Fib数列的递推

矩阵快速幂

#include <iostream>
 #include <cmath>
 #include <algorithm>
 using namespace std; 
 #define N 2
  int mod;
 
 
 #define int long long
  struct matrix {
  	int a[N+2][N+2];
  };
  matrix m1; 
  int n;
  
  void init_(matrix &x){
  	
  	int i,j;
  	for(i=1;i<=2;i++)
  	 for(j=1;j<=2;j++) {
  	 	 x.a[i][j]=0;
  	 	 if(i==j) x.a[i][j]=1;
  	 }
  }
  matrix mul(matrix &x,matrix &y){
 	int i,j,k;
 	matrix z;
 	
 	for(i=1;i<=2;i++)
 	 for(j=1;j<=2;j++){
 	 	z.a[i][j]=0;
 	 	for(k=1;k<=2;k++)
 	 	 z.a[i][j]+=x.a[i][k]*y.a[k][j], z.a[i][j]%=mod;
 	 }
 	
 	return z;
 }
   matrix ksm(matrix &x,int k){
 	matrix tmp=x, ans;
 	init_(ans);
 	
 	while(k){
 		if(k&1) ans=mul(ans,tmp);
 		
 		tmp=mul(tmp,tmp); 
 		k/=2;
 	}
 	return ans;
 }
 
  signed main(){
 	std::ios::sync_with_stdio(0);
 	cin>>n>>mod;
 	
 	for(int i=1;i<=N;i++)
 	 for(int j=1;j<=N;j++) m1.a[i][j]=1;
 	 m1.a[2][2]=0;
 	 
 	 if(n<=2){ 
 	 	cout<<1<<endl; return 0;
 	 }
 	 
 	 matrix ans =ksm(m1,n-2);
 	 cout<<(ans.a[1][1]+ans.a[2][1])%mod<<endl;
 	 
  }