Create fibonacci_formula.c (#961)

DIRECTORY.md

@@ -149,7 +149,7 @@
   * [Spirograph](https://github.com/TheAlgorithms/C/blob/master/graphics/spirograph.c)
 
 ## Greedy Approach
-  * [Djikstra](https://github.com/TheAlgorithms/C/blob/master/greedy_approach/djikstra.c)
+  * [Dijkstra](https://github.com/TheAlgorithms/C/blob/master/greedy_approach/dijkstra.c)
   * [Prim](https://github.com/TheAlgorithms/C/blob/master/greedy_approach/prim.c)
 
 ## Hash
@@ -267,6 +267,7 @@
   * [Fibonacci](https://github.com/TheAlgorithms/C/blob/master/misc/fibonacci.c)
   * [Fibonacci Dp](https://github.com/TheAlgorithms/C/blob/master/misc/fibonacci_dp.c)
   * [Fibonacci Fast](https://github.com/TheAlgorithms/C/blob/master/misc/fibonacci_fast.c)
+  * [Fibonacci Formula](https://github.com/TheAlgorithms/C/blob/master/misc/fibonacci_formula.c)
   * [Gcd](https://github.com/TheAlgorithms/C/blob/master/misc/gcd.c)
   * [Is Armstrong](https://github.com/TheAlgorithms/C/blob/master/misc/is_armstrong.c)
   * [Large Factorials](https://github.com/TheAlgorithms/C/blob/master/misc/large_factorials.c)

misc/fibonacci_formula.c

@@ -0,0 +1,59 @@
+/**
+ * @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;
+}