1073 lines
27 KiB
Plaintext
1073 lines
27 KiB
Plaintext
{
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"cells": [
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{
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"cell_type": "code",
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"id": "initial_id",
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"metadata": {
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"collapsed": true,
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"ExecuteTime": {
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"end_time": "2024-12-14T12:23:31.698030Z",
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"start_time": "2024-12-14T12:23:31.686929Z"
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}
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},
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"source": [
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"import queue\n",
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"\n",
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"# -*- coding: utf-8 -*-\n",
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"\"\"\"Graph module.\n",
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"\n",
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"Provide an implementation of graphs with adjacency lists.\n",
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"\n",
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"In a graph, vertices are considered numbered from 0 to the order of the graph\n",
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"minus one. The vertex key can then be used to access its\n",
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"adjacency list.\n",
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"\n",
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"\"\"\"\n",
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"\n",
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"\n",
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"class Graph:\n",
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" \"\"\" Simple class for graph: adjacency lists\n",
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"\n",
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" Attributes:\n",
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" order (int): Number of vertices.\n",
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" directed (bool): True if the graph is directed. False otherwise.\n",
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" adjlists (List[List[int]]): Lists of connected vertices for each vertex.\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" def __init__(self, order, directed, labels=None):\n",
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" \"\"\"Init graph, allocate adjacency lists\n",
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"\n",
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" Args:\n",
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" order (int): Number of nodes.\n",
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" directed (bool): True if the graph is directed. False otherwise.\n",
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" labels (list[str]): optionnal vector of vertex labels\n",
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" \"\"\"\n",
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"\n",
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" self.order = order\n",
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" self.directed = directed\n",
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" self.adjlists = []\n",
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" for _ in range(order):\n",
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" self.adjlists.append([])\n",
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" self.labels = labels\n",
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"\n",
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" def addedge(self, src, dst):\n",
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" \"\"\"Add egde to graph.\n",
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"\n",
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" Args:\n",
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" src (int): Source vertex.\n",
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" dst (int): Destination vertex.\n",
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"\n",
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" Raises:\n",
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" IndexError: If any vertex index is invalid.\n",
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"\n",
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" \"\"\"\n",
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" if src >= self.order or src < 0:\n",
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" raise IndexError(\"Invalid src index\")\n",
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" if dst >= self.order or dst < 0:\n",
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" raise IndexError(\"Invalid dst index\")\n",
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"\n",
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" self.adjlists[src].append(dst)\n",
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" if not self.directed and dst != src:\n",
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" self.adjlists[dst].append(src)\n",
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"\n",
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"\n",
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" def addvertex(self, number=1, labels=None):\n",
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" \"\"\"Add number vertices to graph.\n",
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"\n",
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" Args:\n",
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" ref (Graph).\n",
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" number (int): Number of vertices to add.\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" # Increment order and extend adjacency list\n",
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" self.order += number\n",
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" for _ in range(number):\n",
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" self.adjlists.append([])\n",
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" if labels:\n",
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" self.labels += labels\n",
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"\n",
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" def removeedge(self, src, dst):\n",
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" \"\"\"Remove egde from the graph.\n",
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"\n",
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" Args:\n",
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" src (int): Source vertex.\n",
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" dst (int): Destination vertex.\n",
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"\n",
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" Raises:\n",
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" IndexError: If any vertex index is invalid.\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" if src >= self.order or src < 0:\n",
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" raise IndexError(\"Invalid src index\")\n",
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" if dst >= self.order or dst < 0:\n",
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" raise IndexError(\"Invalid dst index\")\n",
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" if dst in self.adjlists[src]:\n",
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" self.adjlists[src].remove(dst)\n",
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" if not self.directed and dst != src:\n",
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" self.adjlists[dst].remove(src)\n",
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"\n",
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"def sortgraph(G):\n",
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" \"\"\"\n",
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" sorts adjacency lists -> to have same results as those asked in tutorials/exams\n",
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" \"\"\"\n",
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" for i in range(G.order):\n",
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" G.adjlists[i].sort()\n",
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"\n",
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"def dot(G):\n",
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" \"\"\"Dot format of graph.\n",
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"\n",
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" Args:\n",
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" Graph\n",
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"\n",
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" Returns:\n",
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" str: String storing dot format of graph.\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" if G.directed:\n",
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" s = \"digraph {\\n\"\n",
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" for x in range(G.order):\n",
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" if G.labels:\n",
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" s += \" \" + str(x) + '[label = \"' + G.labels[x] + '\"]\\n'\n",
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" else:\n",
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" s += \" \" + str(x) + '\\n'\n",
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" for y in G.adjlists[x]:\n",
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" s += str(x) + \" -> \" + str(y) + '\\n'\n",
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" else:\n",
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" s = \"graph {\\n\"\n",
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" for x in range(G.order):\n",
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" if G.labels:\n",
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" s += \" \" + str(x) + '[label = \"' + G.labels[x] + '\"]\\n'\n",
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" else:\n",
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" s += \" \" + str(x) + '\\n'\n",
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" for y in G.adjlists[x]:\n",
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" if x <= y:\n",
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" s += str(x) + \" -- \" + str(y) + '\\n'\n",
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" return s + '}'\n",
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"\n",
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"def display(G, eng=None):\n",
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" \"\"\"\n",
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" *Warning:* Made for use within IPython/Jupyter only.\n",
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" eng: graphivz.Source \"engine\" optional argument (try \"neato\", \"fdp\", \"sfdp\", \"circo\")\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" try:\n",
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" from graphviz import Source\n",
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" from IPython.display import display\n",
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" except:\n",
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" raise Exception(\"Missing module: graphviz and/or IPython.\")\n",
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" display(Source(dot(G), engine = eng))\n",
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"\n",
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"\n",
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"# load / save gra format\n",
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"\n",
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"def load(filename):\n",
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" \"\"\"Build a new graph from a GRA file.\n",
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"\n",
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" Args:\n",
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" filename (str): File to load.\n",
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"\n",
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" Returns:\n",
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" Graph: New graph.\n",
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"\n",
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" Raises:\n",
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" FileNotFoundError: If file does not exist.\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" f = open(filename)\n",
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" lines = f.readlines()\n",
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" f.close()\n",
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"\n",
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" infos = {}\n",
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" i = 0\n",
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" while '#' in lines[i]:\n",
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" (key, val) = lines[i][1:].strip().split(\": \")\n",
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" infos[key] = val\n",
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" i += 1\n",
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"\n",
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" directed = bool(int(lines[i]))\n",
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" order = int(lines[i+1])\n",
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"\n",
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" if infos and \"labels\" in infos:\n",
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" labels = infos[\"labels\"].split(',') #labels is a list of str\n",
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" G = Graph(order, directed, labels) # a graph with labels\n",
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" else:\n",
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" G = Graph(order, directed) # a graph without labels\n",
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" if infos:\n",
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" G.infos = infos\n",
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"\n",
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" for line in lines[i+2:]:\n",
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" edge = line.strip().split(' ')\n",
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" (src, dst) = (int(edge[0]), int(edge[1]))\n",
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" G.addedge(src, dst)\n",
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" return G\n",
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"\n",
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"\n",
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"def save(G, fileOut):\n",
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" gra = \"\"\n",
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" if G.labels:\n",
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" lab = \"#labels: \"\n",
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" for i in range(G.order - 1):\n",
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" lab += G.labels[i] + ','\n",
|
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" lab += G.labels[-1]\n",
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" gra += lab + '\\n'\n",
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" gra += str(int(G.directed)) + '\\n'\n",
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" gra += str(G.order) + '\\n'\n",
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" for x in range(G.order):\n",
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" for y in G.adjlists[x]:\n",
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" if G.directed or x >= y:\n",
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" gra += str(x) + \" \" + str(y) + '\\n'\n",
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" fout = open(fileOut, mode='w')\n",
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" fout.write(gra)\n",
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" fout.close()\n"
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],
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"outputs": [],
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"execution_count": 1
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-12-14T12:23:31.740543Z",
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"start_time": "2024-12-14T12:23:31.738488Z"
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}
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},
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"cell_type": "code",
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"source": "",
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"id": "e12f5903c5348752",
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"outputs": [],
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"execution_count": null
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-12-14T12:23:31.807702Z",
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"start_time": "2024-12-14T12:23:31.804575Z"
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}
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},
|
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"cell_type": "code",
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"source": [
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"# -*- coding: utf-8 -*-\n",
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"\"\"\"Queue module.\"\"\"\n",
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"\n",
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"from collections import deque\n",
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"\n",
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"class Queue:\n",
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" \"\"\"Simple class for FIFO (first-in-first-out) container.\"\"\"\n",
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"\n",
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" def __init__(self):\n",
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" \"\"\"Init queue.\"\"\"\n",
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"\n",
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" self.elements = deque()\n",
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"\n",
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" def enqueue(self, elt):\n",
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" \"\"\"Add an element to the queue.\n",
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"\n",
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" Args:\n",
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" elt (Any): Element to enqueue.\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" self.elements.append(elt)\n",
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"\n",
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" def dequeue(self):\n",
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" \"\"\"Remove and return next element from the queue.\n",
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"\n",
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" Returns:\n",
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" Any: Element from the queue.\n",
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"\n",
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" Raises:\n",
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" IndexError: If queue is empty.\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" return self.elements.popleft()\n",
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"\n",
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" def isempty(self):\n",
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" \"\"\"Check whether queue is empty.\n",
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"\n",
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" Returns:\n",
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" bool: True if queue is empty, False otherwise.\n",
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"\n",
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" \"\"\"\n",
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"\n",
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" return len(self.elements) == 0\n"
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],
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"id": "663b49e4f6763d11",
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"outputs": [],
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"execution_count": 2
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": "# Graph figure 2",
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"id": "52a4e079fe9cea35"
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-12-14T12:23:31.826260Z",
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"start_time": "2024-12-14T12:23:31.824156Z"
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}
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},
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"cell_type": "code",
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"source": [
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"G = Graph(10, False)\n",
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"G.adjlists = [[4, 4, 1, 3],\n",
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" [0],\n",
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" [6, 6, 6, 5, 7],\n",
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" [0],\n",
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" [0, 0, 9],\n",
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" [2, 7, 8],\n",
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" [2, 2, 2, 7],\n",
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" [2, 6, 5, 8],\n",
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" [7, 5, 8],\n",
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" [4]]\n",
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"\n"
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],
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"id": "ca54f5a3f1a225b",
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"outputs": [],
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"execution_count": 3
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2024-12-14T12:23:31.853995Z",
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"start_time": "2024-12-14T12:23:31.851762Z"
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}
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},
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"cell_type": "code",
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"source": [
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"print(G.order)\n",
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"print(G.adjlists)\n",
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"print(G.adjlists[1])\n"
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],
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"id": "45b4722e0e0844c6",
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10\n",
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"[[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",
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"[0]\n"
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]
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}
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],
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"execution_count": 4
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},
|
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": "# Graph Figure 1",
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"id": "7b374e3cdb9f773c"
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},
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{
|
|
"metadata": {
|
|
"ExecuteTime": {
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"end_time": "2024-12-14T12:23:31.886996Z",
|
|
"start_time": "2024-12-14T12:23:31.884644Z"
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}
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},
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"cell_type": "code",
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"source": [
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"G1 = Graph(9, True)\n",
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"G1.adjlists = [[4, 1, 1, 1, 5, 3],\n",
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" [4],\n",
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" [3],\n",
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" [6, 6],\n",
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" [],\n",
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" [4, 2, 0],\n",
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" [0, 5],\n",
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" [8, 1, 0],\n",
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" [6, 8]]\n"
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],
|
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"id": "6920c423c0bdfc24",
|
|
"outputs": [],
|
|
"execution_count": 5
|
|
},
|
|
{
|
|
"metadata": {},
|
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"cell_type": "markdown",
|
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"source": "# Exercise 1.3",
|
|
"id": "313f1375b01bcce1"
|
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},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2024-12-14T12:23:31.913924Z",
|
|
"start_time": "2024-12-14T12:23:31.909906Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
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"source": [
|
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"def degrees(G):\n",
|
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" final = []\n",
|
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" for element in G.adjlists:\n",
|
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" final.append(len(element))\n",
|
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" return final\n",
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"\n",
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"degrees(G)"
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],
|
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"id": "55ba6e30c008762e",
|
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"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"[4, 1, 5, 1, 3, 3, 4, 4, 3, 1]"
|
|
]
|
|
},
|
|
"execution_count": 6,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"execution_count": 6
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2024-12-14T12:23:31.946802Z",
|
|
"start_time": "2024-12-14T12:23:31.943693Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def in_out_degrees(G):\n",
|
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" In = [0] * G.order\n",
|
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" Out = [0] * G.order\n",
|
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" for i in range(G.order):\n",
|
|
" for element in G.adjlists[i]:\n",
|
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" In[element] += 1\n",
|
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" Out[i] += 1\n",
|
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" return [In, Out]\n",
|
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"\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": 7,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"execution_count": 7
|
|
},
|
|
{
|
|
"metadata": {},
|
|
"cell_type": "markdown",
|
|
"source": "# Exercise 1.4",
|
|
"id": "4bd26fbd65135589"
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2024-12-14T12:23:32.018541Z",
|
|
"start_time": "2024-12-14T12:23:32.015799Z"
|
|
}
|
|
},
|
|
"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": 8
|
|
},
|
|
{
|
|
"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": "2024-12-14T12:50:54.278706Z",
|
|
"start_time": "2024-12-14T12:50:54.271435Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def aux_colors(G, M, src):\n",
|
|
" new_color = not M[src]\n",
|
|
" for adj in G.adjlists[src]:\n",
|
|
" if M[adj] == None:\n",
|
|
" M[adj] = new_color\n",
|
|
" if not aux_colors(G, M, adj):\n",
|
|
" return False\n",
|
|
" else:\n",
|
|
" if M[adj] != new_color:\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_colors(G, M, src):\n",
|
|
" return False\n",
|
|
" return True\n",
|
|
"\n",
|
|
"two_coloring(G1)"
|
|
],
|
|
"id": "9ed534351df71362",
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"False"
|
|
]
|
|
},
|
|
"execution_count": 26,
|
|
"metadata": {},
|
|
"output_type": "execute_result"
|
|
}
|
|
],
|
|
"execution_count": 26
|
|
},
|
|
{
|
|
"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, fake):\n",
|
|
" q = Queue()\n",
|
|
" q.enqueue(src)\n",
|
|
" stop = False\n",
|
|
" while not q.isempty() and not stop:\n",
|
|
" x = q.dequeue()\n",
|
|
" if M[x] > fake:\n",
|
|
" for adj in G.adjlists[x]:\n",
|
|
" if M[adj] == None:\n",
|
|
" M[adj] = M[x] - 1\n",
|
|
" q.enqueue(adj)\n",
|
|
" else:\n",
|
|
" stop = True\n",
|
|
"\n",
|
|
"def fakenews(G, src, truth):\n",
|
|
" M = [None] * G.order\n",
|
|
" M[src] = truth\n",
|
|
" __fakenews(G, M, src, truth//2)\n",
|
|
" L = []\n",
|
|
" for s in range(G.order):\n",
|
|
" if M[s] == None:\n",
|
|
" L.append(s)\n",
|
|
" return L"
|
|
],
|
|
"id": "c66ac4688a6975c9",
|
|
"outputs": [],
|
|
"execution_count": 34
|
|
},
|
|
{
|
|
"metadata": {},
|
|
"cell_type": "markdown",
|
|
"source": "# 2027 - Exercice 2",
|
|
"id": "b8fa23568b4bd3df"
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2024-12-14T12:27:17.971319Z",
|
|
"start_time": "2024-12-14T12:27:17.967991Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"# Reconstitution du graph du partiel\n",
|
|
"# Initialisation d'un graphe non orienté avec 10 sommets\n",
|
|
"G = Graph(order=10, directed=False)\n",
|
|
"\n",
|
|
"# Ajout des arêtes selon l'image fournie\n",
|
|
"G.addedge(0, 1)\n",
|
|
"G.addedge(0, 2)\n",
|
|
"G.addedge(0, 8)\n",
|
|
"G.addedge(0, 6)\n",
|
|
"G.addedge(1, 2)\n",
|
|
"G.addedge(1, 3)\n",
|
|
"G.addedge(2, 3)\n",
|
|
"G.addedge(2, 8)\n",
|
|
"G.addedge(3, 5)\n",
|
|
"G.addedge(3, 6)\n",
|
|
"G.addedge(4, 5)\n",
|
|
"G.addedge(5, 7)\n",
|
|
"G.addedge(6, 9)\n",
|
|
"G.addedge(7, 9)\n",
|
|
"G.addedge(8, 9)\n",
|
|
"\n",
|
|
"# Tri des listes d'adjacence pour une sortie cohérente\n",
|
|
"sortgraph(G)\n",
|
|
"\n",
|
|
"# Affichage du graphe au format DOT (si tu as graphviz configuré)\n",
|
|
"print(dot(G))\n",
|
|
"\n",
|
|
"# Affichage visuel dans Jupyter Notebook (optionnel)\n",
|
|
"# display(G, eng=\"neato\") # Utilise l'option \"neato\" pour une disposition automatique"
|
|
],
|
|
"id": "f3f003f5ecd72f9e",
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"digraph {\n",
|
|
"0 -- 1\n",
|
|
"0 -- 2\n",
|
|
"0 -- 6\n",
|
|
"0 -- 8\n",
|
|
"1 -- 0\n",
|
|
"1 -- 2\n",
|
|
"1 -- 3\n",
|
|
"2 -- 0\n",
|
|
"2 -- 1\n",
|
|
"2 -- 3\n",
|
|
"2 -- 8\n",
|
|
"3 -- 1\n",
|
|
"3 -- 2\n",
|
|
"3 -- 5\n",
|
|
"3 -- 6\n",
|
|
"4 -- 5\n",
|
|
"5 -- 3\n",
|
|
"5 -- 4\n",
|
|
"5 -- 7\n",
|
|
"6 -- 0\n",
|
|
"6 -- 3\n",
|
|
"6 -- 9\n",
|
|
"7 -- 5\n",
|
|
"7 -- 9\n",
|
|
"8 -- 0\n",
|
|
"8 -- 2\n",
|
|
"8 -- 9\n",
|
|
"9 -- 6\n",
|
|
"9 -- 7\n",
|
|
"9 -- 8\n",
|
|
"}\n"
|
|
]
|
|
}
|
|
],
|
|
"execution_count": 15
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2024-12-14T12:42:59.642392Z",
|
|
"start_time": "2024-12-14T12:42:59.636696Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"\"\"\"\n",
|
|
"def __smallest_level(G, M, src, perLevel):\n",
|
|
" cur = Queue()\n",
|
|
" cur.enqueue(src)\n",
|
|
" cur.enqueue(None)\n",
|
|
" M[src] = True\n",
|
|
" temp = []\n",
|
|
" while not cur.isempty():\n",
|
|
" x = cur.dequeue()\n",
|
|
" if x is None:\n",
|
|
" if (len(temp) != 0 and temp != [src]):\n",
|
|
" perLevel.append(temp)\n",
|
|
" temp = []\n",
|
|
" else:\n",
|
|
" temp.append(x)\n",
|
|
" for adj in G.adjlists[x]:\n",
|
|
" if not M[adj]:\n",
|
|
" M[adj] = True\n",
|
|
" cur.enqueue(adj)\n",
|
|
" cur.enqueue(None)\n",
|
|
"\n",
|
|
"def smallest_level(G, src):\n",
|
|
" M = [False] * G.order\n",
|
|
" perLevel = []\n",
|
|
" __smallest_level(G, M, src, perLevel)\n",
|
|
" min = perLevel[0]\n",
|
|
" for element in perLevel:\n",
|
|
" if len(element) < len(min):\n",
|
|
" min = element\n",
|
|
" return min\n",
|
|
"\"\"\"\n",
|
|
"\n",
|
|
"def smallest(G, src):\n",
|
|
" dist = [None] * G.order\n",
|
|
" q = Queue()\n",
|
|
" q.enqueue(src)\n",
|
|
" dist[src] = 0\n",
|
|
" small = G.order\n",
|
|
" d = 0\n",
|
|
" L = []\n",
|
|
" while not q.isempty():\n",
|
|
" x = q.dequeue()\n",
|
|
" if dist[x] > d:\n",
|
|
" if len(L) < small:\n",
|
|
" small = len(L)\n",
|
|
" Res = L\n",
|
|
" d += 1\n",
|
|
" L = []\n",
|
|
" for y in G.adjlists[x]:\n",
|
|
" if dist[y] == None:\n",
|
|
" dist[y] = dist[x] + 1\n",
|
|
" q.enqueue(y)\n",
|
|
" L.append(y)\n",
|
|
" return Res"
|
|
],
|
|
"id": "9a3a85d15dccbb97",
|
|
"outputs": [],
|
|
"execution_count": 23
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2024-12-14T12:43:03.858284Z",
|
|
"start_time": "2024-12-14T12:43:03.855864Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"for s in range(10):\n",
|
|
" print(s, \"=>\", smallest(G, s))"
|
|
],
|
|
"id": "5be240ac4da2b002",
|
|
"outputs": [
|
|
{
|
|
"name": "stdout",
|
|
"output_type": "stream",
|
|
"text": [
|
|
"0 => [4]\n",
|
|
"1 => [0, 2, 3]\n",
|
|
"2 => [4, 7]\n",
|
|
"3 => [1, 2, 5, 6]\n",
|
|
"4 => [5]\n",
|
|
"5 => [0, 8]\n",
|
|
"6 => [4]\n",
|
|
"7 => [5, 9]\n",
|
|
"8 => [5]\n",
|
|
"9 => [1, 4]\n"
|
|
]
|
|
}
|
|
],
|
|
"execution_count": 24
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 2
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython2",
|
|
"version": "2.7.6"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|