Linked_list.ipynb

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    "## Implementing a linked list\n",
    "\n",
    "Jacob L. Fine\n",
    "\n",
    "June 24th, 2024\n",
    "\n",
    "A linked list uses a node structure to effectively 'sew' each element in the list together. Unlike an array (of which the Python list object is an instance of), which stores all elements in a contiguous memory location, a linked list stores each element in a separate node which are scattered throughout memory. In a singly-linked list, each node contains its value and a pointer to the next node. This particular structure allows linked lists to be dynamic in size, which may speeds up certain operations such inserting, deleting, and searching for elements.\n",
    "\n",
    "Our aim is to create a singly-linked list. Unlike the standard Python list, we will need to manually create this object. We will then compare its performance for insertions, deletions, and searches. To make a singly-linked list, we will make a Node class to represent each element in the list, storing its value and a pointer to the next node, and then create a linked list class to manage the nodes, enabling insertions, deletions, and searches. Afterwards, we will empirically evaluate runtimes for insertions, deletions, and searches.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Node:\n",
    "    def __init__(self, value=None):\n",
    "        # the value stored in the node\n",
    "        self.value = value\n",
    "        # a pointer to the next node\n",
    "        self.next = None\n",
    "\n",
    "class LinkedList:\n",
    "    def __init__(self):\n",
    "        # stores the first node in the list\n",
    "        self.head = None\n",
    "        self.tail = None\n",
    "    \n",
    "    # append_values a value to the list, i.e., can use LinkedList.append_value(value)\n",
    "    def append_value(self, value):\n",
    "        new_node = Node(value)\n",
    "        # if there is no first node, we set the tail and head to the currently considered node value, and exit\n",
    "        if self.head is None:\n",
    "            self.head = new_node\n",
    "            self.tail = new_node  \n",
    "            return\n",
    "        else: \n",
    "            # otherwise, we set the value after the current tail to the new node value we want to add\n",
    "            self.tail.next = new_node\n",
    "            # afterwards, we update the tail of our linked list to be the most recently added value\n",
    "            self.tail = new_node  \n",
    "\n",
    "    def prepend_value(self, value):\n",
    "        # adds an element to the start of the list, i.e., by updating the head of the list. Since every node just references every other node, we can insert here without needing to shift every element's location in memory\n",
    "        new_node = Node(value)\n",
    "        new_node.next = self.head\n",
    "        self.head = new_node\n",
    "\n",
    "    def delete_value(self, value):\n",
    "        # we can now delete a particular value. If the first node is empty, then so is the list, so there is nothing to delete\n",
    "        if self.head is None:\n",
    "            return\n",
    "        # if the value in the head is our value, then we delete it by shifitng its value to the value next in the list, and we end here\n",
    "        if self.head.value == value:\n",
    "            self.head = self.head.next\n",
    "            return\n",
    "        # if the head was not the node we wanted to delete, we set it to the current_node, and traverse through other nodes.\n",
    "        current_node = self.head\n",
    "        # we then traverse through every node, checking if it is our value, and if it is, we shift the list over which effectively deletes it.\n",
    "        while current_node.next:\n",
    "            if current_node.next.value == value:\n",
    "                current_node.next = current_node.next.next\n",
    "                return\n",
    "            # otherwise, we keep things as they were by resetting the current_node \n",
    "            current_node = current_node.next\n",
    "\n",
    "    def search_value(self, value):\n",
    "        # we wish to search_value the index of a particular value. We start by searching from the first ndoe of the list\n",
    "        current_node = self.head\n",
    "        # a counter storing the current_node index in the list during our traversal (assuming we start with 0-indexing)\n",
    "        index = 0\n",
    "        # if there is value in the node we are looking at\n",
    "        while current_node:\n",
    "            # if the node is our value, we return the count from our traversal, which will exactly be our index\n",
    "            if current_node.value == value:\n",
    "                return index\n",
    "            # we then update the current_node we are looking at, and we update our index\n",
    "            current_node = current_node.next\n",
    "            index += 1\n",
    "        return -1\n",
    "\n",
    "    def show_list(self):\n",
    "        # we can now show_list the actual linked list using a list object\n",
    "        elements = []\n",
    "        # the node we start with is the first node\n",
    "        current_node = self.head\n",
    "        # we keep append_valueing the subsequent nodes to the list object until we reach the end of the linked list\n",
    "        while current_node:\n",
    "            elements.append(current_node.value)\n",
    "            current_node = current_node.next\n",
    "        # we print the elements\n",
    "        print(elements)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1800x600 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import time\n",
    "import random\n",
    "import seaborn as sns\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "\n",
    "# We initialize two lists, the linked list class and the standard Python list (an array)\n",
    "linked_list = LinkedList()\n",
    "python_list = []\n",
    "\n",
    "# This will be our dataframe that we store results in\n",
    "columns = [\"operation\", \"runtime (s)\", \"data structure\", \"input size\"]\n",
    "df = pd.DataFrame(columns=columns)\n",
    "\n",
    "# The function that measures run_times for different operations\n",
    "def evaluate_runtime(df, operation, run_time, data_structure, size):\n",
    "    new_row = pd.DataFrame([{\"operation\": operation, \"runtime (s)\": run_time, \"data structure\": data_structure, \"input size\": size}])\n",
    "    \n",
    "    # This portion deals with a Future warning to ensure that na values are handled correctly\n",
    "    df = df.dropna(how='all', axis=1)\n",
    "    df = df.dropna(how='all', axis=0)\n",
    "    \n",
    "    df = pd.concat([df, new_row], ignore_index=True)\n",
    "    \n",
    "    return df\n",
    "\n",
    "# Input sizes to consider\n",
    "test_sizes = [100, 500, 1000, 5000, 10000, 50000, 100000] \n",
    "\n",
    "# Iterate through each input size and compare the two data structures\n",
    "for size in test_sizes:\n",
    "    test_values = [random.randint(1, 50) for _ in range(size)]\n",
    "    \n",
    "    # these three blocks are for measuring insertions, search, and delete for the linked list\n",
    "    start_time = time.time()\n",
    "    for value in test_values:\n",
    "        linked_list.append_value(value)\n",
    "    append_time = time.time() - start_time\n",
    "    df = evaluate_runtime(df, \"insert\", append_time, \"Linked List\", size)\n",
    "\n",
    "\n",
    "    start_time = time.time()\n",
    "    for value in test_values:\n",
    "        linked_list.search_value(value)\n",
    "    search_time = time.time() - start_time\n",
    "    df = evaluate_runtime(df, \"search\", search_time, \"Linked List\", size)\n",
    "\n",
    "    start_time = time.time()\n",
    "    for value in test_values:\n",
    "        linked_list.delete_value(value)\n",
    "    delete_time = time.time() - start_time\n",
    "    df = evaluate_runtime(df, \"delete\", delete_time, \"Linked List\", size)\n",
    "\n",
    "\n",
    "    # these three blocks are for measuring insertions, search, and delete for the standard array\n",
    "    start_time = time.time()\n",
    "    for value in test_values:\n",
    "        python_list.append(value)\n",
    "    append_time = time.time() - start_time\n",
    "    df = evaluate_runtime(df, \"insert\", append_time, \"Array\", size)\n",
    "\n",
    "\n",
    "    start_time = time.time()\n",
    "    for value in test_values:\n",
    "        python_list.index(value)\n",
    "    search_time = time.time() - start_time\n",
    "    df = evaluate_runtime(df, \"search\", search_time, \"Array\", size)\n",
    "\n",
    "    start_time = time.time()\n",
    "    for value in test_values:\n",
    "        if value in python_list:\n",
    "            python_list.remove(value)\n",
    "    delete_time = time.time() - start_time\n",
    "    df = evaluate_runtime(df, \"delete\", delete_time, \"Array\", size)\n",
    "\n",
    "\n",
    "# Plotting the figure with the results below\n",
    "plt.figure(figsize=(18, 6)) \n",
    "\n",
    "# Plot for insert operation\n",
    "plt.subplot(1, 3, 1)\n",
    "sns.lineplot(x=\"input size\", y=\"runtime (s)\", hue=\"data structure\", style=\"operation\",\n",
    "             markers=True, dashes=False,\n",
    "             data=df[df['operation'] == 'insert'])\n",
    "plt.title('insert operation')\n",
    "plt.xlabel('input size')\n",
    "plt.ylabel('runtime (s)')\n",
    "# creates a custom legend with desired properties\n",
    "legend_append = plt.legend(labels=[\"LinkedList\", \"Array\"], title=None, loc='upper right')\n",
    "legend_append.legend_handles[0].set_color('blue')  # sets color for linked list\n",
    "legend_append.legend_handles[1].set_color('orange')  # sets color for array\n",
    "legend_append.get_texts()[0].set_color('blue')  # labels the linkedlist legend item\n",
    "legend_append.get_texts()[1].set_color('orange')  # labels the array legend item\n",
    "\n",
    "# Plot for delete operation\n",
    "plt.subplot(1, 3, 2)\n",
    "sns.lineplot(x=\"input size\", y=\"runtime (s)\", hue=\"data structure\", style=\"operation\",\n",
    "             markers=True, dashes=False,\n",
    "             data=df[df['operation'] == 'delete'])\n",
    "plt.title('delete operation')\n",
    "plt.xlabel('input size')\n",
    "plt.ylabel('runtime (s)')\n",
    "legend_delete = plt.legend(labels=[\"LinkedList\", \"Array\"], title=None, loc='upper right')\n",
    "legend_delete.legend_handles[0].set_color('blue')  \n",
    "legend_delete.legend_handles[1].set_color('orange') \n",
    "legend_delete.get_texts()[0].set_color('blue') \n",
    "legend_delete.get_texts()[1].set_color('orange')  \n",
    "\n",
    "# Plot for search operation\n",
    "plt.subplot(1, 3, 3)\n",
    "sns.lineplot(x=\"input size\", y=\"runtime (s)\", hue=\"data structure\", style=\"operation\",\n",
    "             markers=True, dashes=False,\n",
    "             data=df[df['operation'] == 'search'])\n",
    "plt.title('search operation')\n",
    "plt.xlabel('input size')\n",
    "plt.ylabel('runtime (s)')\n",
    "legend_search = plt.legend(labels=[\"LinkedList\", \"Array\"], title=None, loc='upper right')\n",
    "legend_search.legend_handles[0].set_color('blue') \n",
    "legend_search.legend_handles[1].set_color('orange')  \n",
    "legend_search.get_texts()[0].set_color('blue')  \n",
    "legend_search.get_texts()[1].set_color('orange')  \n",
    "\n",
    "plt.tight_layout()\n",
    "plt.show()"
   ]
  }
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