fibonacci_sum.cpp File Reference

An algorithm to calculate the sum of Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\). More...

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

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Namespaces
namespace	math
	for IO operations
namespace	fibonacci_sum
	Functions for the sum of the Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\).

Typedefs
using	math::fibonacci_sum::matrix = std::vector<std::vector<uint64_t> >

Functions
math::fibonacci_sum::matrix	math::fibonacci_sum::multiply (const math::fibonacci_sum::matrix &T, const math::fibonacci_sum::matrix &A)
math::fibonacci_sum::matrix	math::fibonacci_sum::power (math::fibonacci_sum::matrix T, uint64_t ex)
uint64_t	math::fibonacci_sum::result (uint64_t n)
uint64_t	math::fibonacci_sum::fiboSum (uint64_t n, uint64_t m)
static void	test ()
int	main ()
	Main function.

Detailed Description

An algorithm to calculate the sum of Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\).

An algorithm to calculate the sum of Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\) where \(\mathrm{F}(i)\) denotes the i-th Fibonacci Number . Note that F(0) = 0 and F(1) = 1. The value of the sum is calculated using matrix exponentiation. Reference source: https://stackoverflow.com/questions/4357223/finding-the-sum-of-fibonacci-numbers

Author

Sarthak Sahu

Function Documentation

fiboSum()

uint64_t math::fibonacci_sum::fiboSum	(	uint64_t	n,
		uint64_t	m )

Function to compute sum of fibonacci sequence from n to m.

Parameters

n	start of sequence
m	end of sequence

Returns

uint64_t the sum of sequence

                                         {
    return (result(m + 2) - result(n + 1));
}

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main()

int main

(

void

)

Main function.

Returns

0 on exit

           {
    test();  // execute the tests
    return 0;
}

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multiply()

math::fibonacci_sum::matrix math::fibonacci_sum::multiply	(	const math::fibonacci_sum::matrix &	T,
		const math::fibonacci_sum::matrix &	A )

Function to multiply two matrices

Parameters

T	matrix 1
A	martix 2

Returns

resultant matrix

                                                                       {
    math::fibonacci_sum::matrix result(2, std::vector<uint64_t>(2, 0));
 
    // multiplying matrices
    result[0][0] = T[0][0] * A[0][0] + T[0][1] * A[1][0];
    result[0][1] = T[0][0] * A[0][1] + T[0][1] * A[1][1];
    result[1][0] = T[1][0] * A[0][0] + T[1][1] * A[1][0];
    result[1][1] = T[1][0] * A[0][1] + T[1][1] * A[1][1];
 
    return result;
}

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power()

math::fibonacci_sum::matrix math::fibonacci_sum::power	(	math::fibonacci_sum::matrix	T,
		uint64_t	ex )

Function to compute A^n where A is a matrix.

Parameters

T	matrix
ex	power

Returns

resultant matrix

                                                                      {
    math::fibonacci_sum::matrix A{{1, 1}, {1, 0}};
    if (ex == 0 || ex == 1) {
        return T;
    }
 
    T = power(T, ex / 2);
    T = multiply(T, T);
    if (ex & 1) {
        T = multiply(T, A);
    }
    return T;
}

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result()

uint64_t math::fibonacci_sum::result

(

uint64_t

n

)

Function to compute sum of fibonacci sequence from 0 to n.

Parameters

n

number

Returns

uint64_t ans, the sum of sequence

                            {
    math::fibonacci_sum::matrix T{{1, 1}, {1, 0}};
    T = power(T, n);
    uint64_t ans = T[0][1];
    ans = (ans - 1);
    return ans;
}

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test()

static void test ( )

static

Function for testing fiboSum function. test cases and assert statement.

Returns

void

                   {
    uint64_t n = 0, m = 3;
    uint64_t test_1 = math::fibonacci_sum::fiboSum(n, m);
    assert(test_1 == 4);
    std::cout << "Passed Test 1!" << std::endl;
 
    n = 3;
    m = 5;
    uint64_t test_2 = math::fibonacci_sum::fiboSum(n, m);
    assert(test_2 == 10);
    std::cout << "Passed Test 2!" << std::endl;
 
    n = 5;
    m = 7;
    uint64_t test_3 = math::fibonacci_sum::fiboSum(n, m);
    assert(test_3 == 26);
    std::cout << "Passed Test 3!" << std::endl;
 
    n = 7;
    m = 10;
    uint64_t test_4 = math::fibonacci_sum::fiboSum(n, m);
    assert(test_4 == 123);
    std::cout << "Passed Test 4!" << std::endl;
 
    n = 9;
    m = 12;
    uint64_t test_5 = math::fibonacci_sum::fiboSum(n, m);
    assert(test_5 == 322);
    std::cout << "Passed Test 5!" << std::endl;
}

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