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Update math/fibonacci_sum.cpp

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Co-authored-by: David Leal <halfpacho@gmail.com>
This commit is contained in:
Sarthak Sahu
2020-10-21 02:44:25 +05:30
committed by SarthakSahu1009
parent 28746605e8
commit abbc0456cd
1 changed files with 75 additions and 75 deletions
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math/fibonacci_sum.cpp
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@@ -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<std::vector<int> > multiply(std::vector<std::vector<int> > T, std::vector<std::vector<int> > A) {
std::vector<std::vector<int> > result(2,std::vector<int>(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<std::vector<int> > multiply(std::vector<std::vector<int> > T, std::vector<std::vector<int> > A) {
std::vector<std::vector<int> > result(2,std::vector<int>(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<std::vector<int> > power(std::vector<std::vector<int> > T, int ex) {
std::vector<std::vector<int> > 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<std::vector<int> > power(std::vector<std::vector<int> > T, int ex) {
std::vector<std::vector<int> > 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<std::vector<int> > 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<std::vector<int> > 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;
}