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   "source": [
    "## Problem: Implement SetOfStacks that wraps a list of stacks, where each stack is bound by a capacity.\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",
    "* Can we assume we have a Stack class to use?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Push and pop on an empty stack\n",
    "* Push and pop on a non-empty stack\n",
    "* Push on a capacity stack to create a new one\n",
    "* Pop on a one element stack to destroy it"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "### Push\n",
    "\n",
    "* If there are no stacks or the last stack is full\n",
    "    * Create a new stack\n",
    "* Push to the new stack\n",
    "\n",
    "Complexity:\n",
    "* Time: O(1)\n",
    "* Space: O(1)\n",
    "\n",
    "### Pop\n",
    "\n",
    "* If there are no stacks, return None\n",
    "* Else if the last stack has one element\n",
    "    * Pop the last element's data\n",
    "    * Delete the now empty stack\n",
    "    * Update the last stack pointer\n",
    "* Else Pop the last element's data\n",
    "* Return the last element's 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": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%run stack.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class StackWithCapacity(Stack):\n",
    "    def __init__(self, top=None, capacity=10):\n",
    "        self.capacity = capacity\n",
    "        self.num_items = 0\n",
    "        super(StackWithCapacity, self).__init__(top)\n",
    "\n",
    "    def push(self, data):\n",
    "        if self.num_items < self.capacity:\n",
    "            super(StackWithCapacity, self).push(data)\n",
    "            self.num_items += 1\n",
    "        else:\n",
    "            raise Exception('Stack full')\n",
    "\n",
    "    def pop(self):\n",
    "        data = super(StackWithCapacity, self).pop()\n",
    "        self.num_items -= 1\n",
    "        return data\n",
    "\n",
    "    def is_full(self):\n",
    "        return self.num_items == self.capacity\n",
    "\n",
    "class SetOfStacks(object):\n",
    "    def __init__(self, capacity):\n",
    "        self.capacity = capacity\n",
    "        self.stacks = []\n",
    "        self.last_stack = None\n",
    "\n",
    "    def push(self, data):\n",
    "        if self.last_stack is None or self.last_stack.is_full():\n",
    "            self.last_stack = StackWithCapacity(None, self.capacity)\n",
    "            self.stacks.append(self.last_stack)\n",
    "        self.last_stack.push(data)\n",
    "\n",
    "    def pop(self):\n",
    "        if self.last_stack is None:\n",
    "            return\n",
    "        elif self.last_stack.top.next is None:\n",
    "            data = self.last_stack.pop()\n",
    "            self.stacks.pop()\n",
    "            num_stacks = len(self.stacks)\n",
    "            if num_stacks == 0:\n",
    "                self.last_stack = None\n",
    "            else:\n",
    "                self.last_stack = self.stacks[num_stacks-1]\n",
    "        else:\n",
    "            data = self.last_stack.pop()\n",
    "        return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "print('Push on an empty stack')\n",
    "capacity = 2\n",
    "stacks = SetOfStacks(capacity)\n",
    "stacks.push(3)\n",
    "print('Push on a non-empty stack')\n",
    "stacks.push(5)\n",
    "print('Push on a capacity stack to create a new one')\n",
    "stacks.push('a')\n",
    "print('Pop on a one element stack to destroy it')\n",
    "print(stacks.pop())\n",
    "print('Pop general case')\n",
    "print(stacks.pop())\n",
    "print(stacks.pop())\n",
    "print('Pop on no elements')\n",
    "print(stacks.pop())"
   ]
  }
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