IMPROVE fibonacci algorithms, add constant time solution

Author: Alex0Blackwell

Algorithms/fibonacci.cpp

@@ -2,6 +2,7 @@
 
 #include <vector>
 #include <map>
+#include <math.h>
 
 using namespace std;
 
@@ -77,6 +78,14 @@ int fib5(int num) {
   return res;
 }
 
+/** Constant time solution from solving a recurrence relation :) */
+int fib6(float num) {
+  float sqrt5 = sqrt(5);
+
+  return ( 1.0/sqrt5*pow(0.5+sqrt5/2.0, num) - 1.0/sqrt5*pow(0.5-sqrt5/2.0, num) );
+}
+
+
 
 int main(void) {
   int num;
@@ -91,5 +100,11 @@ int main(void) {
 
   cout << "fib 3: " << fib3(num) << endl;
 
+  cout << "fib 4: " << fib4(num) << endl;
+
+  cout << "fib 5: " << fib5(num) << endl;
+
+  cout << "fib 6: " << fib6(num) << endl;
+
   return 0;
 }

README.md

@@ -87,8 +87,8 @@ Click to expand the 43 *C++ programs*!
     - You are given the array paths, where paths[i] = [cityAi, cityBi] means there exists a direct path going from cityAi to cityBi. Return the destination city, that is, the city without any path outgoing to another city.
     - Leetcode problem [here](https://leetcode.com/problems/destination-city/)
   - fibonacci.cpp
-    - five ways of making the fibonacci sequence
-    - naive recursive, two memoized recursive, two sequential
+    - six ways of making the fibonacci sequence
+    - naive recursive, two memoized recursive, two sequential, one constant
   - flippingAnImage.cpp
     - Given a binary matrix A, we want to flip the image horizontally, then invert it, and return the resulting image.
     - Leetcode problem [here](https://leetcode.com/problems/flipping-an-image/)