Fei Cao 002642021

Submissions/002683914_Xiaoyang_Chen/Xiaoyang_Chen_002683914.md

@@ -0,0 +1 @@
+When I utilize ChatGPT, it typically delivers insightful answers. However, there are moments when it stumbles over fundamental concepts, and at times, it can misconstrue descriptions leading to inaccurate conclusions. Expecting it to provide flawless answers on the first attempt might be unrealistic; often, multiple corrections are needed to fine-tune the response. I've also observed that while ChatGPT's coding abilities are commendable for simpler tasks, it tends to falter with intricate algorithms, especially when not provided with a template or reference. Therefore, it's crucial to critically assess ChatGPT's feedback and maintain an independent line of reasoning. Through this exercise, my understanding of algorithmic analysis and data structures has deepened. Moreover, I've pondered over various scenarios of stable matching and discerned how the algorithm adapts across different contexts.

Submissions/002688252_Zijian_Feng/Zijian_Feng_002688252.md

@@ -0,0 +1,13 @@
+# The Summary of Assignment One
+
+- Student Name:Zijian Feng
+- NUID:002688252
+- Professor: Nik Bear Brown
+
+## The reflection of using ChatGPT
+
+When I use ChatGPT, it tends to be pretty reliable. But there are times when it makes some low-level mistakes. For example, it says that 0.8^n is an exponential level of time complexity, and therefore a very rapid growth. In reality this time complexity is O(1) level. We need to pay attention to the details of his answers and not give up thinking when using ChatGPT.
+
+## What I learned in this assignment
+
+After doing this assignment, I have a better understanding of stable matching and time complexity. And I have also thought about the various situations of stable matching and know how the stable matching algorithm changes in different situations.

Submissions/002700370_Sun_Teng/Assignment-1.readme

@@ -0,0 +1 @@
+This is a readme.

Submissions/002700370_Sun_Teng/assignment1Q9.ipynb

@@ -0,0 +1,299 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 6,
+   "id": "e108b783-044d-4c70-bd63-1eda236f2498",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Matching Result:\n",
+      "Nets matched with Nuggets\n",
+      "Hawks matched with Clippers\n",
+      "76ers matched with Jazz\n",
+      "Celtics matched with Suns\n",
+      "Raptors matched with Mavericks\n",
+      "Knicks matched with Warriors\n",
+      "Heat matched with Blazers\n",
+      "Bucks matched with Lakers\n"
+     ]
+    }
+   ],
+   "source": [
+    "west_teams = [\"Lakers\", \"Clippers\", \"Suns\", \"Warriors\", \"Jazz\", \"Nuggets\", \"Blazers\", \"Mavericks\"]\n",
+    "east_teams = [\"Bucks\", \"Nets\", \"76ers\", \"Celtics\", \"Heat\", \"Hawks\", \"Knicks\", \"Raptors\"]\n",
+    "\n",
+    "west_preferences = {\n",
+    "    \"Lakers\": [\"Bucks\", \"Nets\", \"76ers\", \"Celtics\", \"Heat\", \"Hawks\", \"Knicks\", \"Raptors\"],\n",
+    "    \"Clippers\": [\"Celtics\", \"Nets\", \"Raptors\", \"Heat\", \"Knicks\", \"Bucks\", \"Hawks\", \"76ers\"],\n",
+    "    \"Suns\": [\"Nets\", \"Bucks\", \"Knicks\" , \"Heat\", \"Celtics\", \"Hawks\",\"Raptors\", \"76ers\"],\n",
+    "    \"Warriors\": [\"76ers\", \"Hawks\", \"Bucks\", \"Celtics\", \"Heat\", \"Knicks\", \"Raptors\", \"Nets\"],\n",
+    "    \"Jazz\": [\"Celtics\", \"Heat\", \"Nets\", \"Hawks\", \"76ers\", \"Knicks\", \"Raptors\", \"Bucks\"],\n",
+    "    \"Nuggets\": [\"Heat\",\"Bucks\", \"Nets\", \"76ers\", \"Knicks\", \"Hawks\", \"Raptors\", \"Celtics\"],\n",
+    "    \"Blazers\": [\"Hawks\",\"Bucks\", \"Nets\", \"Raptors\", \"76ers\", \"Celtics\", \"Heat\", \"Knicks\"],\n",
+    "    \"Mavericks\": [\"Nets\", \"76ers\", \"Knicks\", \"Celtics\", \"Hawks\", \"Heat\", \"Bucks\", \"Raptors\"]\n",
+    "}\n",
+    "\n",
+    "east_preferences = {\n",
+    "    \"Bucks\": [\"Lakers\", \"Nuggets\", \"Clippers\", \"Warriors\", \"Mavericks\", \"Jazz\", \"Suns\", \"Blazers\"],\n",
+    "    \"Nets\": [\"Lakers\", \"Clippers\", \"Suns\", \"Warriors\", \"Jazz\", \"Nuggets\", \"Blazers\", \"Mavericks\"],\n",
+    "    \"76ers\": [\"Nuggets\", \"Clippers\", \"Blazers\", \"Lakers\", \"Jazz\", \"Suns\", \"Warriors\", \"Mavericks\"],\n",
+    "    \"Celtics\": [\"Lakers\", \"Clippers\", \"Mavericks\", \"Suns\", \"Warriors\", \"Nuggets\", \"Blazers\", \"Jazz\"],\n",
+    "    \"Heat\": [\"Nuggets\", \"Lakers\", \"Suns\", \"Clippers\", \"Warriors\", \"Jazz\", \"Mavericks\", \"Blazers\"],\n",
+    "    \"Hawks\": [\"Warriors\", \"Mavericks\", \"Lakers\", \"Clippers\", \"Nuggets\", \"Suns\", \"Jazz\", \"Blazers\"],\n",
+    "    \"Knicks\": [\"Suns\", \"Lakers\", \"Warriors\",\"Clippers\", \"Mavericks\", \"Jazz\", \"Nuggets\", \"Blazers\"],\n",
+    "    \"Raptors\": [\"Clippers\", \"Warriors\", \"Suns\", \"Nuggets\", \"Blazers\", \"Jazz\", \"Mavericks\", \"Lakers\"]\n",
+    "}\n",
+    "import random\n",
+    "\n",
+    "def gale_shapley(proposers, acceptors):\n",
+    "    # Initialize empty matching\n",
+    "    matching = {}\n",
+    "    \n",
+    "    # Create dictionaries to store preferences\n",
+    "    proposer_preferences = {team: random.sample(acceptors, len(acceptors)) for team in proposers}\n",
+    "    acceptor_preferences = {team: random.sample(proposers, len(proposers)) for team in acceptors}\n",
+    "    \n",
+    "    # Initialize proposers without partners\n",
+    "    free_proposers = list(proposers)\n",
+    "    \n",
+    "    while free_proposers:\n",
+    "        proposer = free_proposers.pop(0)\n",
+    "        proposer_prefs = proposer_preferences[proposer]\n",
+    "        \n",
+    "        for acceptor in proposer_prefs:\n",
+    "            current_partner = matching.get(acceptor)\n",
+    "            \n",
+    "            if current_partner is None:\n",
+    "                # Acceptor is free, match them with proposer\n",
+    "                matching[acceptor] = proposer\n",
+    "                break\n",
+    "            else:\n",
+    "                # Check if acceptor prefers proposer over current partner\n",
+    "                acceptor_prefs = acceptor_preferences[acceptor]\n",
+    "                if acceptor_prefs.index(proposer) < acceptor_prefs.index(current_partner):\n",
+    "                    # Acceptor prefers proposer, unmatch them and match proposer\n",
+    "                    matching[acceptor] = proposer\n",
+    "                    free_proposers.append(current_partner)\n",
+    "                    break\n",
+    "    \n",
+    "    return matching\n",
+    "\n",
+    "if __name__ == \"__main__\":\n",
+    "    western_teams = [\"Lakers\", \"Clippers\", \"Suns\", \"Warriors\", \"Jazz\", \"Nuggets\", \"Blazers\", \"Mavericks\"]\n",
+    "    eastern_teams = [\"Bucks\", \"Nets\", \"76ers\", \"Celtics\", \"Heat\", \"Hawks\", \"Knicks\", \"Raptors\"]\n",
+    "    \n",
+    "    matching = gale_shapley(western_teams, eastern_teams)\n",
+    "    \n",
+    "    print(\"Matching Result:\")\n",
+    "    for acceptor, proposer in matching.items():\n",
+    "        print(f\"{acceptor} matched with {proposer}\")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "9b477a8b-afb2-450c-b23d-bd9252eaf6f7",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Percentage of stable playoff matches after 1000 iterations: 37.4%\n"
+     ]
+    }
+   ],
+   "source": [
+    "import random\n",
+    "\n",
+    "def gale_shapley(proposers, acceptors, proposer_preferences, acceptor_preferences):\n",
+    "    # Initialize empty matching\n",
+    "    matching = {}\n",
+    "    \n",
+    "    # Initialize proposers without partners\n",
+    "    free_proposers = list(proposers)\n",
+    "    \n",
+    "    while free_proposers:\n",
+    "        proposer = free_proposers.pop(0)\n",
+    "        proposer_prefs = proposer_preferences[proposer]\n",
+    "        \n",
+    "        for acceptor in proposer_prefs:\n",
+    "            current_partner = matching.get(acceptor)\n",
+    "            \n",
+    "            if current_partner is None:\n",
+    "                # Acceptor is free, match them with proposer\n",
+    "                matching[acceptor] = proposer\n",
+    "                break\n",
+    "            else:\n",
+    "                # Check if acceptor prefers proposer over current partner\n",
+    "                acceptor_prefs = acceptor_preferences[acceptor]\n",
+    "                if acceptor_prefs.index(proposer) < acceptor_prefs.index(current_partner):\n",
+    "                    # Acceptor prefers proposer, unmatch them and match proposer\n",
+    "                    matching[acceptor] = proposer\n",
+    "                    free_proposers.append(current_partner)\n",
+    "                    break\n",
+    "    \n",
+    "    return matching\n",
+    "\n",
+    "def is_stable_match(matching, proposer_preferences, acceptor_preferences):\n",
+    "    # Check if the current matching is stable\n",
+    "    for acceptor, proposer in matching.items():\n",
+    "        acceptor_prefs = acceptor_preferences[acceptor]\n",
+    "        current_partner_index = acceptor_prefs.index(proposer)\n",
+    "        for other_proposer in acceptor_prefs[:current_partner_index]:\n",
+    "            if proposer_preferences[other_proposer].index(acceptor) < proposer_preferences[proposer].index(acceptor):\n",
+    "                return False\n",
+    "    return True\n",
+    "\n",
+    "def calculate_stability_percentage(proposers, acceptors, num_iterations):\n",
+    "    stable_matches = 0\n",
+    "    \n",
+    "    for _ in range(num_iterations):\n",
+    "        # Create random preference lists for proposers and acceptors\n",
+    "        proposer_preferences = {team: random.sample(acceptors, len(acceptors)) for team in proposers}\n",
+    "        acceptor_preferences = {team: random.sample(proposers, len(proposers)) for team in acceptors}\n",
+    "        \n",
+    "        # Perform Gale-Shapley matching\n",
+    "        matching = gale_shapley(proposers, acceptors, proposer_preferences, acceptor_preferences)\n",
+    "        \n",
+    "        # Check if the matching is stable\n",
+    "        if is_stable_match(matching, proposer_preferences, acceptor_preferences):\n",
+    "            stable_matches += 1\n",
+    "    \n",
+    "    stability_percentage = (stable_matches / num_iterations) * 100\n",
+    "    return stability_percentage\n",
+    "\n",
+    "if __name__ == \"__main__\":\n",
+    "    west_teams = [\"Lakers\", \"Clippers\", \"Suns\", \"Warriors\", \"Jazz\", \"Nuggets\", \"Blazers\", \"Mavericks\"]\n",
+    "    east_teams = [\"Bucks\", \"Nets\", \"76ers\", \"Celtics\", \"Heat\", \"Hawks\", \"Knicks\", \"Raptors\"]\n",
+    "    \n",
+    "    num_iterations = 1000\n",
+    "    \n",
+    "    stability_percentage = calculate_stability_percentage(\n",
+    "        west_teams, east_teams, num_iterations\n",
+    "    )\n",
+    "    \n",
+    "    print(f\"Percentage of stable playoff matches after {num_iterations} iterations: {stability_percentage}%\")\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 8,
+   "id": "557a0b14-9805-4a48-85ea-ae910d750a97",
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Number of Teams: 8, Execution Time: 0.000000 seconds\n",
+      "Number of Teams: 16, Execution Time: 0.000000 seconds\n",
+      "Number of Teams: 32, Execution Time: 0.000000 seconds\n",
+      "Number of Teams: 64, Execution Time: 0.008048 seconds\n",
+      "Number of Teams: 128, Execution Time: 0.016365 seconds\n"
+     ]
+    }
+   ],
+   "source": [
+    "import random\n",
+    "import time\n",
+    "\n",
+    "def gale_shapley(proposers, acceptors, proposer_preferences, acceptor_preferences):\n",
+    "    # Initialize empty matching\n",
+    "    matching = {}\n",
+    "    \n",
+    "    # Initialize proposers without partners\n",
+    "    free_proposers = list(proposers)\n",
+    "    \n",
+    "    while free_proposers:\n",
+    "        proposer = free_proposers.pop(0)\n",
+    "        proposer_prefs = proposer_preferences[proposer]\n",
+    "        \n",
+    "        for acceptor in proposer_prefs:\n",
+    "            current_partner = matching.get(acceptor)\n",
+    "            \n",
+    "            if current_partner is None:\n",
+    "                # Acceptor is free, match them with proposer\n",
+    "                matching[acceptor] = proposer\n",
+    "                break\n",
+    "            else:\n",
+    "                # Check if acceptor prefers proposer over current partner\n",
+    "                acceptor_prefs = acceptor_preferences[acceptor]\n",
+    "                if acceptor_prefs.index(proposer) < acceptor_prefs.index(current_partner):\n",
+    "                    # Acceptor prefers proposer, unmatch them and match proposer\n",
+    "                    matching[acceptor] = proposer\n",
+    "                    free_proposers.append(current_partner)\n",
+    "                    break\n",
+    "    \n",
+    "    return matching\n",
+    "\n",
+    "def generate_teams_and_preferences(num_teams):\n",
+    "    teams = [f\"Team {i}\" for i in range(1, num_teams + 1)]\n",
+    "    preferences = {}\n",
+    "    \n",
+    "    for team in teams:\n",
+    "        other_teams = list(teams)\n",
+    "        other_teams.remove(team)\n",
+    "        random.shuffle(other_teams)\n",
+    "        preferences[team] = other_teams\n",
+    "    \n",
+    "    return teams, preferences\n",
+    "\n",
+    "if __name__ == \"__main__\":\n",
+    "    # Initial number of teams\n",
+    "    num_teams = 8\n",
+    "    \n",
+    "    # Number of iterations\n",
+    "    num_iterations = 10\n",
+    "    \n",
+    "    # Measure execution time for different sizes of teams\n",
+    "    for i in range(5):\n",
+    "        teams, preferences = generate_teams_and_preferences(num_teams)\n",
+    "        \n",
+    "        start_time = time.time()\n",
+    "        for _ in range(num_iterations):\n",
+    "            matching = gale_shapley(teams, teams, preferences, preferences)\n",
+    "        end_time = time.time()\n",
+    "        \n",
+    "        execution_time = end_time - start_time\n",
+    "        print(f\"Number of Teams: {num_teams}, Execution Time: {execution_time:.6f} seconds\")\n",
+    "        \n",
+    "        # Double the number of teams for the next iteration\n",
+    "        num_teams *= 2\n"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "a6784e53-6b92-42ee-a47a-aba4aaf8fce5",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "metadata": {
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "language": "python",
+   "name": "python3"
+  },
+  "language_info": {
+   "codemirror_mode": {
+    "name": "ipython",
+    "version": 3
+   },
+   "file_extension": ".py",
+   "mimetype": "text/x-python",
+   "name": "python",
+   "nbconvert_exporter": "python",
+   "pygments_lexer": "ipython3",
+   "version": "3.9.12"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}