added a last min code change

_100-days-of-code/2018-01-01-100-days-of-code-day010.markdown

@@ -17,3 +17,79 @@ channel with lots of math and science themed videos. That is where I found
 these tutorials. Here is a
 [link](https://www.youtube.com/watch?v=Qk0zUZW-U_M&list=PLi01XoE8jYohWFPpC17Z-wWhPOSuh8Er-&index=18)
 to the python video on the fibonacci sequence.
+##### No Cache
+
+```python
+
+#!/usr/bin/env python3
+# this shows the fibonacci sequence with basic recursion.
+# note that it gets very slow at the end due to the recursion
+
+
+def fibonacci(n):
+    if n == 1:
+        return 1
+    elif n == 2:
+        return 1
+    elif n > 2:
+        return fibonacci(n-1) + fibonacci(n-2)
+
+
+for n in range(1, 101):
+    print(n, ":", fibonacci(n))
+```
+#### Cache
+```python
+
+#!/usr/bin/env python3
+# this introduces recursive fibonacci with a cache of recent function calls
+# this is introducing memoization: caching recent function call results
+
+fibonacci_cache = {}
+
+
+def fibonacci(n):
+    # If we have cached the value, then return it
+    if n in fibonacci_cache:
+        return fibonacci_cache[n]
+
+    # compute nth term
+    if n == 1:
+        value = 1
+    elif n == 2:
+        value = 1
+    elif n > 2:
+        value = fibonacci(n-1) + fibonacci(n-2)
+
+    fibonacci_cache[n] = value
+    return value
+
+
+for n in range(1, 101):
+    print(n, ":", fibonacci(n))
+```
+#### Cache using functools lru_cache
+```python
+#!/usr/bin/env python3
+from functools import lru_cache
+
+@lru_cache(maxsize = 1000)
+def fibonacci(n):
+    # check if type is positive int
+    if type(n) != int:
+        raise TypeError("n must be a positive int")
+    if n < 1:
+        raise ValueError("n must be a positive int")
+
+    if n == 1:
+        return 1
+    elif n == 2:
+        return 1
+    elif n > 2:
+        return fibonacci(n-1) + fibonacci(n-2)
+
+
+for n in range(1, 501):
+    print(n, ":", fibonacci(n))
+```
+