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