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    "## 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": {
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   "source": [
    "num_items = 10"
   ]
  },
  {
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   "execution_count": null,
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   "source": [
    "def fib_recursive(n):\n",
    "    if n == 0 or n == 1:\n",
    "        return n\n",
    "    else:\n",
    "        return fib_recursive(n-1) + fib_recursive(n-2)\n",
    "\n",
    "for i in xrange(0, num_items):\n",
    "    print(fib_recursive(i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
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   },
   "outputs": [],
   "source": [
    "cache = [None] * (num_items + 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, num_items):\n",
    "    print(fib_dynamic(i))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "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, num_items):\n",
    "    print(fib_iterative(i))"
   ]
  }
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