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