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   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Given a list of stock prices, find the max profit from 1 buy and 1 sell.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Are all prices positive ints?\n",
    "    * Yes\n",
    "* Is the output an int?\n",
    "    * Yes\n",
    "* If profit is negative, do we return the smallest negative loss?\n",
    "    * Yes\n",
    "* If there are less than two prices, what do we return?\n",
    "    * Exception\n",
    "* Can we assume the inputs are valid?\n",
    "    * No\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* None -> TypeError\n",
    "* Zero or one price -> ValueError\n",
    "* No profit\n",
    "    * [8, 5, 3, 2, 1] -> -1\n",
    "* General case\n",
    "    * [5, 3, 7, 4, 2, 6, 9] -> 7"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We'll use a greedy approach and iterate through the prices once.\n",
    "\n",
    "* Loop through the prices\n",
    "    * Update current profit (price = min_price)\n",
    "    * Update the min price\n",
    "    * Update the max profit\n",
    "* Return max profit\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "\n",
    "class Solution(object):\n",
    "\n",
    "    def find_max_profit(self, prices):\n",
    "        if prices is None:\n",
    "            raise TypeError('prices cannot be None')\n",
    "        if len(prices) < 2:\n",
    "            raise ValueError('prices must have at least two values')\n",
    "        min_price = prices.pop(0)\n",
    "        max_profit = prices[0] - min_price\n",
    "        for price in prices:\n",
    "            profit = price - min_price\n",
    "            min_price = min(price, min_price)\n",
    "            max_profit = max(profit, max_profit)\n",
    "        return max_profit"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_max_profit.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_max_profit.py\n",
    "from nose.tools import assert_equal, assert_raises\n",
    "\n",
    "\n",
    "class TestMaxProfit(object):\n",
    "\n",
    "    def test_max_profit(self):\n",
    "        solution = Solution()\n",
    "        assert_raises(TypeError, solution.find_max_profit, None)\n",
    "        assert_raises(ValueError, solution.find_max_profit, [])\n",
    "        assert_equal(solution.find_max_profit([8, 5, 3, 2, 1]), -1)\n",
    "        assert_equal(solution.find_max_profit([5, 3, 7, 4, 2, 6, 9]), 7)\n",
    "        print('Success: test_max_profit')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestMaxProfit()\n",
    "    test.test_max_profit()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Success: test_max_profit\n"
     ]
    }
   ],
   "source": [
    "%run -i test_max_profit.py"
   ]
  }
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