fibonacci_matrix_exponentiation.cpp File Reference

This program computes the N^th Fibonacci number in modulo mod input argument . More...

#include <iostream>
#include <vector>
#include <cassert>

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Functions
uint64_t	fibo (uint64_t n, uint64_t mod)
void	test ()
int	main ()

Detailed Description

This program computes the N^th Fibonacci number in modulo mod input argument .

Takes O(logn) time to compute nth Fibonacci number

Author

villayatali123

[unknown author]()

See also

fibonacci.cpp, fibonacci_fast.cpp, string_fibonacci.cpp, fibonacci_large.cpp

Function Documentation

fibo()

uint64_t fibo	(	uint64_t	n,
		uint64_t	mod
	)

This function finds nth fibonacci number in a given modulus

Parameters

n	nth fibonacci number
mod	modulo number

{
    std::vector<uint64_t> result(2,0);
    std::vector<std::vector<uint64_t>> transition(2,std::vector<uint64_t>(2,0));
    std::vector<std::vector<uint64_t>> Identity(2,std::vector<uint64_t>(2,0));
    n--;
    result[0]=1, result[1]=1;
    Identity[0][0]=1; Identity[0][1]=0;
    Identity[1][0]=0; Identity[1][1]=1;
     
    transition[0][0]=0;
    transition[1][0]=transition[1][1]=transition[0][1]=1;
    
    while(n)
    {
        if(n%2)
        {
            std::vector<std::vector<uint64_t>> res(2, std::vector<uint64_t>(2,0));
                    for(int i=0;i<2;i++)
            {
                for(int j=0;j<2;j++)
                {
                    for(int k=0;k<2;k++)
                        {
                            res[i][j]=(res[i][j]%mod+((Identity[i][k]%mod*transition[k][j]%mod))%mod)%mod;
                        }
                }
            }
                for(int i=0;i<2;i++)
            {
                for(int j=0;j<2;j++)
                {
                Identity[i][j]=res[i][j];
                }
                }
            n--;
        }
        else{
            std::vector<std::vector<uint64_t>> res1(2, std::vector<uint64_t>(2,0));
            for(int i=0;i<2;i++)
            {
                for(int j=0;j<2;j++)
                {
                    for(int k=0;k<2;k++)
                    {
                        res1[i][j]=(res1[i][j]%mod+((transition[i][k]%mod*transition[k][j]%mod))%mod)%mod;
                    }
                }
            }
            for(int i=0;i<2;i++)
            {
                for(int j=0;j<2;j++)
                {
                    transition[i][j]=res1[i][j];
                }
            } 
            n=n/2;
            }
    }
    return ((result[0]%mod*Identity[0][0]%mod)%mod+(result[1]%mod*Identity[1][0]%mod)%mod)%mod;
}

main()

int main

(

void

)

Main function

{
    test();
    uint64_t mod=1000000007;
    std::cout<<"Enter the value of N: ";
    uint64_t n=0; std::cin>>n; 
    std::cout<<n<<"th Fibonacci number in modulo " << mod << ": "<< fibo( n , mod) << std::endl;
}

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test()

void test

(

)

Function to test above algorithm

{
    assert(fibo(6, 1000000007 ) == 8);
    std::cout << "test case:1 passed\n";
    assert(fibo(5, 1000000007  ) == 5);
    std::cout << "test case:2 passed\n";
    assert(fibo(10 , 1000000007) == 55);
    std::cout << "test case:3 passed\n";
    assert(fibo(500 , 100) == 25);
    std::cout << "test case:3 passed\n";
    assert(fibo(500 , 10000) == 4125);
    std::cout << "test case:3 passed\n";
    std::cout << "--All tests passed--\n";
}

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