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   "source": [
    "## Problem: Implement a stack with push, pop, and min methods running O(1) time.\n",
    "\n",
    "* [Clarifying Questions](#Clarifying-Questions)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Clarifying Questions\n",
    "\n",
    "* Is this a stack of ints?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Push/pop on empty stack\n",
    "* Push/pop 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 the 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(n)\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": null,
   "metadata": {
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   },
   "outputs": [],
   "source": [
    "%run stack.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import sys\n",
    "\n",
    "class MyStack(Stack):\n",
    "    def __init__(self, top=None):\n",
    "        self.min_vals = Stack()\n",
    "        super(MyStack, self).__init__(top)\n",
    "\n",
    "    def min(self):\n",
    "        if self.min_vals.top is None:\n",
    "            return sys.maxint\n",
    "        else:\n",
    "            return self.min_vals.peek()\n",
    "\n",
    "    def push(self, data):\n",
    "        super(MyStack, self).push(data)\n",
    "        if data < self.min():\n",
    "            self.min_vals.push(data)\n",
    "\n",
    "    def pop(self):\n",
    "        data = super(MyStack, self).pop()\n",
    "        if data == self.min():\n",
    "            self.min_vals.pop()\n",
    "        return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": [
    "print('Push on empty stack, non-empty stack')\n",
    "stack = MyStack()\n",
    "stack.push(5)\n",
    "print('Push:', stack.peek(), 'Min after push:', stack.min())\n",
    "stack.push(1)\n",
    "print('Push:', stack.peek(), 'Min after push:', stack.min())\n",
    "stack.push(3)\n",
    "print('Push:', stack.peek(), 'Min after push:', stack.min())\n",
    "stack.push(0)\n",
    "print('Push:', stack.peek(), 'Min after push:', stack.min())\n",
    "print('Pop on non-empty stack')\n",
    "print('Pop:', stack.pop(), 'Min after pop:', stack.min())\n",
    "print('Pop:', stack.pop(), 'Min after pop:', stack.min())\n",
    "print('Pop:', stack.pop(), 'Min after pop:', stack.min())\n",
    "print('Pop:', stack.pop(), 'Min after pop:', stack.min())\n",
    "print('Stack contents:', stack.peek())\n",
    "print('Pop empty stack:', stack.pop())"
   ]
  }
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