j < ; j++)
             A.a[i][j] = a[i][j];

     int T; scanf("%d", &T);
     while(T--) {
         scanf("%lld", &n);
         if(n == ) {
             puts("");
             continue;
         }
         Matrix B = A ^ (n - );
         LL ans = B.a[][] + B.a[][] *  + B.a[][] *  + B.a[][] *  + B.a[][];
         ans %= mod;
         printf("%lld\n", ans);
     }
     return ;
 }
 /*
 */