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   "source": [
    "This notebook was prepared by [Donne Martin](http://donnemartin.com). 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: Implement a stack with push, pop, and min methods running O(1) time.\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",
    "* Can we assume this is a stack of ints?\n",
    "    * Yes\n",
    "* Can we assume the input values for push are valid?\n",
    "    * Yes\n",
    "* If we call this function on an empty stack, can we return sys.maxsize?\n",
    "    * Yes\n",
    "* Can we assume we already have a stack class that can be used for this problem?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Push/pop on empty stack\n",
    "* Push/pop on non-empty stack\n",
    "* Min on empty stack\n",
    "* Min on non-empty stack"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "We'll use a second stack to keep track of the minimum values.\n",
    "\n",
    "### Min\n",
    "\n",
    "* If the second stack is empty, return an error code (max int value)\n",
    "* Else, return the top of the stack, without popping it\n",
    "\n",
    "Complexity:\n",
    "* Time: O(1)\n",
    "* Space: O(1)\n",
    "\n",
    "### Push\n",
    "\n",
    "* Push the data\n",
    "* If the data is less than min\n",
    "    * Push data to second stack\n",
    "\n",
    "Complexity:\n",
    "* Time: O(1)\n",
    "* Space: O(1)\n",
    "\n",
    "### Pop\n",
    "\n",
    "* Pop the data\n",
    "* If the data is equal to min\n",
    "    * Pop the top of the second stack\n",
    "* Return the data\n",
    "\n",
    "Complexity:\n",
    "* Time: O(1)\n",
    "* Space: O(1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run ../stack/stack.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "\n",
    "class StackMin(Stack):\n",
    "\n",
    "    def __init__(self, top=None):\n",
    "        super(StackMin, self).__init__(top)\n",
    "        self.stack_of_mins = Stack()\n",
    "\n",
    "    def minimum(self):\n",
    "        if self.stack_of_mins.top is None:\n",
    "            return sys.maxsize\n",
    "        else:\n",
    "            return self.stack_of_mins.peek()\n",
    "\n",
    "    def push(self, data):\n",
    "        super(StackMin, self).push(data)\n",
    "        if data < self.minimum():\n",
    "            self.stack_of_mins.push(data)\n",
    "\n",
    "    def pop(self):\n",
    "        data = super(StackMin, self).pop()\n",
    "        if data == self.minimum():\n",
    "            self.stack_of_mins.pop()\n",
    "        return data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_stack_min.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_stack_min.py\n",
    "from nose.tools import assert_equal\n",
    "\n",
    "\n",
    "class TestStackMin(object):\n",
    "\n",
    "    def test_stack_min(self):\n",
    "        print('Test: Push on empty stack, non-empty stack')\n",
    "        stack = StackMin()\n",
    "        stack.push(5)\n",
    "        assert_equal(stack.peek(), 5)\n",
    "        assert_equal(stack.minimum(), 5)\n",
    "        stack.push(1)\n",
    "        assert_equal(stack.peek(), 1)\n",
    "        assert_equal(stack.minimum(), 1)\n",
    "        stack.push(3)\n",
    "        assert_equal(stack.peek(), 3)\n",
    "        assert_equal(stack.minimum(), 1)\n",
    "        stack.push(0)\n",
    "        assert_equal(stack.peek(), 0)\n",
    "        assert_equal(stack.minimum(), 0)\n",
    "\n",
    "        print('Test: Pop on non-empty stack')\n",
    "        assert_equal(stack.pop(), 0)\n",
    "        assert_equal(stack.minimum(), 1)\n",
    "        assert_equal(stack.pop(), 3)\n",
    "        assert_equal(stack.minimum(), 1)\n",
    "        assert_equal(stack.pop(), 1)\n",
    "        assert_equal(stack.minimum(), 5)\n",
    "        assert_equal(stack.pop(), 5)\n",
    "        assert_equal(stack.minimum(), sys.maxsize)\n",
    "\n",
    "        print('Test: Pop empty stack')\n",
    "        assert_equal(stack.pop(), None)\n",
    "\n",
    "        print('Success: test_stack_min')\n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestStackMin()\n",
    "    test.test_stack_min()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test: Push on empty stack, non-empty stack\n",
      "Test: Pop on non-empty stack\n",
      "Test: Pop empty stack\n",
      "Success: test_stack_min\n"
     ]
    }
   ],
   "source": [
    "run -i test_stack_min.py"
   ]
  }
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