Here you will find solutions of many problems on spoj. If you want solution of some problem which is not listed in blog or have doubt regarding any spoj problem (which i have solved) or any programming concept (data structure) you can mail me @ raj.nishant360@gmail.com
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Monday, July 14, 2014

FIBONACCI SERIES - IN LOGN TIME COMPLEXITY

Here, is code below to calculate nth term of Fibonacci series in log(n) time complexity. Do comment if find any bug. Thanks E-mail  :- surajjumpy@gmail.com


#include<iostream>

using namespace std;

void ope(int F[2][2], int M[2][2])
{
  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;
}

void mul(int M[2][2],int n)
{
    if(n <= 1)
        return;

    int F[2][2]={1,1,1,0};

    mul(M,n/2);

    ope(M,M);

    if(n&1)
        ope(M,F);
}

int fab(int n)
{
    if(n == 0)
        return 0;

    int M[2][2] = {1,1,1,0};

    mul(M,n-1);

    return M[0][0];
}

int main()
{
    int i;

    cout<<"Enter the term   no. ";
    cin>>i;

    cout<<"\nThe "<<i<<" term is    :   "<<fab(i);

    return 0;
}