recursion/fibonacci.ipynb

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    "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]"
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   "source": [
    "efficient_fibonacci(12)"
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