added fibonacci examples and bubblesort example

algorithms/fibonacci.py

@@ -0,0 +1,16 @@
+#!/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))

algorithms/fibonacci_with_cache.py

@@ -0,0 +1,27 @@
+#!/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))
+