From 8e9cbfd87f3b5a40e171c869695e0e3d7f97a654 Mon Sep 17 00:00:00 2001
From: Mia von Steinkirch <mia@quantumgravityresearch.org>
Date: Mon, 13 May 2019 16:08:11 -0700
Subject: [PATCH] more

---
 interview_cake/math/fib.py           | 36 ++++++++++++++++++++++++++++
 interview_cake/math/recursive_per.py | 32 +++++++++++++++++++++++++
 2 files changed, 68 insertions(+)
 create mode 100644 interview_cake/math/fib.py
 create mode 100644 interview_cake/math/recursive_per.py

diff --git a/interview_cake/math/fib.py b/interview_cake/math/fib.py
new file mode 100644
index 0000000..8654152
--- /dev/null
+++ b/interview_cake/math/fib.py
@@ -0,0 +1,36 @@
+#!/bin/python
+
+"""
+Write a function fib() that takes an integer nn and returns the nnth Fibonacci number.
+"""
+
+# this is O(2^n)
+def fib(n):
+    if n in [1, 0]:
+        return n
+    return fib(n - 1) + fib(n - 2)
+    
+
+print fib(10)
+
+
+# this is O(n)
+def fib(n):
+    if n < 0:
+        raise ValueError('Index was negative. No such thing as a '
+                         'negative index in a series.')
+    elif n in [0, 1]:
+        return n
+
+    prev_prev = 0  # 0th fibonacci
+    prev = 1       # 1st fibonacci
+
+    for _ in range(n - 1):
+        current = prev + prev_prev
+        prev_prev = prev
+        prev = current
+
+    return current
+        
+
+print fib(10)
\ No newline at end of file
diff --git a/interview_cake/math/recursive_per.py b/interview_cake/math/recursive_per.py
new file mode 100644
index 0000000..0c9d00f
--- /dev/null
+++ b/interview_cake/math/recursive_per.py
@@ -0,0 +1,32 @@
+#!/bin/python
+
+"""
+Write a recursive function for generating all permutations of an input string. Return them as a set.
+"""
+
+def get_permutations(string):
+
+    if len(string) < 2:
+        return set([string])
+
+    all_chars_except_last = string[:-1]
+    last_char = string[-1]
+
+    permutations_of_all_chars_except_last = get_permutations(all_chars_except_last)
+
+    permutations = set()
+    for permutation_of_all_chars_except_last in permutations_of_all_chars_except_last:
+        for position in range(len(all_chars_except_last) + 1):
+            permutation = (
+                permutation_of_all_chars_except_last[:position]
+                + last_char
+                + permutation_of_all_chars_except_last[position:]
+            )
+            permutations.add(permutation)
+
+    
+    return permutations
+
+
+str = "abcd"
+print get_permutations(str)
\ No newline at end of file