{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2024-12-14T10:54:32.699159Z",
     "start_time": "2024-12-14T10:54:32.688460Z"
    }
   },
   "source": [
    "import queue\n",
    "\n",
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"Graph module.\n",
    "\n",
    "Provide an implementation of graphs with adjacency lists.\n",
    "\n",
    "In a graph, vertices are considered numbered from 0 to the order of the graph\n",
    "minus one. The vertex key can then be used to access its\n",
    "adjacency list.\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "class Graph:\n",
    "    \"\"\" Simple class for graph: adjacency lists\n",
    "\n",
    "    Attributes:\n",
    "        order (int): Number of vertices.\n",
    "        directed (bool): True if the graph is directed. False otherwise.\n",
    "        adjlists (List[List[int]]): Lists of connected vertices for each vertex.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, order, directed, labels=None):\n",
    "        \"\"\"Init graph, allocate adjacency lists\n",
    "\n",
    "        Args:\n",
    "            order (int): Number of nodes.\n",
    "            directed (bool): True if the graph is directed. False otherwise.\n",
    "            labels (list[str]): optionnal vector of vertex labels\n",
    "        \"\"\"\n",
    "\n",
    "        self.order = order\n",
    "        self.directed = directed\n",
    "        self.adjlists = []\n",
    "        for _ in range(order):\n",
    "            self.adjlists.append([])\n",
    "        self.labels = labels\n",
    "\n",
    "    def addedge(self, src, dst):\n",
    "        \"\"\"Add egde to graph.\n",
    "\n",
    "        Args:\n",
    "            src (int): Source vertex.\n",
    "            dst (int): Destination vertex.\n",
    "\n",
    "        Raises:\n",
    "            IndexError: If any vertex index is invalid.\n",
    "\n",
    "        \"\"\"\n",
    "        if src >= self.order or src < 0:\n",
    "            raise IndexError(\"Invalid src index\")\n",
    "        if dst >= self.order or dst < 0:\n",
    "            raise IndexError(\"Invalid dst index\")\n",
    "\n",
    "        self.adjlists[src].append(dst)\n",
    "        if not self.directed and dst != src:\n",
    "            self.adjlists[dst].append(src)\n",
    "\n",
    "\n",
    "    def addvertex(self, number=1, labels=None):\n",
    "        \"\"\"Add number vertices to graph.\n",
    "\n",
    "        Args:\n",
    "            ref (Graph).\n",
    "            number (int): Number of vertices to add.\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        # Increment order and extend adjacency list\n",
    "        self.order += number\n",
    "        for _ in range(number):\n",
    "            self.adjlists.append([])\n",
    "        if labels:\n",
    "            self.labels += labels\n",
    "\n",
    "    def removeedge(self, src, dst):\n",
    "        \"\"\"Remove egde from the graph.\n",
    "\n",
    "        Args:\n",
    "            src (int): Source vertex.\n",
    "            dst (int): Destination vertex.\n",
    "\n",
    "        Raises:\n",
    "            IndexError: If any vertex index is invalid.\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        if src >= self.order or src < 0:\n",
    "            raise IndexError(\"Invalid src index\")\n",
    "        if dst >= self.order or dst < 0:\n",
    "            raise IndexError(\"Invalid dst index\")\n",
    "        if dst in self.adjlists[src]:\n",
    "            self.adjlists[src].remove(dst)\n",
    "            if not self.directed and dst != src:\n",
    "                self.adjlists[dst].remove(src)\n",
    "\n",
    "def sortgraph(G):\n",
    "    \"\"\"\n",
    "    sorts adjacency lists -> to have same results as those asked in tutorials/exams\n",
    "    \"\"\"\n",
    "    for i in range(G.order):\n",
    "        G.adjlists[i].sort()\n",
    "\n",
    "def dot(G):\n",
    "    \"\"\"Dot format of graph.\n",
    "\n",
    "    Args:\n",
    "        Graph\n",
    "\n",
    "    Returns:\n",
    "        str: String storing dot format of graph.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    if G.directed:\n",
    "        s = \"digraph {\\n\"\n",
    "        for x in range(G.order):\n",
    "            if G.labels:\n",
    "                s += \"  \" + str(x) + '[label = \"' + G.labels[x] + '\"]\\n'\n",
    "            else:\n",
    "                s += \"  \" + str(x) + '\\n'\n",
    "            for y in G.adjlists[x]:\n",
    "                s += str(x) + \" -> \" + str(y) + '\\n'\n",
    "    else:\n",
    "        s = \"graph {\\n\"\n",
    "        for x in range(G.order):\n",
    "            if G.labels:\n",
    "                s += \"  \" + str(x) + '[label = \"' + G.labels[x] + '\"]\\n'\n",
    "            else:\n",
    "                s += \"  \" + str(x) + '\\n'\n",
    "            for y in G.adjlists[x]:\n",
    "                if x <= y:\n",
    "                    s += str(x) + \" -- \" + str(y) + '\\n'\n",
    "    return s + '}'\n",
    "\n",
    "def display(G, eng=None):\n",
    "    \"\"\"\n",
    "    *Warning:* Made for use within IPython/Jupyter only.\n",
    "    eng: graphivz.Source \"engine\" optional argument (try \"neato\", \"fdp\", \"sfdp\", \"circo\")\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    try:\n",
    "        from graphviz import Source\n",
    "        from IPython.display import display\n",
    "    except:\n",
    "        raise Exception(\"Missing module: graphviz and/or IPython.\")\n",
    "    display(Source(dot(G), engine = eng))\n",
    "\n",
    "\n",
    "# load / save gra format\n",
    "\n",
    "def load(filename):\n",
    "    \"\"\"Build a new graph from a GRA file.\n",
    "\n",
    "    Args:\n",
    "        filename (str): File to load.\n",
    "\n",
    "    Returns:\n",
    "        Graph: New graph.\n",
    "\n",
    "    Raises:\n",
    "        FileNotFoundError: If file does not exist.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    f = open(filename)\n",
    "    lines = f.readlines()\n",
    "    f.close()\n",
    "\n",
    "    infos = {}\n",
    "    i = 0\n",
    "    while '#' in lines[i]:\n",
    "        (key, val) = lines[i][1:].strip().split(\": \")\n",
    "        infos[key] = val\n",
    "        i += 1\n",
    "\n",
    "    directed = bool(int(lines[i]))\n",
    "    order = int(lines[i+1])\n",
    "\n",
    "    if infos and \"labels\" in infos:\n",
    "        labels = infos[\"labels\"].split(',') #labels is a list of str\n",
    "        G = Graph(order, directed, labels)  # a graph with labels\n",
    "    else:\n",
    "        G = Graph(order, directed)  # a graph without labels\n",
    "    if infos:\n",
    "        G.infos = infos\n",
    "\n",
    "    for line in lines[i+2:]:\n",
    "        edge = line.strip().split(' ')\n",
    "        (src, dst) = (int(edge[0]), int(edge[1]))\n",
    "        G.addedge(src, dst)\n",
    "    return G\n",
    "\n",
    "\n",
    "def save(G, fileOut):\n",
    "    gra = \"\"\n",
    "    if G.labels:\n",
    "        lab = \"#labels: \"\n",
    "        for i in range(G.order - 1):\n",
    "            lab += G.labels[i] + ','\n",
    "        lab += G.labels[-1]\n",
    "        gra += lab + '\\n'\n",
    "    gra += str(int(G.directed)) + '\\n'\n",
    "    gra += str(G.order) + '\\n'\n",
    "    for x in range(G.order):\n",
    "        for y in G.adjlists[x]:\n",
    "            if G.directed or x >= y:\n",
    "                gra += str(x) + \" \" + str(y) + '\\n'\n",
    "    fout = open(fileOut, mode='w')\n",
    "    fout.write(gra)\n",
    "    fout.close()\n"
   ],
   "outputs": [],
   "execution_count": 3
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-14T10:54:33.640420Z",
     "start_time": "2024-12-14T10:54:33.634885Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"Graph module.\n",
    "\n",
    "Provide an implementation of graphs with adjacency matrix.\n",
    "This can also be called static implementation.\n",
    "\n",
    "In a graph, vertices are considered numbered from 0 to the order of the graph\n",
    "minus one.\n",
    "\n",
    "\"\"\"\n",
    "\n",
    "\n",
    "class GraphMat:\n",
    "    \"\"\" Simple class for static graph.\n",
    "\n",
    "    Attributes:\n",
    "        order (int): Number of vertices.\n",
    "        directed (bool): True if the graph is directed. False otherwise.\n",
    "        adj (List[List[int]]): Adjacency matrix\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, order, directed):\n",
    "        \"\"\"\n",
    "        Args:\n",
    "            order (int): Number of nodes.\n",
    "            directed (bool): True if the graph is directed. False otherwise.\n",
    "        \"\"\"\n",
    "\n",
    "        self.order = order\n",
    "        self.directed = directed\n",
    "        self.adj = [[0 for j in range(order)] for i in range(order)]\n",
    "\n",
    "\n",
    "    def addedge(self, src, dst):\n",
    "        \"\"\"Add egde to graph.\n",
    "\n",
    "        Args:\n",
    "            src (int): Source vertex.\n",
    "            dst (int): Destination vertex.\n",
    "\n",
    "        Raises:\n",
    "            IndexError: If any vertex index is invalid.\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        if src >= self.order or src < 0:\n",
    "            raise IndexError(\"Invalid src index\")\n",
    "        if dst >= self.order or dst < 0:\n",
    "            raise IndexError(\"Invalid dst index\")\n",
    "\n",
    "        self.adj[src][dst] += 1\n",
    "        if not self.directed and dst != src:\n",
    "            self.adj[dst][src] += 1\n",
    "\n",
    "\n",
    "\n",
    "def dot(G):\n",
    "    \"\"\"Dot format of graph.\n",
    "\n",
    "    Args:\n",
    "        GraphMat\n",
    "\n",
    "    Returns:\n",
    "        str: String storing dot format of graph.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    if G.directed:\n",
    "        s = \"digraph {\\n\"\n",
    "        link = \" -> \"\n",
    "        for x in range(G.order):\n",
    "            for y in range(G.order):\n",
    "                s += (str(x) + link + str(y) + '\\n') * G.adj[x][y]\n",
    "    else:\n",
    "        s = \"graph {\\n\"\n",
    "        link = \" -- \"\n",
    "        for x in range(G.order):\n",
    "            for y in range(x+1):\n",
    "                s += (str(x) + link + str(y) + '\\n') * G.adj[x][y]\n",
    "    return s + '}'\n",
    "\n",
    "\n",
    "\n",
    "def display(G, eng=None):\n",
    "    \"\"\"\n",
    "    *Warning:* Made for use within IPython/Jupyter only.\n",
    "    eng: graphivz.Source \"engine\" optional argument (try \"neato\", \"fdp\", \"sfdp\", \"circo\")\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    try:\n",
    "        from graphviz import Source\n",
    "        from IPython.display import display\n",
    "    except:\n",
    "        raise Exception(\"Missing module: graphviz and/or IPython.\")\n",
    "    display(Source(dot(G), engine = eng))\n",
    "\n",
    "\n",
    "# load / save gra format    (do not manage labels and other infos)\n",
    "\n",
    "def load(filename,):\n",
    "    \"\"\"Build a new graph from a GRA file.\n",
    "\n",
    "    Args:\n",
    "        filename (str): File to load.\n",
    "\n",
    "    Returns:\n",
    "        Graph: New graph.\n",
    "\n",
    "    Raises:\n",
    "        FileNotFoundError: If file does not exist.\n",
    "\n",
    "    \"\"\"\n",
    "\n",
    "    f = open(filename)\n",
    "    directed = bool(int(f.readline()))\n",
    "    order = int(f.readline())\n",
    "    g = GraphMat(order, directed)\n",
    "    for line in f.readlines():\n",
    "        edge = line.strip().split(' ')\n",
    "        (src, dst) = (int(edge[0]), int(edge[1]))\n",
    "        g.addedge(src, dst)\n",
    "    f.close()\n",
    "    return g\n",
    "\n",
    "def save(G, fileOut):\n",
    "    gra = str(int(G.directed)) + '\\n'\n",
    "    gra += str(G.order) + '\\n'\n",
    "    for x in range(G.order):\n",
    "        if G.directed:\n",
    "            n = G.order\n",
    "        else:\n",
    "            n = x + 1\n",
    "        for y in range(n):\n",
    "            for i in range(G.adj[x][y]):\n",
    "                gra += str(x) + \" \" + str(y) + '\\n'\n",
    "    fout = open(fileOut, mode='w')\n",
    "    fout.write(gra)\n",
    "    fout.close()\n"
   ],
   "id": "e12f5903c5348752",
   "outputs": [],
   "execution_count": 4
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-14T10:54:34.476061Z",
     "start_time": "2024-12-14T10:54:34.472348Z"
    }
   },
   "cell_type": "code",
   "source": [
    "# -*- coding: utf-8 -*-\n",
    "\"\"\"Queue module.\"\"\"\n",
    "\n",
    "from collections import deque\n",
    "\n",
    "class Queue:\n",
    "    \"\"\"Simple class for FIFO (first-in-first-out) container.\"\"\"\n",
    "\n",
    "    def __init__(self):\n",
    "        \"\"\"Init queue.\"\"\"\n",
    "\n",
    "        self.elements = deque()\n",
    "\n",
    "    def enqueue(self, elt):\n",
    "        \"\"\"Add an element to the queue.\n",
    "\n",
    "        Args:\n",
    "            elt (Any): Element to enqueue.\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        self.elements.append(elt)\n",
    "\n",
    "    def dequeue(self):\n",
    "        \"\"\"Remove and return next element from the queue.\n",
    "\n",
    "        Returns:\n",
    "            Any: Element from the queue.\n",
    "\n",
    "        Raises:\n",
    "            IndexError: If queue is empty.\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        return self.elements.popleft()\n",
    "\n",
    "    def isempty(self):\n",
    "        \"\"\"Check whether queue is empty.\n",
    "\n",
    "        Returns:\n",
    "            bool: True if queue is empty, False otherwise.\n",
    "\n",
    "        \"\"\"\n",
    "\n",
    "        return len(self.elements) == 0\n"
   ],
   "id": "663b49e4f6763d11",
   "outputs": [],
   "execution_count": 5
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Graph figure 2",
   "id": "52a4e079fe9cea35"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-14T10:54:38.976275Z",
     "start_time": "2024-12-14T10:54:38.973873Z"
    }
   },
   "cell_type": "code",
   "source": [
    "G = Graph(10, False)\n",
    "G.adjlists = [[4, 4, 1, 3],\n",
    "               [0],\n",
    "               [6, 6, 6, 5, 7],\n",
    "               [0],\n",
    "               [0, 0, 9],\n",
    "               [2, 7, 8],\n",
    "               [2, 2, 2, 7],\n",
    "               [2, 6, 5, 8],\n",
    "               [7, 5, 8],\n",
    "               [4]]\n",
    "\n"
   ],
   "id": "ca54f5a3f1a225b",
   "outputs": [],
   "execution_count": 6
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-14T10:54:39.957846Z",
     "start_time": "2024-12-14T10:54:39.955269Z"
    }
   },
   "cell_type": "code",
   "source": [
    "print(G.order)\n",
    "print(G.adjlists)\n",
    "print(G.adjlists[1])\n"
   ],
   "id": "45b4722e0e0844c6",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "10\n",
      "[[4, 4, 1, 3], [0], [6, 6, 6, 5, 7], [0], [0, 0, 9], [2, 7, 8], [2, 2, 2, 7], [2, 6, 5, 8], [7, 5, 8], [4]]\n",
      "[0]\n"
     ]
    }
   ],
   "execution_count": 7
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Graph Figure 1",
   "id": "7b374e3cdb9f773c"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-14T10:54:41.253023Z",
     "start_time": "2024-12-14T10:54:41.250277Z"
    }
   },
   "cell_type": "code",
   "source": [
    "G1 = Graph(9, True)\n",
    "G1.adjlists = [[4, 1, 1, 1, 5, 3],\n",
    "               [4],\n",
    "               [3],\n",
    "               [6, 6],\n",
    "               [],\n",
    "               [4, 2, 0],\n",
    "               [0, 5],\n",
    "               [8, 1, 0],\n",
    "               [6, 8]]\n"
   ],
   "id": "6920c423c0bdfc24",
   "outputs": [],
   "execution_count": 8
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Exercise 1.3",
   "id": "313f1375b01bcce1"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T14:48:04.596974Z",
     "start_time": "2024-12-09T14:48:04.592782Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def degrees(G):\n",
    "    final = []\n",
    "    for element in G.adjlists:\n",
    "        final.append(len(element))\n",
    "    return final\n",
    "\n",
    "degrees(G)"
   ],
   "id": "55ba6e30c008762e",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[4, 1, 5, 1, 3, 3, 4, 4, 3, 1]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 8
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T14:48:05.120730Z",
     "start_time": "2024-12-09T14:48:05.116518Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def in_out_degrees(G):\n",
    "    In = [0] * G.order\n",
    "    Out = [0] * G.order\n",
    "    for i in range(G.order):\n",
    "        for element in G.adjlists[i]:\n",
    "            In[element] += 1\n",
    "            Out[i] += 1\n",
    "    return [In, Out]\n",
    "\n",
    "in_out_degrees(G1)"
   ],
   "id": "1b1a1615d90dc209",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[[3, 4, 1, 2, 3, 2, 3, 0, 2], [6, 1, 1, 2, 0, 3, 2, 3, 2]]"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 9
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Exercise 1.4",
   "id": "4bd26fbd65135589"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T14:48:06.156919Z",
     "start_time": "2024-12-09T14:48:06.154020Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def dot(G):\n",
    "    string = \"digraph {\\n\"\n",
    "    if G.directed:\n",
    "        for i in range(G.order):\n",
    "            for element in G.adjlists[i]:\n",
    "                string += f\"{i} --> {element}\\n\"\n",
    "    elif not G.directed:\n",
    "        for i in range(G.order):\n",
    "            for element in G.adjlists[i]:\n",
    "                string += f\"{i} -- {element}\\n\"\n",
    "    string += \"}\"\n",
    "    return string\n",
    "\n",
    "print(dot(G1))\n",
    "print(dot(G))"
   ],
   "id": "f7602fcf61e82a17",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "digraph {\n",
      "0 --> 4\n",
      "0 --> 1\n",
      "0 --> 1\n",
      "0 --> 1\n",
      "0 --> 5\n",
      "0 --> 3\n",
      "1 --> 4\n",
      "2 --> 3\n",
      "3 --> 6\n",
      "3 --> 6\n",
      "5 --> 4\n",
      "5 --> 2\n",
      "5 --> 0\n",
      "6 --> 0\n",
      "6 --> 5\n",
      "7 --> 8\n",
      "7 --> 1\n",
      "7 --> 0\n",
      "8 --> 6\n",
      "8 --> 8\n",
      "}\n",
      "digraph {\n",
      "0 -- 4\n",
      "0 -- 4\n",
      "0 -- 1\n",
      "0 -- 3\n",
      "1 -- 0\n",
      "2 -- 6\n",
      "2 -- 6\n",
      "2 -- 6\n",
      "2 -- 5\n",
      "2 -- 7\n",
      "3 -- 0\n",
      "4 -- 0\n",
      "4 -- 0\n",
      "4 -- 9\n",
      "5 -- 2\n",
      "5 -- 7\n",
      "5 -- 8\n",
      "6 -- 2\n",
      "6 -- 2\n",
      "6 -- 2\n",
      "6 -- 7\n",
      "7 -- 2\n",
      "7 -- 6\n",
      "7 -- 5\n",
      "7 -- 8\n",
      "8 -- 7\n",
      "8 -- 5\n",
      "8 -- 8\n",
      "9 -- 4\n",
      "}\n"
     ]
    }
   ],
   "execution_count": 10
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Exercise 2.1 (BFS)\n",
   "id": "ebfdd54aefc25650"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-14T10:59:44.343779Z",
     "start_time": "2024-12-14T10:59:44.337510Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def aux(G, M, src):\n",
    "    cur = Queue()\n",
    "    cur.enqueue(src)\n",
    "    M[src] = True\n",
    "    while not cur.isempty():\n",
    "        x = cur.dequeue()\n",
    "        print(x, end=\" \")\n",
    "        for adj in G.adjlists[x]:\n",
    "            if not M[adj]:\n",
    "                M[adj] = True\n",
    "                cur.enqueue(adj)\n",
    "\n",
    "\n",
    "def dfs(G):\n",
    "    M = [False]*G.order\n",
    "    for src in range(G.order):\n",
    "        if not M[src]:\n",
    "            aux(G, M, src)\n",
    "            print()\n",
    "BFS(G)"
   ],
   "id": "b8bf6413a1d63515",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4 1 3 9 \n",
      "2 6 5 7 8 \n"
     ]
    }
   ],
   "execution_count": 20
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Exercise 2.2 (DFS)",
   "id": "55b1247fe428aa0d"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-14T11:01:46.103932Z",
     "start_time": "2024-12-14T11:01:46.101045Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def auxDFS(G, M, src):\n",
    "    M[src] = True\n",
    "    print(src, end=\" \")\n",
    "    for adj in G.adjlists[src]:\n",
    "        if not M[adj]:\n",
    "            auxDFS(G, M, adj)\n",
    "\n",
    "def DFS(G):\n",
    "    M = [False] * G.order\n",
    "    for src in range(G.order):\n",
    "        if not M[src]:\n",
    "            aux(G, M, src)\n",
    "            print()\n",
    "DFS(G)"
   ],
   "id": "507b403020a6f941",
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0 4 1 3 9 \n",
      "2 6 5 7 8 \n"
     ]
    }
   ],
   "execution_count": 23
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Exercise 3.1 (Connect)",
   "id": "a30c671c43131bb2"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T15:03:14.627181Z",
     "start_time": "2024-12-09T15:03:14.622512Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def __components(G, M, src, nbComponents):\n",
    "    M[src] = nbComponents\n",
    "    for adj in G.adjlists[src]:\n",
    "        if not M[adj]:\n",
    "            M[adj] = nbComponents\n",
    "            __components(G, M, adj, nbComponents)\n",
    "\n",
    "def components(G):\n",
    "    M = [False] * G.order\n",
    "    nbComponents = 0\n",
    "    for src in range(G.order):\n",
    "        if not M[src]:\n",
    "            nbComponents += 1\n",
    "            __components(G, M, src, nbComponents)\n",
    "    return (nbComponents, M)\n",
    "\n",
    "components(G)\n"
   ],
   "id": "b8b8a6ec16fc88a5",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2, [1, 1, 2, 1, 1, 2, 2, 2, 2, 1])"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 16
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# Exercise 3.2 (That's the way)",
   "id": "dae9cdccb36ac9d5"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T15:09:02.024738Z",
     "start_time": "2024-12-09T15:09:02.020400Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def __path(G, src, dst, M, path):\n",
    "    M[src] = True\n",
    "    for adj in G.adjlists[src]:\n",
    "        if not M[src]:\n",
    "            if adj == dst or __path(G, src, dst, M, path):\n",
    "                path.append(adj)\n",
    "                return True\n",
    "    return False\n",
    "\n",
    "def path(G, src, dst):\n",
    "    M = [False] * G.order\n",
    "    path = []\n",
    "    if __path(G, src, dst, M, path):\n",
    "        path.append(src)\n",
    "        path.reverse()\n",
    "    return path\n",
    "\n",
    "path(G, 0, 9)"
   ],
   "id": "67b1808a9c9996e1",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[]"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 26
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "",
   "id": "9b679ab534f329fb"
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": "",
   "id": "71f4c39123fe94c1"
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# 2025 - Exercise 1",
   "id": "b67ef07f6d7c99b0"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T15:48:15.121203Z",
     "start_time": "2024-12-09T15:48:15.116918Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def aux(G, M, src):\n",
    "    newColor = not M[src]\n",
    "    for adj in G.adjlists[src]:\n",
    "        if M[adj] == None:\n",
    "            M[adj] = newColor\n",
    "            if not aux(G, M, adj):\n",
    "                return False\n",
    "        else:\n",
    "            if M[adj] != newColor:\n",
    "                return False\n",
    "    return True\n",
    "\n",
    "\n",
    "def two_coloring(G):\n",
    "    M = [None] * G.order\n",
    "    for src in range(G.order):\n",
    "        if M[src] == None:\n",
    "            M[src] = True\n",
    "        if not aux(G, M, src):\n",
    "            return False\n",
    "    return True\n",
    "\n",
    "two_coloring(G1)"
   ],
   "id": "9ed534351df71362",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "execution_count": 32
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# 2025 - Exercise 2",
   "id": "38c3d4e952147c50"
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2024-12-09T16:08:14.367172Z",
     "start_time": "2024-12-09T16:08:14.361769Z"
    }
   },
   "cell_type": "code",
   "source": [
    "def __fakenews(G, M, src, truth):\n",
    "    cur = Queue()\n",
    "    cur.enqueue(src)\n",
    "    stop = False\n",
    "    while not cur.isempty() and not stop:\n",
    "        x = cur.dequeue()\n",
    "        if M[x] > truth + 1:\n",
    "            for adj in G.adjlists[x]:\n",
    "                if M[adj] == None:\n",
    "                    M[adj] = M[x] - 1\n",
    "                    cur.enqueue(adj)\n",
    "        else:\n",
    "            stop = True\n",
    "\n",
    "def fakenews(G, src, truth):\n",
    "    if (truth <= 2):\n",
    "        raise Exception(\"truth should be > 2\")\n",
    "    M = [False] * G.order\n",
    "    M[src] = truth\n",
    "    fake = []\n",
    "    __fakenews(G, M, src, truth // 2)\n",
    "    for i in range(G.order):\n",
    "        if M[i] == None:\n",
    "            fake.append(i)\n",
    "    return truth"
   ],
   "id": "c66ac4688a6975c9",
   "outputs": [],
   "execution_count": 34
  },
  {
   "metadata": {},
   "cell_type": "markdown",
   "source": "# 2027 - Exercice 1",
   "id": "b8fa23568b4bd3df"
  },
  {
   "metadata": {},
   "cell_type": "code",
   "outputs": [],
   "execution_count": null,
   "source": [
    "def __longest_path(G, dist, src):\n",
    "\n",
    "\n",
    "def longest_path(G):\n",
    "    dist = [None] * G.order\n",
    "    for src in range(G.order):\n",
    "        __longest_path(G, dist, src)"
   ],
   "id": "9a3a85d15dccbb97"
  }
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