Added code and a few test cases

README.md

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+Fibonacci
+==
+
+The simple recursion:
+
+```
+fib(0) = 0
+fib(1) = 1
+fib(n) = fib(n - 1) + fib(n - 2)
+```
+
+e.g.:
+```
+fib(4) = [fib(3)] + [fib(2)] = [fib(2) + fib(1)] + [fib(1) + fib(0)] = [(fib(1) + fib(0)) + 1] + [1 + 0] = 3
+```
+
+With this approach we have to repeat a lot of calculations.
+
+With dynamic programming techniques we only calculate each value one time.
+
+
+Execution use cases
+==
+
+```
+Calculating Fibonacci of 10 recursively took 2.508100033082883e-05 seconds.
+Calculating Fibonacci of 10 with dynamic programming took 7.996000022103544e-06 seconds.
+```
+
+```
+Calculating Fibonacci of 20 recursively took 0.0030608279998887156 seconds.
+Calculating Fibonacci of 20 with dynamic programming took 2.0420000055310084e-05 seconds.
+```
+
+```
+Calculating Fibonacci of 30 recursively took 0.2475134070000422 seconds.
+Calculating Fibonacci of 30 with dynamic programming took 1.4527999610436382e-05 seconds.
+```
+
+```
+Calculating Fibonacci of 35 recursively took 2.728477938999731 seconds.
+Calculating Fibonacci of 35 with dynamic programming took 1.7669000044406857e-05 seconds.
+```
+
+```
+Calculating Fibonacci of 38 recursively took 11.392906241000219 seconds.
+Calculating Fibonacci of 38 with dynamic programming took 1.8928999907075195e-05 seconds.
+```
+
+```
+Calculating Fibonacci of 40 recursively took 34.496809830000075 seconds.
+Calculating Fibonacci of 40 with dynamic programming took 2.2804999844083795e-05 seconds.
+```
+
+```
+Calculating Fibonacci of 45 recursively took 367.38581775700004 seconds.
+Calculating Fibonacci of 45 with dynamic programming took 2.579200008767657e-05 seconds.
+```

fibonacci.py

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+import functools, timeit
+
+def fibo_rec(num):
+    if num == 0:
+        return 0
+    elif num == 1:
+        return 1
+    else:
+        return fibo_rec(num - 1) + fibo_rec(num - 2)
+
+
+def fibonacci_dp(num, table):
+   if table[num] >= 0:
+       return table[num]
+
+   if (num == 0 or num == 1):
+       res = num
+   else:
+       res = fibonacci_dp(num - 1, table) + fibonacci_dp(num - 2, table)
+
+   table[num] = res
+
+   return res
+
+
+def fibo_dp(num):
+    table = [-1] * (num + 1)
+    return fibonacci_dp(num, table)
+
+
+number = int(input('Enter a number: '))
+
+
+recursive_timer = timeit.Timer(functools.partial(fibo_rec, number))
+recursive_time = recursive_timer.timeit(1)
+print(f'Calculating Fibonacci of {number} recursively took {recursive_time} seconds.')
+
+dp_timer = timeit.Timer(functools.partial(fibo_dp, number))
+dp_time = dp_timer.timeit(1)
+print(f'Calculating Fibonacci of {number} with dynamic programming took {dp_time} seconds.')
+
+
+