mirror of
https://github.com/TheAlgorithms/C
synced 2024-11-22 13:31:21 +03:00
60 lines
1.6 KiB
C
60 lines
1.6 KiB
C
/**
|
||
* @file
|
||
* @brief Finding Fibonacci number of any `n` number using [Binet's closed form formula](https://en.wikipedia.org/wiki/Fibonacci_number#Binet's_formula)
|
||
* compute \f$f_{nth}\f$ Fibonacci number using the binet's formula:
|
||
* Fn = 1√5 * (1+√5 / 2)^n+1 − 1√5 * (1−√5 / 2)^n+1
|
||
* @author [GrandSir](https://github.com/GrandSir/)
|
||
*/
|
||
|
||
#include <math.h> /// for pow and sqrt
|
||
#include <stdio.h> /// for printf
|
||
#include <assert.h> /// for assert
|
||
|
||
/**
|
||
* @param n index of number in Fibonacci sequence
|
||
* @returns nth value of fibonacci sequence for all n >= 0
|
||
*/
|
||
int fib(unsigned int n) {
|
||
float seq = (1 / sqrt(5) * pow(((1 + sqrt(5)) / 2), n + 1)) - (1 / sqrt(5) * pow(((1 - sqrt(5)) / 2), n + 1));
|
||
|
||
// removing unnecessary fractional part by implicitly converting float to int
|
||
return seq;
|
||
}
|
||
|
||
/**
|
||
* @brief Self-test implementations
|
||
* @returns void
|
||
*/
|
||
static void test () {
|
||
/* this ensures that the first 10 number of fibonacci sequence
|
||
* (1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89)
|
||
* matches with algorithm
|
||
*/
|
||
assert(fib(0) == 1);
|
||
assert(fib(1) == 1);
|
||
assert(fib(2) == 2);
|
||
assert(fib(3) == 3);
|
||
assert(fib(4) == 5);
|
||
assert(fib(5) == 8);
|
||
assert(fib(6) == 13);
|
||
assert(fib(7) == 21);
|
||
assert(fib(8) == 34);
|
||
assert(fib(9) == 55);
|
||
assert(fib(10) == 89);
|
||
|
||
printf("All tests have successfully passed!\n");
|
||
}
|
||
|
||
/**
|
||
* @brief Main function
|
||
* @returns 0 on exit
|
||
*/
|
||
int main() {
|
||
test(); // run self-test implementations
|
||
|
||
for(int i = 0; i <= 10; i++){
|
||
printf("%d. fibonacci number is: %d\n", i, fib(i));
|
||
}
|
||
return 0;
|
||
}
|