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Fibonacci_Log(N)_MatrixExponentiation.cpp
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Fibonacci_Log(N)_MatrixExponentiation.cpp
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// Fibonacci Series using Optimized Method
#include <bits/stdc++.h>
using namespace std;
void multiply(int F[2][2], int M[2][2]);
void power(int F[2][2], int n);
// Function that returns nth Fibonacci number
int fib(int n)
{
int F[2][2] = {{1, 1}, {1, 0}};
if (n == 0)
return 0;
power(F, n - 1);
return F[0][0];
}
// Optimized version of power() in method 4
void power(int F[2][2], int n)
{
if(n == 0 || n == 1)
return;
int M[2][2] = {{1, 1}, {1, 0}};
power(F, n / 2);
multiply(F, F);
if (n % 2 != 0)
multiply(F, M);
}
void multiply(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;
}
// Driver code
int main()
{
int n = 9;
cout << fib(9);
getchar();
return 0;
}
// This code is contributed by Aayush Garg