diff --git a/math/fibonacci_sum.cpp b/math/fibonacci_sum.cpp index 4a3daa785..e8485b20d 100644 --- a/math/fibonacci_sum.cpp +++ b/math/fibonacci_sum.cpp @@ -2,9 +2,9 @@ * @file * @brief An algorithm to calculate the sum of Fibonacci Sequence: \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$ * @details An algorithm to calculate the sum of Fibonacci Sequence: \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$ where \f$\mathrm{F}(i)\f$ - * denotes the i-th Fibonacci Number . Note that F(0) = 0 and F(1) = 1. + * 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. - * + * @source https://stackoverflow.com/questions/4357223/finding-the-sum-of-fibonacci-numbers * @author [Sarthak Sahu](https://github.com/SarthakSahu1009) */ @@ -17,81 +17,81 @@ * @brief Mathematical algorithms */ namespace math { -/** - * @namespace fibonacci_sum - * @brief Functions for the sum of the Fibonacci Sequence: \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$ - */ -namespace fibonacci_sum { - /** - * Function to multiply two matrices - * @param T matrix 1 - * @param A martix 2 - * @returns resultant matrix + * @namespace fibonacci_sum + * @brief Functions for the sum of the Fibonacci Sequence: \f$\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\f$ */ - std::vector > multiply(std::vector > T, std::vector > A) { - - std::vector > result(2,std::vector(2)); - - // multiplying matrices - for(int i=0;i<2;i++) { - for(int j=0;j<2;j++) { - result[i][j]=0; - for(int k=0;k<2;k++) { - result[i][j]=(result[i][j]+(T[i][k]*A[k][j])); + namespace fibonacci_sum { + + /** + * Function to multiply two matrices + * @param T matrix 1 + * @param A martix 2 + * @returns resultant matrix + */ + std::vector > multiply(std::vector > T, std::vector > A) { + + std::vector > result(2,std::vector(2)); + + // multiplying matrices + for(int i=0;i<2;i++) { + for(int j=0;j<2;j++) { + result[i][j]=0; + for(int k=0;k<2;k++) { + result[i][j]=(result[i][j]+(T[i][k]*A[k][j])); + } } } + + return result; } - - return result; - } - - /** - * Function to compute A^n where A is a matrix. - * @param T matrix - * @param ex power - * @returns resultant matrix - */ - std::vector > power(std::vector > T, int ex) { - - std::vector > A{{1,1},{1,0}}; - if(ex == 0 || ex == 1) { + + /** + * Function to compute A^n where A is a matrix. + * @param T matrix + * @param ex power + * @returns resultant matrix + */ + std::vector > power(std::vector > T, int ex) { + + std::vector > 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; } - - T = power(T,ex/2); - T = multiply(T,T); - if(ex&1) { - T = multiply(T,A); + + /** + * Function to compute sum of fibonacci sequence from 0 to n. + * @param n number + * @returns int ans, the sum of sequence + */ + int result(int n) { + std::vector > T{{1,1},{1,0}}; + T = power(T,n); + int ans=T[0][1]; + ans = (ans - 1); + return ans; } - return T; - } - - /** - * Function to compute sum of fibonacci sequence from 0 to n. - * @param n number - * @returns int ans, the sum of sequence - */ - int result(int n) { - std::vector > T{{1,1},{1,0}}; - T = power(T,n); - int ans=T[0][1]; - ans = (ans - 1); - return ans; - } - - /** - * Function to compute sum of fibonacci sequence from n to m. - * @param n start of sequence - * @param m end of sequence - * @returns int the sum of sequence - */ - int fiboSum(int n,int m){ - return (result(m+2) - result(n+1)); - } -} // namespace fibonacci_sum + + /** + * Function to compute sum of fibonacci sequence from n to m. + * @param n start of sequence + * @param m end of sequence + * @returns int the sum of sequence + */ + int fiboSum(int n,int m){ + return (result(m+2) - result(n+1)); + } + } // namespace fibonacci_sum } // namespace math - + /** * Function for testing fiboSum function. * test cases and assert statement. @@ -99,30 +99,30 @@ namespace fibonacci_sum { */ static void test() { int n = 0, m = 3; - int test_1 = math::fiboSum(n,m); + int test_1 = math::fibonacci_sum::fiboSum(n,m); assert(test_1 == 4); std::cout << "Passed Test 1!" << std::endl; n = 3; m = 5; - int test_2 = math::fiboSum(n,m); + int test_2 = math::fibonacci_sum::fiboSum(n,m); assert(test_2 == 10); std::cout << "Passed Test 2!" << std::endl; n = 5; m = 7; - int test_3 = math::fiboSum(n,m); + int test_3 = math::fibonacci_sum::fiboSum(n,m); assert(test_3 == 26); std::cout << "Passed Test 3!" << std::endl; n = 7; m = 10; - int test_4 = math::fiboSum(n,m); + int test_4 = math::fibonacci_sum::fiboSum(n,m); assert(test_4 == 123); std::cout << "Passed Test 4!" << std::endl; n = 9; m = 12; - int test_5 = math::fiboSum(n,m); + int test_5 = math::fibonacci_sum::fiboSum(n,m); assert(test_5 == 322); std::cout << "Passed Test 5!" << std::endl; -} +} /** * @brief Main function @@ -130,6 +130,6 @@ static void test() { */ int main() { - test(); + test(); // execute the tests return 0; }