Check out example codes for "fibonacci series i logn java". It will help you in understanding the concepts better.

Code Example 1

class fibonacci 
{ 
      
    static int fib(int n) 
    { 
    int F[][] = new int[][]{{1,1},{1,0}}; 
    if (n == 0) 
        return 0; 
    power(F, n-1); 
      
       return F[0][0]; 
    } 
       
     /* Helper function that multiplies 2 matrices F and M of size 2*2, and 
     puts the multiplication result back to F[][] */
    static void multiply(int F[][], int M[][]) 
    { 
    int x =  F[0][0]*M[0][0] + F[0][1]*M[1][0]; 
    int y =  F[0][0]*M[0][1] + F[0][1]*M[1][1]; 
    int z =  F[1][0]*M[0][0] + F[1][1]*M[1][0]; 
    int w =  F[1][0]*M[0][1] + F[1][1]*M[1][1]; 
       
    F[0][0] = x; 
    F[0][1] = y; 
    F[1][0] = z; 
    F[1][1] = w; 
    } 
  
    /* Helper function that calculates F[][] raise to the power n and puts the 
    result in F[][] 
    Note that this function is designed only for fib() and won't work as general 
    power function */
    static void power(int F[][], int n) 
    { 
    int i; 
    int M[][] = new int[][]{{1,1},{1,0}}; 
      
    // n - 1 times multiply the matrix to {{1,0},{0,1}} 
    for (i = 2; i <= n; i++) 
        multiply(F, M); 
    } 
       
    /* Driver program to test above function */
    public static void main (String args[]) 
    { 
    int n = 9; 
    System.out.println(fib(n)); 
    } 
} 
/* This code is contributed by Rajat Mishra */

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