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    "## Problem: Implement n stacks using a single array.\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",
    "* Are the stacks and array a fixed size?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "* Test the following on the three stacks:\n",
    "    * Push to full stack\n",
    "    * Push to non-full stack\n",
    "    * Pop on empty stack\n",
    "    * Pop on non-empty stack"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "* Initialize array\n",
    "* Initialize stack pointers to -1\n",
    "\n",
    "### Push\n",
    "\n",
    "* If stack is full, throw exception\n",
    "* Else\n",
    "    * Increment stack pointer\n",
    "    * Get the absolute array index\n",
    "    * Insert the value to this index\n",
    "\n",
    "Complexity:\n",
    "* Time: O(1)\n",
    "* Space: O(1)\n",
    "\n",
    "### Pop\n",
    "\n",
    "* If stack is empty, throw exception\n",
    "* Else\n",
    "    * Store the value contained in the absolute array index\n",
    "    * Set the value in the absolute array index to None\n",
    "    * Decrement stack pointer\n",
    "    * return value\n",
    "\n",
    "Complexity:\n",
    "* Time: O(1)\n",
    "* Space: O(1)\n",
    "\n",
    "\n",
    "### Absolute Index\n",
    "\n",
    "* return stack size * stack index + stack pointer\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": [
    "class Stacks(object):\n",
    "    def __init__(self, num_stacks, stack_size):\n",
    "        self.num_stacks = num_stacks\n",
    "        self.stack_size = stack_size\n",
    "        self.stack_pointers = [-1] * num_stacks\n",
    "        self.stack_array = [None] * num_stacks * stack_size\n",
    "\n",
    "    def abs_index(self, stack_index):\n",
    "        return stack_index * self.stack_size + self.stack_pointers[stack_index]\n",
    "\n",
    "    def push(self, stack_index, data):\n",
    "        if self.stack_pointers[stack_index] == self.stack_size - 1:\n",
    "            raise Exception('Stack is full')\n",
    "        else:\n",
    "            self.stack_pointers[stack_index] += 1\n",
    "            array_index = self.abs_index(stack_index)\n",
    "            self.stack_array[array_index] = data\n",
    "\n",
    "    def pop(self, stack_index):\n",
    "        if self.stack_pointers[stack_index] == -1:\n",
    "            raise Exception('Stack is empty')\n",
    "        else:\n",
    "            array_index = self.abs_index(stack_index)            \n",
    "            data = self.stack_array[array_index]\n",
    "            self.stack_array[array_index] = None\n",
    "            self.stack_pointers[stack_index] -= 1\n",
    "            return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "num_stacks = 3\n",
    "stack_size = 100\n",
    "print('Pop on empty stack')\n",
    "stacks = Stacks(num_stacks, stack_size)\n",
    "try:\n",
    "    stacks.pop(0)\n",
    "except Exception as e:\n",
    "    print(e)\n",
    "print('Push to non-full stack')\n",
    "stacks.push(0, 1)\n",
    "stacks.push(0, 2)\n",
    "stacks.push(1, 3)\n",
    "stacks.push(2, 4)\n",
    "print('Pop on non-empty stack')\n",
    "print(stacks.pop(0))\n",
    "print(stacks.pop(0))\n",
    "print(stacks.pop(1))\n",
    "print(stacks.pop(2))\n",
    "print('Push to full stack')\n",
    "for i in xrange(0, stack_size):\n",
    "    stacks.push(2, i)\n",
    "try:\n",
    "    stacks.push(2, stack_size)\n",
    "except Exception as e:\n",
    "    print(e)"
   ]
  }
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