Added notebook solving the following: Implement fibonacci recursively, dynamically, and iteratively.

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Donne Martin 2015-05-30 10:48:46 -04:00
parent 9f012acca6
commit bfd143ca81
2 changed files with 146 additions and 1 deletions

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@ -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

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{
"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"
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"nbformat": 4,
"nbformat_minor": 0
}