[chore] replace py file with notebook

Author: gitgik

recursion/fibonacci.ipynb

@@ -0,0 +1,97 @@
+{
+ "metadata": {
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.0-final"
+  },
+  "orig_nbformat": 2,
+  "kernelspec": {
+   "name": "python3",
+   "display_name": "Python 3.9.0 64-bit",
+   "metadata": {
+    "interpreter": {
+     "hash": "aee8b7b246df8f9039afb4144a1f6fd8d2ca17a180786b69acc140d282b71a49"
+    }
+   }
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 2,
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def fibonacci(n, memoize={1:0, 2: 1}):\n",
+    "    \"\"\"\n",
+    "    Nth fibonacci number using memoization.\n",
+    "    \n",
+    "    O(n) space and time\n",
+    "    \"\"\"\n",
+    "    if n < 0:\n",
+    "        raise TypeError('Value of n must be a positive integer')\n",
+    "    if n in memoize:\n",
+    "        return memoize[n]\n",
+    "    else:\n",
+    "        memoize[n] = fibonacci(n - 1, memoize) + fibonacci(n - 2, memoize)\n",
+    "        return memoize[n]\n",
+    "\n",
+    "\n",
+    "def efficient_fibonacci(n):\n",
+    "    \"\"\"\n",
+    "    nth fibonacci number iteratively.\n",
+    "\n",
+    "    Complexity:\n",
+    "        O(n) time,\n",
+    "        O(1) space, since we are only storing two array values at any given time.\n",
+    "    \"\"\"\n",
+    "    last_two = [0, 1]\n",
+    "\n",
+    "    counter = 3\n",
+    "    while counter <= n:\n",
+    "        next_fibonacci = sum(last_two)\n",
+    "        last_two = [last_two[1], next_fibonacci]\n",
+    "        counter += 1\n",
+    "    # the else clause caters for the edge case of the first fibo number == 0\n",
+    "    return last_two[1] if n > 1 else last_two[0]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "metadata": {},
+   "outputs": [
+    {
+     "output_type": "execute_result",
+     "data": {
+      "text/plain": [
+       "89"
+      ]
+     },
+     "metadata": {},
+     "execution_count": 3
+    }
+   ],
+   "source": [
+    "efficient_fibonacci(12)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ]
+}