From bfd143ca815fb3c96fe4d233225421f7fd4f03b3 Mon Sep 17 00:00:00 2001
From: Donne Martin <donne.martin@gmail.com>
Date: Sat, 30 May 2015 10:48:46 -0400
Subject: [PATCH] Added notebook solving the following: Implement fibonacci
 recursively, dynamically, and iteratively.

---
 README.md                         |   2 +-
 recursion-dynamic/fibonacci.ipynb | 145 ++++++++++++++++++++++++++++++
 2 files changed, 146 insertions(+), 1 deletion(-)
 create mode 100644 recursion-dynamic/fibonacci.ipynb

diff --git a/README.md b/README.md
index e50207e..8bf545c 100644
--- a/README.md
+++ b/README.md
@@ -67,7 +67,7 @@ Most solutions are in Python.
 
 ## Recursion and Dynamic Programming
 
-[Coming Soon]
+* [Implement fibonacci recursively, dynamically, and iteratively](http://nbviewer.ipython.org/github/donnemartin/algorithms-data-structures/blob/master/recursion-dynamic/fibonacci.ipynb#)
 
 ## Trees and Graphs
 
diff --git a/recursion-dynamic/fibonacci.ipynb b/recursion-dynamic/fibonacci.ipynb
new file mode 100644
index 0000000..17963e7
--- /dev/null
+++ b/recursion-dynamic/fibonacci.ipynb
@@ -0,0 +1,145 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Problem: Implement fibonacci recursively, dynamically, and iteratively.\n",
+    "\n",
+    "* [Clarifying Questions](#Clarifying-Questions)\n",
+    "* [Test Cases](#Test-Cases)\n",
+    "* [Algorithm](#Algorithm)\n",
+    "* [Code](#Code)\n",
+    "* [Pythonic-Code](#Pythonic-Code)"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Clarifying Questions\n",
+    "\n",
+    "* None"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Test Cases\n",
+    "\n",
+    "* n = 0\n",
+    "* n = 1\n",
+    "* n > 1"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Algorithm\n",
+    "\n",
+    "* Fibonacci is as follows: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34...\n",
+    "* If n = 0 or 1, return n\n",
+    "* Else return fib(n-1) + fib(n+2)\n",
+    "\n",
+    "Complexity:\n",
+    "* Time: O(2^n) if recursive or iterative, O(n) if dynamic\n",
+    "* Space: O(n) if recursive, O(1) if iterative, O(1) if dynamic"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Code"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "def fib_recursive(n):\n",
+    "    if n == 0 or n == 1:\n",
+    "        return n\n",
+    "    else:\n",
+    "        return fib(n-1) + fib(n-2)\n",
+    "\n",
+    "for i in xrange(0, 10):\n",
+    "    print(fib_recursive(i))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [],
+   "source": [
+    "n = 7\n",
+    "cache = [None] * (n + 1)\n",
+    "\n",
+    "def fib_dynamic(n):\n",
+    "    if n == 0 or n == 1:\n",
+    "        return n\n",
+    "    if cache[n] != None:\n",
+    "        return cache[n]\n",
+    "    cache[n] = fib_dynamic(n-1) + fib_dynamic(n-2)\n",
+    "    return cache[n]\n",
+    "\n",
+    "for i in xrange(0, 10):\n",
+    "    print(fib_dynamic(i))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {
+    "collapsed": true
+   },
+   "outputs": [],
+   "source": [
+    "def fib_iterative(n):\n",
+    "    if n == 0 or n == 1:\n",
+    "        return n\n",
+    "    else:\n",
+    "        n_minus_2 = 0        \n",
+    "        n_minus_1 = 1\n",
+    "        total = 0\n",
+    "        for _ in xrange(2, n+1):\n",
+    "            total = n_minus_2 + n_minus_1\n",
+    "            n_minus_2, n_minus_1 = n_minus_1, total\n",
+    "        return total\n",
+    "\n",
+    "for i in xrange(0, 10):\n",
+    "    print(fib_iterative(i))"
+   ]
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 2",
+   "language": "python",
+   "name": "python2"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 2
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython2",
+   "version": "2.7.9"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 0
+}