{ "nbformat": 4, "nbformat_minor": 0, "metadata": { "colab": { "provenance": [] }, "kernelspec": { "name": "python3", "display_name": "Python 3" }, "language_info": { "name": "python" } }, "cells": [ { "cell_type": "markdown", "source": [ "# Lecture 12 - Depth First Search\n", "\n", "In today's lecture we will discuss -\n", "\n", "1. Adjacency list vs Matrix representations\n", "2. Connectivity in Graphs\n", "3. Maze solving\n", "4. Idea of exploring a graph\n", "5. Systematic implementation of graph exploration - DFS\n", "6. DFS algorithm and its implementation\n", "\n", "#Learning Objectives -\n", "\n", "1. Working with adj list/matrix representations to print edges of a graph\n", "2. Identifying connected vs not connected pairs of vertices\n", "3. Modeling maze solving as a graph problem\n", "4. Identifying connectivity as the problem that resolves it\n", "5. Outline for DFS algorithm\n", "6. Applications of DFS - path finding\n", "\n", "\n", "**Announcements**\n", "\n", "1. Lab 5 deadline extended to Friday\n", "2. Homework 3 out on PL\n", "3. Early feedback link - https://docs.google.com/forms/d/19L6qPU_KCp46LmQmLyYdTCYLnbIZMhZzcfyDJihnFdg/edit\n", "4. Office hours today (5pm-7pm)\n", "\n", "\n", "\n" ], "metadata": { "id": "XhPlcYEeJ8jm" } }, { "cell_type": "markdown", "source": [ "# Discovery clicker\n", "\n", "Scan and use join code 277\n", "\n", "OR Visit clicker.cs.illinois.edu and use join code 277\n", "\n", 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)" ], "metadata": { "id": "LktxlwG4nuPs" } }, { "cell_type": "markdown", "source": [ "# Graph Fundamentals\n", "\n", "\n", "\n", "* Graph $G$ is specified by a set of Vertices $V$ and a set of Edges $E$ between select pairs of vertices - $G = (V,E)$\n", "* Typically, we will consider $V = \\{1,2,3,\\dots,n\\}$ and $E = \\{(u,v):u,v \\in V$ and $u,v$ are connected in $G$\\}\n", "\n", "* In the flight network graph, there is an edge between Champaign (CMI) and Chicago (ORD) since there are flights between these airports whereas there is no edge between Champaign (CMI) and San Francisco (SFO) since there are no flights between them.\n", "\n", "* The degree of a vertex is the number of edges incident on the vertex." ], "metadata": { "id": "yNhs1xkXPYhz" } }, { "cell_type": "markdown", "source": [ "# Types of Graphs\n", "\n", "There are different types of graphs that we will encounter -\n", "\n", "\n", "* Undirected Graphs - Graphs where connections are symmetric - $(u,v)\\in E ⇔ (v,u) \\in E$\n", "* Directed Graphs - Graphs where connections are not necessarily symmetric - $(u,v)\\in E \\not⇔ (v,u) \\in E$\n", "\n", "\n", "Classify each of the following graphs as undirected or directed -\n", "\n", "1. Flight route network\n", "2. LinkedIn network\n", "3. Instagram network\n", "4. Course prerequisite graph\n", "5. Cities/Towns road connections\n", "\n" ], "metadata": { "id": "AVfqR-YYVWIU" } }, { "cell_type": "markdown", "source": [ "# Examples\n", "\n", "Consider the graph $G$ with vertex set $V = \\{A,B,C\\} $ having undirected edges (A,C) and (A,C). We can represent this graph using the diagram -\n", "\n", "![Screenshot 2026-02-18 143621.png](data:image/png;base64,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)\n", "\n", "\n", "\n", "> Undirected graph on A,B,C with edges (A,B) and (A,C)\n", "\n", "$deg(A) = 2, deg(B) = 1, deg(C) = 1$" ], "metadata": { "id": "ULLumviwaE6M" } }, { "cell_type": "markdown", "source": [ "![Screenshot 2026-02-18 143553.png](data:image/png;base64,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)\n", "\n", "\n", "\n", "> Directed graph on A,B,C with edges (A,B) and (A,C)\n", "\n", "$in-deg(A) = 0, in-deg(B) = 1, in-deg(C) = 1$\n", "\n", "$out-deg(A) = 2, out-deg(B) = 0, out-deg(C) = 0$\n", "\n", "> In directed graphs degree can refer to either indegree or out-degree - we must be specific." ], "metadata": { "id": "GOvcB8Dueu-8" } }, { "cell_type": "markdown", "source": [ "# More types of graphs\n", "\n", "Say we want to find the cheapest way to travel from CMI to SFO for spring break. Can we use our flight nework graph to figure this out?\n", "\n", "Not quite, because the network does not have sufficient information to help us out in this regard. We need more information about the edges - cost of flights between airports (weights)!\n", "\n", "* Unweighted graphs - Graphs with no weights assigned to edges. Formally, $G = (V,E)$.\n", "* Weighted graphs - Graphs with weights assigned to edges. Formally, $G = (V,E, W)$ where $W : E → \\mathbb{R}$.\n", "\n", "Identify which of these graphs could be weighted (and what these weights could represent)-\n", "\n", "1. Flight route network\n", "2. LinkedIn network\n", "3. Instagram network\n", "4. Course prerequisite graph\n", "5. Cities/Towns road connections\n" ], "metadata": { "id": "d_zhxpYSXeXn" } }, { "cell_type": "markdown", "source": [ "# Graph representation\n", "\n", "There are two fundamental ways in which graphs can be represented:\n", "\n", "1. **Adjacency Matrix** - $n \\times n$ matrix with edges represented using 1 and non-edges represented using 0.\n", "\n", "For example, consider the undirected graph on A,B,C with edges (A,B) and (A,C).\n", "\n", "![Screenshot 2026-02-18 145816.png](data:image/png;base64,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)\n", "\n", "\n", "\n", "> Adjacency Matrix representation for graph G\n", "\n", "![Screenshot 2026-02-18 143621.png](data:image/png;base64,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)" ], "metadata": { "id": "U6ys_QrUgwOL" } }, { "cell_type": "markdown", "source": [ "2. **Adjacency List** - $n$ lists representing adjacency lists for vertices.\n", "\n", "\n", "\n", "A -> B,C\n", "\n", "B -> A\n", "\n", "C -> A\n", "\n", "> Adjacency list representation for G with vertices A,B,C and edges (A,B),(A,C)\n", "\n", "\n", "![Screenshot 2026-02-18 143621.png](data:image/png;base64,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)\n", "\n", "\n", "\n" ], "metadata": { "id": "yiiEWGlEji3E" } }, { "cell_type": "markdown", "source": [ "# Adjacency matrix vs Adjacency list\n", "\n", "Consider graph $G$ with $V = \\{1,2,3,\\dots,n\\}$ and edge set $E$. Let $|V| = n$ and $|E| = m$.\n", "\n", "* **Space** - Adjacency matrix requires $O(n^2)$ space vs Adjacency list requires $O(m)$ space. \n", "* **Access** - In an adjacency matrix we can retrieve edge $(u,v)$ in $O(1)$ time whereas adjacency list requires $O(deg(u))$ time (which can be as large as $O(n)$).\n", "\n", "\n", "\n", "> Adjacency list is space efficient, while adjacency matrix is time efficient!\n", "\n", "\n", "\n" ], "metadata": { "id": "Y9GWwN79kYLe" } }, { "cell_type": "markdown", "source": [ "# Problems on graphs\n", "\n", "\n", "\n", "1. Flight route network - Cheapest way to travel from $u$ to $v$\n", "2. LinkedIn network - Do users $u$ and $v$ \"know\" each other? How far apart are they?\n", "3. Road network - Can we go from location $u$ to location $v$ by car? If so, what is the shortest path?\n", "4. Course prequisite graph - What is the fewest semesters in which I can graduate?\n", " \n", "\n" ], "metadata": { "id": "Jsn-etPgme_i" } }, { "cell_type": "markdown", "source": [ "# Adjacency matrix representation\n", "\n", "As we discussed last time, there is a rather straightforward representation of a graph $G = (V,E)$ with $V=\\{0,1,2,\\dots,(n-1)\\}$ involving the adjacency matrix $A_{n \\times n}$- specifically,\n", " $$(i,j) \\in E ⇔ A[i][j] = 1$$\n", " and\n", " $$(i,j) \\not\\in E ⇔ A[i][j] = 0$$\n", "\n", " ![Screenshot 2026-02-23 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)" ], "metadata": { "id": "-Xdf4q1x6N-p" } }, { "cell_type": "code", "execution_count": 2, "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "0HgF1dCj5ZKp", "outputId": "19d6fe64-2811-428e-9ea7-797750c3bf88" }, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[[0, 1, 1, 0, 1], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 0], [0, 0, 0, 0, 0]]\n", "Outgoing edge from vertex 0 to vertex 1\n", "Outgoing edge from vertex 0 to vertex 2\n", "Outgoing edge from vertex 0 to vertex 4\n", "Outgoing edge from vertex 1 to vertex 2\n", "Outgoing edge from vertex 2 to vertex 3\n" ] } ], "source": [ "#Adjacency matrix representation for graphs - List of lists\n", "\n", "A = [[0,1,1,0,1],[0,0,1,0,0],[0,0,0,1,0],[0,0,0,0,0],[0,0,0,0,0]]\n", "print(A)\n", "n = len(A)\n", "#Outgoing edges of vertex i - list A[i] contains 0 for non-edges and 1 for edge\n", "\n", "for i in range(n):\n", " for j in range(n):\n", " if(A[i][j]==1):\n", " print(\"Outgoing edge from vertex \" + str(i) + \" to vertex \" + str(j))\n" ] }, { "cell_type": "markdown", "source": [ "# Adjacency List representation\n", "\n", "The adjacency list representation uses lists to represent edges of each vertex in the graph. For an $n$ vertex graph, there are $n$ adjacency lists - $A[0],A[1],A[2],\\dots,A[n-1]$ representing outgoing edges of each vertex.\n", "\n", "For example, $A[i]$ is the list consisting of all outgoing edges of vertex $i$.\n", "\n", "![Screenshot 2026-02-23 134007.png](data:image/png;base64,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)" ], "metadata": { "id": "QlZ3mG9R-xsu" } }, { "cell_type": "code", "source": [ "#Adjacency list representation for Graphs - lists of outgoing edges\n", "\n", "A=[[1,2,4],[2],[3],[ ],[ ]]\n", "print(A)\n", "n = len(A)\n", "#Outgoing edges of vertex i - list A[i] contains vertices to which i has an outgoing edge\n", "\n", "for i in range(n):\n", " for j in A[i]:\n", " print(\"Outgoing edge from vertex \" + str(i) + \" to vertex \" + str(j))\n", "\n" ], "metadata": { "colab": { "base_uri": "https://localhost:8080/" }, "id": "yTPnUJBc-Ff9", "outputId": "135ebfcf-80b5-4736-b215-af49135e4043" }, "execution_count": 3, "outputs": [ { "output_type": "stream", "name": "stdout", "text": [ "[[1, 2, 4], [2], [3], [], []]\n", "Outgoing edge from vertex 0 to vertex 1\n", "Outgoing edge from vertex 0 to vertex 2\n", "Outgoing edge from vertex 0 to vertex 4\n", "Outgoing edge from vertex 1 to vertex 2\n", "Outgoing edge from vertex 2 to vertex 3\n" ] } ] }, { "cell_type": "markdown", "source": [ "# Preferred choice - Adjacency list\n", "\n", "Due to the compact nature of representing a graph, we will generally prefer the adjacency list representation of graphs in our graph problems.\n", "\n", "\n", "\n", "> In the adjacency list representation, what is the time complexity of finding out if edge $(i,j)$ exists?\n", "\n" ], "metadata": { "id": "u4dJrWzAD1Kb" } }, { "cell_type": "markdown", "source": [ "# Connectivity in graphs\n", "\n", "Consider the following graph $G$ - ![Screenshot 2026-02-23 140356.png](data:image/png;base64,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)\n", "\n", "One of the most important questions we would like to understand is whether two vertices $u,v \\in V$ are \"connected\"? What do we mean by this? Well, we would like to understand if there is some way of reaching vertex $v$ starting from vertex $u$.\n", "\n", "Note that there are two ways of reaching vertex 3 from vertex 0 -\n", "\n", "1. Use edge (0,2) to go from 0 to 2 and then edge (2,3) to go from 2 to 3.\n", "2. Use edge (0,1) to go from 0 to 1, then edge (1,2) to go from 1 to 2 and finally edge (2,3) to go from 2 to 3.\n", "\n", "However, if we were to ask whether we could reach vertex 0 from vertex 3, the answer is no since the graph's edges do not support this (in fact, there is no way to go from 3 to any other vertex!)\n", "\n", " Let us give some formal definitions to this end.\n", "\n", "#Path\n", "\n", "* Path - A sequence of vertices with the property that each consecutive pair of vertices has an edge in $G$.\n", "\n", "For example, in the above graph, 0,1,2,3 is a path as there is an edge between (0,1),(1,2) and (2,3).\n", "\n", "For this graph, 0,2,4 is not a path since there is no edge between (2,4) (even though there is an edge between (0,2)).\n", "\n", "In the above graph, there are two paths from 0 to 3 while there are no paths from 3 to 0 - and this captures the essence of connectivity between these vertices.\n", "\n", "\n", "---\n", "# Cycle\n", "\n", "* Cycle - A cycle is a path $v_{1},v_{2},v_{3},\\dots,v_{k}$ in which the first $(k-1)$ vertices are distinct and $v_{1} = v_{k}$. That is, this is a path that cycles back to vertex $v_{1}$. In this case, this cycle has length $(k-1)$.\n", "\n", "In the above graph, there is no cycle as there is no such path that ends with the starting vertex.\n", "\n", "![Screenshot 2026-02-23 143042.png](data:image/png;base64,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)\n", "\n", "\n", "In this graph, since A,B,C,A is a valid path (as edges (A,B),(B,C) and (C,A) exist), this is a cycle of length 3." ], "metadata": { "id": "sB3OuHQHEloA" } }, { "cell_type": "markdown", "source": [ "# Connected graphs (Undirected)\n", "\n", "We say that a graph $G$ is connected, if for every pair of vertices $(u,v) \\in V \\times V$, there is a path from $u$ to $v$.\n", "\n", "![Screenshot 2026-02-23 143042.png](data:image/png;base64,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)\n", "\n", "In the graph above, observe that each of the following pairs have a path between them - (A,B), (A,C), (A,D), (B,A), (B,C), (B,D), (C,A), (C,B), (C,D), (D,A), (D,B), (D,C) as well as (A,A), (B,B), (C,C), (D,D). Some examples -\n", "\n", "\n", "* (A,C) - path A,B,C or path A,C\n", "* (B,D) - path B,C,D or path B,C,D,C,A,C,D (not simple)\n", "\n", "\n", "Hence, this graph is **connected** - that is, there is atleast one path between any two vertices.\n", "\n", "> **Simple paths** are paths with all *distinct* vertices.\n", "\n", "\n", "\n", "![Screenshot 2026-02-23 144357.png](data:image/png;base64,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)\n", "\n", "In this graph, however, since there is no path between (A,D), the graph is **not connected**." ], "metadata": { "id": "wK-E4OtxN1f_" } }, { "cell_type": "markdown", "source": [ "# Establishing connectivity in (Undirected) graphs\n", "\n", "Given a graph $G$, how can we decide if it is connected?\n", "\n", "Before we get to that, let us consider the problem of solving a maze.\n", "\n", "Maze resource -\n", "\n", "https://medium.com/swlh/solving-mazes-with-depth-first-search-e315771317ae\n", "\n", "![Screenshot 2026-10-05 at 1.33.16 PM.png](data:image/png;base64,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)\n", "\n", "As you try to solve the maze, answer the following questions-\n", "\n", "\n", "* When is it the case that the maze has a \"solution\"? When does it not?\n", "* How do you go about finding a path from the start to the end?\n", "* When do you decide against following a path?\n", "* How do you retract from such paths and move forward along a different path?\n", "* What information do you need to be able to execute such moves?\n", "\n", "\n", "\n" ], "metadata": { "id": "dgb80cwMQVqZ" } }, { "cell_type": "markdown", "source": [ "# s-t connectivity problem\n", "\n", "Typically, $s$ is the source vertex and $t$ is the target vertex. The $s-t$ connectivity problem asks whether $s$ is connected to $t$?\n", "\n", "![Screenshot 2026-02-25 at 12.36.31 PM.png](data:image/png;base64,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)\n", "\n", "\n", "\n", "> We want to know whether there is a path from $s$ to $t$ in the given graph $G$.\n", "\n", "\n", "\n", "\n", "The adjacency list representation for this graph is as follows -\n", "\n", "\n", "* a : [b,s]\n", "* b : [a,s,t]\n", "* s : [a,b]\n", "* t : [b]\n", "\n" ], "metadata": { "id": "QX7Xp3YOBh4E" } }, { "cell_type": "markdown", "source": [ "# Exploring a graph\n", "\n", "In order to find whether there is a path from $s$ to $t$ in the given graph, we will explore the graph starting from vertex $s$ by following edges of the graph. If our exploration leads us to $t$, we have found a way to go from $s$ to $t$ in the graph!\n", "\n", "There are primarily two ways of exploring paths in graphs -\n", "\n", "\n", "* **Depth** based exploration\n", "\n", " Go as deep as you can along any path, and then track back to explore different paths (again in a depth oriented manner).\n", "\n", "* **Breadth** based exploration\n", "\n", " Look at all neighbors of the starting vertex and then proceed to explore the graph in frontiers/waves.\n", "\n", " For now, we will focus on the depth based exploration called Depth First Search.\n", "\n" ], "metadata": { "id": "tK59IM1cHHO2" } }, { "cell_type": "markdown", "source": [ "# Depth First Search\n", "\n", "Given a graph $G$, one search strategy is to explore the graph in a depth first manner - going along a path as deep as possible before exploring other paths.\n", "\n", "This search algorithm is called Depth First Search." ], "metadata": { "id": "o8yxCSYAWD1z" } }, { "cell_type": "markdown", "source": [ "# Depth First Search\n", "\n", "Main idea -\n", "\n", "* Start from a vertex of your choice and explore the graph in a depth oriented manner. That is, go as deep as you can along a path until you cannot go any further.\n", "\n", "* Then, track back and explore a different path until you cannot go further. \n", "* Repeat this process until the entire graph is explored." ], "metadata": { "id": "rgj-AY64IscY" } }, { "cell_type": "markdown", "source": [ "\n", "DFS visualization resource -\n", "https://www.cs.usfca.edu/~galles/visualization/DFS.html" ], "metadata": { "id": "u46yGgq4Vf8O" } }, { "cell_type": "code", "source": [ "# Exploring graph in a depth first manner\n", "\n", "# Input - Graph G, \"start vertex\" s\n", "\n", "# Output - A list of all vertices reachable from s, A list of all parent vertices\n", "\n", "# Strategy - start from s, explore paths to their deep ends before tracking back and exploring other paths" ], "metadata": { "id": "rHy1Rpf0WZPW" }, "execution_count": null, "outputs": [] }, { "cell_type": "code", "source": [ "# DFS code for adjacency lists\n", "\n", "#defining graph G\n", "\n", "G = [[2,4,7],[3,5,6,7],[0],[1,5],[0,6],[1,3,7],[1,4],[0,1,5]]\n", "\n", "visited = [False]*len(G)\n", "parent = [None]*len(G)\n", "\n", "#code for dfs on graph G\n", "\n", "def dfs(G):\n", "\n", "#initializing the visited list to false for all vertices\n", " for i in range(len(G)):\n", " visited[i] = False\n", "\n", "#exploring vertices if they are not already visited\n", " for v in range(len(G)):\n", " if(visited[v] == False):\n", " explore(G,v)\n", " return\n", "\n", "#explore function that explores G starting from vertex v\n", "\n", "def explore(G,v):\n", " #setting visited value for v to be true in order to prevent processing explore(G,v) again\n", " visited[v]=True\n", "\n", " #for each edge (v,u) in G, calling explore(G,u) if u is not already visited\n", " for u in G[v]:\n", " #setting parent of u to be v since explore(G,u) was called by explore(G,v) and recursive call to explore G through vertex u\n", " if(visited[u]==False):\n", " parent[u] = v\n", " explore(G,u)\n", " return\n", "\n", "dfs(G)" ], "metadata": { "id": "aqOD928EOSNw" }, "execution_count": null, "outputs": [] }, { "cell_type": "markdown", "source": [ "#Simulation of DFS on an undirected graph\n", "\n", "![Screenshot 2026-02-25 at 1.39.23 PM.png](data:image/png;base64,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)\n", "\n", "The adjacency list representation for this graph is -\n", "\n", "* a : [b,s]\n", "* b : [a,s,t]\n", "* s : [a,b]\n", "* t : [b]\n", "\n", "\n", "\n", "DFS expected behavior -\n", "\n", " * Let's start from vertex $s$. Since the first edge in the adjacency list of $s$ is $(s,a)$, we will pick this edge to explore a path.\n", " * Now, we are at vertex $a$. Since the first edge of $a$ is $(a,b)$, we will pick this edge to further our exploration path.\n", " * Now, we are at vertex $b$. The first edge of $b$ is $(b,a)$. Should we go to $a$ next? ... not quite, since we have already visited $a$. Let's try the next edge of $b$ - $(b,s)$. Should we go to $s$ next? ... again, we have already visited $s$. So, let's try another edge - $(b,t)$ is next. Since $t$ is not yet visited, we will pick this edge to further our exploration.\n", " * Now, we are at vertex $t$. The first edge of $t$ is $(t,b)$. Since $b$ is already visited, we will pick another edge. But there are no more edges! So, we cannot explore this path ($s-a-b-t$) any further. Let's track back to explore a different path!\n", "\n", " * We go back to $b$ since that is what led us to $t$. Note that we have already looked at all edges of $b$ - $(b,a)$ , $(b,s)$, $(b,t)$. So, we cannot explore any further paths from $b$. Let's track back!\n", "\n", " * We go back to $a$ since that is what led us to $a$. We have already looked at edge $(a,b)$, so now let's try the next edge - $(a,s)$. Hold on... $s$ is already visited. So, we will try a different edge of $a$ to explore ... of which there are none! So, we cannot explore any further paths from $a$. Let's track back!\n", "\n", " * We go back to $s$ since that is what led us to $a$. The next edge of $s$ is $(s,b)$. But, $b$ has already been visited! No luck. Since $s$ has no more edges left to explore, we cannot explore any further from $s$. Let's track back ...\n", "\n", " * That's it - we have reached the end of our exploration of $G$ as there are no more edges left to be processed.\n", "\n" ], "metadata": { "id": "g7RzfqLJJrn0" } }, { "cell_type": "markdown", "source": [ "# DFS code unpacking\n", "\n", "At the end of dfs(G) - we have -\n", "\n", "* visited[i] = True for i = 0,1,2,3\n", "* parent[0] = None, parent[1] = 0, parent[2] = 1, parent[3] = 2\n", "\n", "\n", "\n", "\n", "---\n", "\n", "\n", "Observations\n", "\n", "* visited - helps us keep track of vertices that are already visited that prevents indefinite looping!\n", "* parent - keeps track of the parent of each vertex which can help trace out our desired $s-t$ path.\n", "* explore - is the function that starts at vertex $v$ and explores the graph from $v$ (it avoids visiting already visited vertices)\n", "\n", "* explore is a **recursive function**\n", "\n", "\n", "* Every edge of $G$ is processed exactly twice.\n", "\n", " For example, the edge $(s,a)$ is processed (and pursued) in explore$(s)$ in the first step and then the edge $(a,s)$ is processed (and ignored) in explore$(a)$ towards the end.\n", "\n", " * At any point in time, the recursive seqeunce of calls represents a path in the original graph $G$.\n", "\n", "\n", "\n" ], "metadata": { "id": "EouMP_ZnSZNB" } }, { "cell_type": "markdown", "source": [ "# Applications of DFS\n", "\n", "\n", "1. $s-t$ connectivity\n", "\n", "2. Checking number of connected components in $G$\n", "\n", "3. Checking if $G$ has a cycle (Hw 3)\n", "\n", "\n" ], "metadata": { "id": "9qJ_k2iWduCH" } }, { "cell_type": "markdown", "source": [ "# Number of connected components\n", "\n", "**Connected component**\n", "\n", "For an undirected graph $G$, a connected component is a set of vertices that are all connected to each other.\n", "\n", "![Screenshot 2026-02-25 at 12.36.31 PM.png](data:image/png;base64,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)\n", "\n", "\n", " The graph above has 1 connected component - $\\{s,a,b,t\\}$ since all vertices are connected to each other.\n", "\n", "\n", " ![Screenshot 2026-02-25 at 12.36.41 PM.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAmQAAAE4CAYAAAD1te+tAAAMS2lDQ1BJQ0MgUHJvZmlsZQAASImVVwdYU8kWnltSIQQIhCIl9CaISAkgJYQWQHoRRCUkAUKJMSGo2NFlV3DtIoIVXQVRdHUFRGzYlUWx98WCirIuFuzKmxBAl33le+f75t7//nPmn3POnVsGAHoHXyrNRTUByJPky2JDAljjk1NYpGcAAXqADgyAA18gl3KioyMAtMHz3+3tNegN7bKjUuuf/f/VtIQiuQAAJBridKFckAfxbwDgzQKpLB8AohTyFtPypUq8CmIdGQwQ4molzlThZiVOV+GL/T7xsVyIHwFAVufzZZkAaPRAnlUgyIQ6dJgtcJYIxRKI/SH2zcubIoR4HsS20AfOSVfqs9O/08n8m2b6kCafnzmEVbn0GzlQLJfm8mf8n+X435aXqxicwwY29SxZaKwyZ1i3RzlTwpVYHeL3kvTIKIi1AUBxsbDfX4mZWYrQBJU/aiuQc2HNABPisfLcON4AHyvkB4ZDbARxhiQ3MmLApyhDHKz0gfVDy8X5vHiI9SGuFsmD4gZ8jsqmxA7Oey1DxuUM8E/5sv4YlPpfFTkJHJU+pp0l4g3oY06FWfFJEFMhDiwQJ0ZCrAFxpDwnLnzAJ7Uwixs56CNTxCpzsYRYJpKEBKj0sbIMWXDsgP+OPPlg7tjRLDEvcgBfys+KD1XVCnsk4PfHD3PBekQSTsKgjkg+PmIwF6EoMEiVO04WSRLiVDyuL80PiFWNxe2ludED/niAKDdEyZtDHC8viBscW5APF6dKHy+W5kfHq+LEK7L5YdGqePA9IAJwQSBgAQVs6WAKyAbitu6Gbnil6gkGfCADmUAEHAeYwRFJ/T0SeIwDheBPiERAPjQuoL9XBAog/2UYq+TEQ5zq6AgyBvqUKjngMcR5IBzkwmtFv5JkKIJE8Agy4n9ExIdNAHPIhU3Z/+/5QfYbw4FMxACjGJyRRR/0JAYRA4mhxGCiHW6I++LeeAQ8+sPmgrNxz8E8vvkTHhPaCQ8IVwkdhJuTxUWyYVGOAx1QP3igPunf1we3hppueADuA9WhMs7EDYEj7grn4eB+cGY3yHIH4lZWhTVM+28ZfHeHBvwozhSUokfxp9gOH6lhr+E2pKKs9ff1UcWaPlRv7lDP8Pm531VfCM/hwz2xn7B92GnsGHYWa8YaAAs7gjVirdghJR5acY/6V9zgbLH98eRAneFr5tudVVZS7lzr3OX8WdWXL5qer3wYuVOkM2TizKx8Fgd+MUQsnkTgNJLl4uziDoDy+6N6vb2O6f+uIMzWb9yCPwDwOdLX13fwGxd2BIBfPeAr4cA3zpYNPy1qAJw5IFDIClQcrjwQ4JuDDp8+A2ACLIAtzMcFuANv4A+CQBiIAvEgGUyC0WfBdS4D08AsMB8Ug1KwDKwGFWAj2AKqwS6wFzSAZnAMnALnwUVwFdyGq6cTPAc94C34hCAICaEhDMQAMUWsEAfEBWEjvkgQEoHEIslIGpKJSBAFMgtZgJQiK5AKZDNSg/yKHECOIWeRduQmch/pQl4hH1EMVUd1UGPUGh2FslEOGo7GoxPRTHQqWoguRJeg5WgVuhOtR4+h59GraAf6HO3FAKaGMTEzzBFjY1wsCkvBMjAZNgcrwcqwKqwOa4L3+TLWgXVjH3AizsBZuCNcwaF4Ai7Ap+Jz8MV4BV6N1+Mn8Mv4fbwH/0qgEYwIDgQvAo8wnpBJmEYoJpQRthH2E07CZ6mT8JZIJDKJNkQP+CwmE7OJM4mLieuJu4lHie3Eh8ReEolkQHIg+ZCiSHxSPqmYtJa0k3SEdInUSXpPViObkl3IweQUsoRcRC4j7yAfJl8iPyF/omhSrChelCiKkDKDspSyldJEuUDppHyialFtqD7UeGo2dT61nFpHPUm9Q32tpqZmruapFqMmVpunVq62R+2M2n21D+ra6vbqXPVUdYX6EvXt6kfVb6q/ptFo1jR/Wgotn7aEVkM7TrtHe6/B0HDS4GkINeZqVGrUa1zSeEGn0K3oHPokeiG9jL6PfoHerUnRtNbkavI152hWah7QvK7Zq8XQGq0VpZWntVhrh9ZZrafaJG1r7SBtofZC7S3ax7UfMjCGBYPLEDAWMLYyTjI6dYg6Njo8nWydUp1dOm06Pbrauq66ibrTdSt1D+l2MDGmNZPHzGUuZe5lXmN+1DPW4+iJ9Bbp1eld0nunP0LfX1+kX6K/W/+q/kcDlkGQQY7BcoMGg7uGuKG9YYzhNMMNhicNu0fojPAeIRhRMmLviFtGqJG9UazRTKMtRq1GvcYmxiHGUuO1xseNu02YJv4m2SarTA6bdJkyTH1NxaarTI+YPmPpsjisXFY56wSrx8zILNRMYbbZrM3sk7mNeYJ5kflu87sWVAu2RYbFKosWix5LU8txlrMsay1vWVGs2FZZVmusTlu9s7axTrL+0brB+qmNvg3PptCm1uaOLc3Wz3aqbZXtFTuiHdsux2693UV71N7NPsu+0v6CA+rg7iB2WO/QPpIw0nOkZGTVyOuO6o4cxwLHWsf7TkynCKcipwanF6MsR6WMWj7q9Kivzm7Ouc5bnW+P1h4dNrpodNPoVy72LgKXSpcrY2hjgsfMHdM45qWrg6vIdYPrDTeG2zi3H91a3L64e7jL3OvcuzwsPdI81nlcZ+uwo9mL2Wc8CZ4BnnM9mz0/eLl75Xvt9frL29E7x3uH99OxNmNFY7eOfehj7sP32ezT4cvyTfPd5NvhZ+bH96vye+Bv4S/03+b/hGPHyebs5LwIcA6QBewPeMf14s7mHg3EAkMCSwLbgrSDEoIqgu4FmwdnBtcG94S4hcwMORpKCA0PXR56nWfME/BqeD1hHmGzw06Eq4fHhVeEP4iwj5BFNI1Dx4WNWznuTqRVpCSyIQpE8aJWRt2NtomeGn0whhgTHVMZ8zh2dOys2NNxjLjJcTvi3sYHxC+Nv51gm6BIaEmkJ6Ym1iS+SwpMWpHUMX7U+NnjzycbJouTG1NIKYkp21J6JwRNWD2hM9UttTj12kSbidMnnp1kOCl30qHJ9Mn8yfvSCGlJaTvSPvOj+FX83nRe+rr0HgFXsEbwXOgvXCXsEvmIVoieZPhkrMh4mumTuTKzK8svqyyrW8wVV4hfZodmb8x+lxOVsz2nLzcpd3ceOS8t74BEW5IjOTHFZMr0Ke1SB2mxtGOq19TVU3tk4bJtckQ+Ud6YrwN/9FsVtoofFPcLfAsqC95PS5y2b7rWdMn01hn2MxbNeFIYXPjLTHymYGbLLLNZ82fdn82ZvXkOMid9Tstci7kL53bOC5lXPZ86P2f+70XORSuK3ixIWtC00HjhvIUPfwj5obZYo1hWfP1H7x83/oT/JP6pbdGYRWsXfS0RlpwrdS4tK/28WLD43M+jfy7/uW9JxpK2pe5LNywjLpMsu7bcb3n1Cq0VhSserhy3sn4Va1XJqjerJ68+W+ZatnENdY1iTUd5RHnjWsu1y9Z+rsiquFoZULl7ndG6ReverReuv7TBf0PdRuONpRs/bhJvurE5ZHN9lXVV2RbiloItj7cmbj39C/uXmm2G20q3fdku2d5RHVt9osajpmaH0Y6ltWitorZrZ+rOi7sCdzXWOdZt3s3cXboH7FHsefZr2q/X9obvbdnH3lf3m9Vv6/Yz9pfUI/Uz6nsasho6GpMb2w+EHWhp8m7af9Dp4PZms+bKQ7qHlh6mHl54uO9I4ZHeo9Kj3ccyjz1smdxy+/j441dOxJxoOxl+8syp4FPHT3NOHznjc6b5rNfZA+fY5xrOu5+vb3Vr3f+72+/729zb6i94XGi86HmxqX1s++FLfpeOXQ68fOoK78r5q5FX268lXLtxPfV6xw3hjac3c2++vFVw69PteXcId0ruat4tu2d0r+oPuz92d7h3HLofeL/1QdyD2w8FD58/kj/63LnwMe1x2RPTJzVPXZ42dwV3XXw24Vnnc+nzT93Ff2r9ue6F7Yvf/vL/q7VnfE/nS9nLvleLXxu83v7G9U1Lb3Tvvbd5bz+9K3lv8L76A/vD6Y9JH598mvaZ9Ln8i92Xpq/hX+/05fX1Sfkyfv+vAAaUW5sMAF5tB4CWDAAD7hupE1T7w35DVHvafgT+E1btIfsN/rnUwX/6mG74d3MdgD1bAbCG+vRUAKJpAMR7AnTMmKE2uJfr33cqjQj3BpvivqTnpYN/Y6o96XdxDz8DpaorGH7+F1pqgySvLNmnAAAABGNJQ1AMDQABbgPj7wAAAIplWElmTU0AKgAAAAgABAEaAAUAAAABAAAAPgEbAAUAAAABAAAARgEoAAMAAAABAAIAAIdpAAQAAAABAAAATgAAAAAAAACQAAAAAQAAAJAAAAABAAOShgAHAAAAEgAAAHigAgAEAAAAAQAAAmSgAwAEAAAAAQAAATgAAAAAQVNDSUkAAABTY3JlZW5zaG90XQMXVQAAAAlwSFlzAAAWJQAAFiUBSVIk8AAAAdZpVFh0WE1MOmNvbS5hZG9iZS54bXAAAAAAADx4OnhtcG1ldGEgeG1sbnM6eD0iYWRvYmU6bnM6bWV0YS8iIHg6eG1wdGs9IlhNUCBDb3JlIDYuMC4wIj4KICAgPHJkZjpSREYgeG1sbnM6cmRmPSJodHRwOi8vd3d3LnczLm9yZy8xOTk5LzAyLzIyLXJkZi1zeW50YXgtbnMjIj4KICAgICAgPHJkZjpEZXNjcmlwdGlvbiByZGY6YWJvdXQ9IiIKICAgICAgICAgICAgeG1sbnM6ZXhpZj0iaHR0cDovL25zLmFkb2JlLmNvbS9leGlmLzEuMC8iPgogICAgICAgICA8ZXhpZjpQaXhlbFlEaW1lbnNpb24+MzEyPC9leGlmOlBpeGVsWURpbWVuc2lvbj4KICAgICAgICAgPGV4aWY6UGl4ZWxYRGltZW5zaW9uPjYxMjwvZXhpZjpQaXhlbFhEaW1lbnNpb24+CiAgICAgICAgIDxleGlmOlVzZXJDb21tZW50PlNjcmVlbnNob3Q8L2V4aWY6VXNlckNvbW1lbnQ+CiAgICAgIDwvcmRmOkRlc2NyaXB0aW9uPgogICA8L3JkZjpSREY+CjwveDp4bXBtZXRhPgrHtv8WAAAAHGlET1QAAAACAAAAAAAAAJwAAAAoAAAAnAAAAJwAABcC0BITUAAAFs5JREFUeAHs3X9o1dUfx/F3YoosRcmyNgj6IZmJ/dKiDLJIgzLdkoUlwylkU/FXqIVuJFZQ0E+TqP6xsh8UEplOLegfrUzSoM1SalsWg9BKW8OGG/b97pz42HZ/7H5+fz7nfJ4Xwt17P+d8zudx7h+vzvve8znnf70P4YEAAggggAACCCCQmMA5BLLE7DkxAggggAACCCCgBQhkfBAQQAABBBBAAIGEBQhkCU8Ap0cAAQQQQAABBAhkfAYQMFTg6NGjcuDAAWlpaZGuri7p6emRoUOHSllZmYwfP14mT54sF1xwgaFXx7ARQACBbAkQyLI131ytwQIdHR3y5ptvyq5du+TgwYM6hF1//fUybtw4HcLOPfdcOX36tHR2dkpTU5P+76KLLtLBrKqqSqqrq2XIkCEGCzB0BBBAwF4BApm9c8uVWSJw6NAh2bRpk7z77rsyZcoUmTNnjg5ZKogNGjSo6FV2d3frULZ//37ZvHmztLe3y0MPPSR1dXVSUVFRtB1vIIAAAgjEL0Agi9+cMyLgSuDEiROydOlS2blzp9TW1srixYtl7NixrtoWOuirr77Swe6jjz6S5cuXy+OPP86KWSEoXkMAAQQSECCQJYDOKREoJbBjxw5ZuHCh3HnnnbJx40YZOXJkqSau329ra5MFCxbIyZMndQn02muvdd2WAxFAAAEEohEgkEXjSq8I+BI4c+aMXgnbtm2bvP766zJz5kxf/ZRqpPaDfumll/Qq2fr162XlypWlmvA+AggggECEAgSyCHHpGgEvAiqM1dTUiFrBUitko0eP9tLc17GHDx+W6dOny6JFi2Tt2rW++qARAggggEBwAQJZcEN6QCCwQN8w9umnn8qIESMC9+m2g9bWVpk6dSqhzC0YxyGAAAIRCBDIIkClSwS8CqjvdH3//fcSdxhzxumEsjVr1ugfEjiv8y8CCCCAQDwCBLJ4nDkLAkUFtm7dKitWrJDm5mYZNWpU0eOifkNtr6G21fjyyy/l6quvjvp09I8AAggg0EeAQNYHgz8RiFvg+PHjMmHCBNmyZYvcddddcZ8+73xPP/20qICotsgYPHhw3vu8gAACCCAQjQCBLBpXekXAlcDs2bPl/PPP17+odNUg4oPUd9nUKtk999wjDQ0NEZ+N7hFAAAEEHAECmSPBvwjELLBv3z5RtzT68ccfZfjw4TGfvfjp1C8vb7zxRvnll18SLaEWHyHvIIAAAvYJEMjsm1OuyBCBuXPnyuWXXy4bNmxI3Yjvvfdeue2222TVqlWpGxsDQgABBGwUIJDZOKtcU+oFjh07JpdddpleHSsvL0/deD/55BO9DUZLS8uA98tM3cAZEAIIIGCoAIHM0Ilj2GYLPPHEE/pXlR988EEqL0Tt5K9uXv7cc8/JjBkzUjlGBoUAAgjYJEAgs2k2uRZjBNR3tNSX5lVpMKxHd3d3qDcLV6Gxvb1dXnvttbCGSD8IIIAAAkUECGRFYHgZgagEenp69Jf4f/75ZxkzZkyg0/z222/ywgsvyM6dO+XIkSMyadIkefnll0Vt9KpWuaqrq333v3v3blm3bp0cPHjQdx80RAABBBBwJ0Agc+fEUQiEJqACjvp1pfoVY5CHCmBqe4q//vpLXn31VX0j8rfffluWLFkiXV1d+l6YKrD5ffzxxx9y8cUXS2dnpwwdOtRvN7RDAAEEEHAhQCBzgcQhCIQpoEqA6kvzH374oe9u1VYZN910k3R0dIhayZo2bdrZvtSvI/fs2SN33HGHfPbZZ2df9/PHpZdeKu+//77eBsNPe9oggAACCLgTIJC5c+IoBEITeOSRR6SsrEzUd7T8Pu6++27ZtWuXqL7UF+/7PmbOnCnbt2+XJ598Upcc+77n9W/1Hbf7779fampqvDbleAQQQAABDwIEMg9YHIpAGAJ1dXWiVp4effRRX92psKVCl3qobSnUXmbO459//tE7///555/6npQ333yz85avf+fMmSO33367PPzww77a0wgBBBBAwJ0AgcydE0chEJrA/PnzZeLEibJy5UpffT744IPy3nvv6XtgqhuS93188803csMNN8h5550nJ0+eDHw/ynnz5un+li1b1vc0/I0AAgggELIAgSxkULpDoJRA0BWyK6+8Un744Qcd6J5//vl+p3v22Wdl9erV+kbl6rtlQR+skAUVpD0CCCDgToBA5s6JoxAITSDId8hOnTqlt8xQW1qoTWVzt7VQv7pUW2A89dRTsnbtWn0nAPULyUsuucTX+PkOmS82GiGAAAKeBQhknslogEAwgSC/slTbWagfBKhA9u233+rSpzMatTHs6NGj9TYVX3zxhdxyyy36l5aq3FhZWekc5ulffmXpiYuDEUAAAd8CBDLfdDREwJ9A0H3I1D0wf/rpJ/n8889lypQpZwfx2GOPyTPPPKN361d7h504cUL/eODXX3+VkSNHnj3O7R+///67VFRU6H3O2IfMrRrHIYAAAv4ECGT+3GiFgG+BoDv1O98Tq6+v11tnqF9Wqs1gVany+PHjOpCp/cnUthpff/21fPzxx77Gyk79vthohAACCPgSIJD5YqMRAsEEgtzLUgWwRYsWyebNm0VtAnv48GEZO3asvPXWW9LY2ChLly6V8ePHy7Fjx0SVLvtui+Fl1NzL0osWxyKAAALBBAhkwfxojYAvARV21JYV6ov5fh/qXpjq15ZXXHGFLk06/ahbMqn9ydQeZMOGDXNe9vSv+o7auHHj9KazM2bM8NSWgxFAAAEEvAsQyLyb0QKBwAJq9Up9F0zdAqm8vDxwf2F3oG7tpFbhVLAbNGhQ2N3THwIIIIBAjgCBLAeEpwjEJTB37lxdTtywYUNcp3R9HrXdhSqHrlq1ynUbDkQAAQQQ8C9AIPNvR0sEAgns27dPqqqq9CrZ8OHDA/UVZuMjR47I5MmTRZU+R40aFWbX9IUAAgggUESAQFYEhpcRiENg9uzZeu8wtTdZGh5nzpyRW2+9VdTNyxsaGtIwJMaAAAIIZEKAQJaJaeYi0yqgtqmYMGGCbNmyRd/uKOlxqn3Mtm7dKmr1bvDgwUkPh/MjgAACmREgkGVmqrnQtAqoAKRuNK5+delnA9ewruvQoUN6o1kVxtS2GTwQQAABBOITIJDFZ82ZECgqsGDBAr2fmPp144gRI4oeF9Ubra2tMnXqVFmzZo3exyyq89AvAggggEBhAQJZYRdeRSBWAfXdrZqaGn1LpLhDmRPG1DYX6obkPBBAAAEE4hcgkMVvzhkRKCjQN5Rt375df9m/4IEhvqh2+Z8+fbrec4wwFiIsXSGAAAIeBQhkHsE4HIEoBVQoW7x4sWzbtk3ULy9nzZoVyenUTvwvvviirF+/Xv+nvsPGAwEEEEAgOQECWXL2nBmBogKvvPKKqA1jp02bJhs3bgx1P7C2tjaZP3++vhG56ludgwcCCCCAQLICBLJk/Tk7AnkCf//9t0ycOFFWr14te/bs0TcMr62tlSVLluibiOc1cPmC+vXkpk2b9OrbihUr5NSpU/pemOqG5DwQQAABBJIVIJAl68/ZEcgTWL58ub6HpBOUvvvuOx2k3nnnHb0txQMPPCCTJk3SN/8e6D6T3d3d0tTUJPv375fNmzdLe3u7LFy4UOrq6vT9M1Xwu+aaa2TdunWiAh8PBBBAAIHkBAhkydlzZgTyBNSKWGVlpd6TrKKiot/7HR0d8sYbb8ju3bvlwIEDcvr0abnuuuvkqquukmHDhsmQIUP0a52dnTqIqX3NxowZo8PbfffdJ9XV1fqYvp3u3btXn08Ft9zz9T2OvxFAAAEEohUgkEXrS+8IuBZwSpX19fWuVqyOHj2qg1lLS4t0dXVJT0+PDB06VMrKyvTGrmoV7cILLyx5/twVuZINOAABBBBAIHQBAlnopHSIgD+BpIIRpUt/80UrBBBAIEwBAlmYmvSFgE+BgUqVPrv01IzSpScuDkYAAQRCFyCQhU5Khwh4E/BaqvTWu/ujk1qhcz9CjkQAAQTsFSCQ2Tu3XJkhAmkJQpQuDfnAMEwEELBSgEBm5bRyUaYIJF2qzHWidJkrwnMEEEAgHgECWTzOnAWBPIG0lCpzB5aWFbvccfEcAQQQsFmAQGbz7HJtqRZIa/ChdJnqjw2DQwABSwUIZJZOLJeVboG0lSpztShd5orwHAEEEIhWgEAWrS+9I5AnkNZSZe5A07qClztOniOAAAI2CBDIbJhFrsEoAVOCDqVLoz5WDBYBBAwXIJAZPoEM3yyBtJcqczUpXeaK8BwBBBCIRoBAFo0rvSKQJ2BKqTJ34Kas6OWOm+cIIICASQIEMpNmi7EaLWBqsKF0afTHjsEjgIAhAgQyQyaKYZotYFqpMleb0mWuCM8RQACBcAUIZOF60hsCeQKmlipzL8TUFb7c6+A5AgggkEYBAlkaZ4UxWSVgS5CxJVha9eHiYhBAwBoBApk1U8mFpFHA9FJlrqm6nqqqKmlqapKKiorct3mOAAIIIOBTgEDmE45mCJQSsHVFyZYVv1Lzx/sIIIBAnAIEsji1OVemBGwNLrYGzUx9OLlYBBBInQCBLHVTwoBsELCtVJk7J5Quc0V4jgACCAQTIJAF86M1AnkCWVlBsnUFMG9CeQEBBBCIQYBAFgMyp8iWQFaCSlaCZ7Y+vVwtAggkJUAgS0qe81opYHupMnfSKF3mivAcAQQQ8CdAIPPnRisE8gSyumKUlRXBvAnnBQQQQCBEAQJZiJh0lW2BrAaTrAbRbH/auXoEEAhbgEAWtij9ZVIga6XK3EmmdJkrwnMEEEDAmwCBzJsXRyOQJ8AK0b8kWV0hzPtA8AICCCDgQ4BA5gONJgj0FSCI/KvhBNOGhgaZN29eXyL+RgABBBAoIUAgKwHE2wgMJJD1UmWuDaXLXBGeI4AAAu4ECGTunDgKgTwBZ0Wovr5eamtr897P6gusGGZ15rluBBAIIkAgC6JH20wLEDwKT78TVCldFvbhVQQQQKCQAIGskAqvIVBCgFLlwECULgf24V0EEEAgV4BAlivCcwRKCDgrQJQqB4ZiBXFgH95FAAEE+goQyPpq8DcCLgQIGi6Qeg9xgiulS3deHIUAAtkWIJBle/65eo8ClCq9gVG69ObF0QggkF0BAll2554r9yjgrPhQqvQGt2zZMmltbZXGxkZvDTkaAQQQyJAAgSxDk82lBhOgVOnPzwmylC79+dEKAQSyIUAgy8Y8c5UBBShVBgOkdBnMj9YIIGC/AIHM/jnmCgMKOCs8lCqDQVK6DOZHawQQsFuAQGb3/HJ1IQhQqgwBsbcLJ9hSugzHk14QQMAuAQKZXfPJ1YQsQKkyXFBKl+F60hsCCNgjQCCzZy65kpAFnBUdSpXhwlK6DNeT3hBAwA4BApkd88hVRCBAqTIC1N4unaBL6TIaX3pFAAEzBQhkZs4bo45YgFJltMCULqP1pXcEEDBPgEBm3pwx4ogFnBUcSpXRQlO6jNaX3hFAwCwBAplZ88VoYxCgVBkDcu8pnOBL6TIeb86CAALpFiCQpXt+GF3MApQq4wWndBmvN2dDAIH0ChDI0js3jCxmAWfFhlJlvPCULuP15mwIIJBOAQJZOueFUSUgQKkyAfTeUzpBmNJlMv6cFQEE0iFAIEvHPDCKhAUoVSY7AZQuk/Xn7AggkLwAgSz5OWAECQs4KzSUKpOdCEqXyfpzdgQQSFaAQJasP2dPgQClyhRMQu8QnGBM6TId88EoEEAgXgECWbzenC1lApQq0zUhlC7TNR+MBgEE4hMgkMVnzZlSJuCsyFCqTNfEULpM13wwGgQQiEeAQBaPM2dJoQClyhROSu+QnKBM6TKd88OoEEAgGgECWTSu9JpyAUqV6Z4gp3TZ3Nws5eXl6R4so0MAAQRCECCQhYBIF2YJOCswlCrTPW+qdNnW1iY7duxI90AZHQIIIBCCAIEsBES6MEuAUqUZ8+UEZ0qXZswXo0QAgWACBLJgfrQ2TIBSpVkTRunSrPlitAgg4F+AQObfjpaGCTgrLpQqzZo4SpdmzRejRQABfwIEMn9utDJQgFKlgZPWO2QnSFO6NHP+GDUCCLgTIJC5c+IowwUoVZo9gZQuzZ4/Ro8AAqUFCGSljTjCcAFnhYVSpdkTSenS7Plj9AggMLAAgWxgH961QIBSpQWT2HsJTrCmdGnHfHIVCCDQX4BA1t+DZ5YJUKq0a0IpXdo1n1wNAgj8J0Ag+8+CvywTcFZUKFXaNbGULu2aT64GAQT+FSCQ8UmwVoBSpZ1T6wRtSpd2zi9XhUBWBQhkWZ15y6+bUqXdE0zp0u755eoQyKIAgSyLs275NTsrKJQq7Z5oSpd2zy9Xh0DWBAhkWZvxDFwvpcoMTHLvJTrBm9JlNuabq0TAdgECme0znLHro1SZrQmndJmt+eZqEbBZgEBm8+xm7NqcFRNKldmaeEqX2ZpvrhYBWwUIZLbObAavi1JlBie995KdIE7pMpvzz1UjYIsAgcyWmcz4dVCqzPYHgNJltuefq0fABgECmQ2zmPFrcFZIKFVm+4NA6TLb88/VI2C6AIHM9Blk/EKpkg+BEnCCOaVLPg8IIGCiAIHMxFljzGcFKFWepeCPXgFKl3wMEEDAVAECmakzx7jProhQquTD0FeA0mVfDf5GAAFTBAhkpswU48wToFSZR8ILvQKULvkYIICAiQIEMhNnjTHr0lRlZaU0NzdLRUUFIgj0E6B02Y+DJwggYIAAgcyASWKI/QWcFRBKlf1deNZfgNJlfw+eIYBAugUIZOmeH0ZXQIBSZQEUXsoTcII7v7rMo+EFBBBIoQCBLIWTwpCKC/CryuI2vJMvQOky34RXEEAgnQIEsnTOC6MqIOCseFCqLIDDS0UFKF0WpeENBBBIkQCBLEWTwVAGFqBUObAP7xYWcII8pcvCPryKAALpECCQpWMeGEUJgb1798qsWbP4VWUJJ94uLEDpsrALryKAQHoECGTpmQtGUkTAWeGgVFkEiJddCVC6dMXEQQggkJAAgSwheE7rXoBSpXsrjiwu4AR7SpfFjXgHAQSSEyCQJWfPmV0IqFKl2gC2qamJDWBdeHHIwAKULgf24V0EEEhOgECWnD1nLiHgrGhQqiwBxdueBChdeuLiYAQQiEmAQBYTNKfxLkCp0rsZLUoLOEGf0mVpK45AAIH4BAhk8VlzJg8ClCo9YHGoZwFKl57JaIAAAhELEMgiBqZ77wLOCgalSu92tHAvQOnSvRVHIoBA9AIEsuiNOYNHAUqVHsE43JeAE/wpXfrioxECCIQsQCALGZTugglQqgzmR2tvApQuvXlxNAIIRCdAIIvOlp49CjgrFpQqPcJxeCABSpeB+GiMAAIhCRDIQoKkm+AClCqDG9KDdwHnfwQoXXq3owUCCIQnQCALz5KeAghQqgyAR9PAApQuAxPSAQIIBBQgkAUEpHlwAWeFglJlcEt68C9A6dK/HS0RQCC4AIEsuCE9BBSgVBkQkOahCDj/Y0DpMhROOkEAAY8CBDKPYBwergClynA96S2YgFO65N6pwRxpjQAC3gUIZN7NaBGSgLMiQakyJFC6CUVAlS5bW1ulsbExlP7oBAEEEHAjQCBzo8QxkQhQqoyElU4DCjj/o0DpMiAkzRFAwJMAgcwTFweHJeCUKpubm6W8vDysbukHgVAEKF2GwkgnCCDgQYBA5gGLQ8MRcFYgKFWG40kv0QhQuozGlV4RQKCwAIGssAuvRihAqTJCXLoOTcD5HwdKl6GR0hECCAwgQCAbAIe3whegVBm+KT1GJ0DpMjpbekYAgf4C/wcAAP//3qZAFQAAIQhJREFU7Z0N+N9T+cePFEOXp0rsZ2UUTdk0o1IpXUyobEIPI48pZktZiVlFpaJUY5560C6hSUitSGUoyeNspdgkpKRk1ZSkzv9+n//1XXv6PXy/n6dzzud1rsv12/fzcM59XvfH53Ofc59z32t4K44CgRoI/OMf/3CjR492J510kjvkkENqaJEmIFCcwNSpU919993n5s6dW7wyaoAABCDQD4E1MMj6IcPh0gm8733vc4sXL+bDVjpZKqySQGcgMWPGDHfwwQdX2RR1QwACLSaAQdZi5dfZ9RtvvNFNmDDBLVy40A0fPrzOpmkLAoUJ3HDDDW7ixIluwYIFrq+vr3B9VAABCEBgZQIYZCsT4XfpBDozDLgqS0dLhTUSwHVZI2yagkALCWCQtVDpdXcZV2XdxGmvCgKdgQWuyyroUicEIIBBxjNQKQFclZXipfKaCeC6rBk4zUGgRQQwyFqk7Lq72plRwFVZN3naq5IArssq6VI3BNpLAIOsvbqvvOe4KitHTAMNEOgMNHBdNgCfJiGQMQEMsoyV22TXcFU2SZ+2qyaA67JqwtQPgfYRwCBrn84r77FmEMaMGeOmT59OANjKadNAUwSYAW6KPO1CIE8CGGR56rXRXh177LFu0aJFBIBtVAs0XjWBjuuSNZJVk6Z+CLSDAAZZO/RcWy9xVdaGmoYiIIDrMgIlIAIEMiGAQZaJImPoBjMGMWgBGeomwK7LuonTHgTyJIBBlqdeG+kVa2oawU6jDRNgINKwAmgeApkQwCDLRJFNdwNXZdMaoP0mCeC6bJI+bUMgDwIYZHnosdFeMEPQKH4aj4QArstIFIEYEEiUAAZZooqLSWxclTFpA1maIsDApCnytAuBPAhgkOWhx8Z6gauyMfQ0HCEBXJcRKgWRIJAIAQyyRBQVo5jMCMSoFWRqmgCuy6Y1QPsQSJMABlmaeotCalyVUagBISIjwEAlMoUgDgQSIYBBloiiYhMTV2VsGkGemAjguoxJG8gCgTQIYJCloaeopGQGICp1IEykBHBdRqoYxIJApAQwyCJVTMxi4aqMWTvIFgsBBi6xaAI5IJAGAQyyNPQUjZS4KqNRBYIkQADXZQJKQkQIREIAgywSRaQgBiP+FLSEjLERwHUZm0aQBwJxEsAgi1MvUUqFqzJKtSBU5AQYyESuIMSDQCQEMMgiUUTsYuCqjF1DyBczAVyXMWsH2SAQBwEMsjj0ELUUjPCjVg/CJUIA12UiikJMCDREAIOsIfApNYurMiVtIWusBBjYxKoZ5IJAHAQwyOLQQ7RS4KqMVjUIliABXJcJKg2RIVATAQyymkCn2Awj+hS1hsyxE8B1GbuGkA8CzRDAIGuGexKt4qpMQk0ImRgBBjqJKQxxIVATAQyymkCn1kzHVblgwQLX19eXmvjIC4GoCeC6jFo9CAeBRghgkDWCPe5GGcHHrR+ky4MArss89EgvIFAWAQyyskhmVA+uyoyUSVeiJcDAJ1rVIBgEGiGAQdYI9ngbxVUZr26QLD8CuC7z0yk9gkCvBDDIeiWX4X2M2DNUKl2KngCuy+hVhIAQqIUABlktmNNoBFdlGnpCyrwIMBDKS5/0BgK9EsAg65VcZvfhqsxMoXQnKQK4LpNSF8JCoBICGGSVYE2rUkboaekLafMkgOsyT73SKwgMlQAG2VBJZXwdrsqMlUvXkiHAwCgZVSEoBCohgEFWCdZ0KsVVmY6ukDR/Argu89cxPYRAfwQwyPoj04LjjMhboGS6mBwBXJfJqQyBIVAKAQyyUjCmWQmuyjT1htR5E2CglLd+6R0E+iOAQdYfmcyP46rMXMF0L2kCuC6TVh/CQ6AnAhhkPWFL+yZG4GnrD+nbQQDXZTv0TC8h0CGAQdYh0aK/uCpbpGy6miwBBk7Jqg7BIdATAQyynrClexOuynR1h+TtI4Drsn06p8ftJYBB1iLdM+JukbLpajYEcF1mo0o6AoEBCWCQDYgnr5O4KvPSJ71pBwEGUu3QM72EAAZZS54BXJUtUTTdzJIArsss1UqnILACAQyyFXDk+YMRdp56pVftIoDrsl36prftI4BB1gKd46psgZLpYvYEGFhlr2I62HICGGSZPwC4KjNXMN1rFQFcl61SN51tGQEMsowVzog6Y+XStdYSwHXZWtXT8cwJYJBlrGBclRkrl661lgADrdaqno5nTgCDLFMFy1W5zz77uIULF7q+vr5Me0m3INBOAnJdTpgwgf+/26l+ep0pAQyyDBXLCDpDpdIlCKxEANflSkD4CYHECWCQJa7A1YmPq3J1VDgGgbwIMPDKS5/0BgIYZJk9A7gqM1Mo3YHAAARwXQ4Ah1MQSIwABlliChtIXEbMA9HhHATyJIDrMk+90qv2EcAgy0jnuCozUiZdgcAQCTAQGyIoLoNA5AQwyCJX0FDFw1U5VFJcB4H8COC6zE+n9Kh9BDDIMtA5I+QMlEgXIFCQAK7LggC5HQINE8Aga1gBZTSPq7IMitQBgbQJMDBLW39IDwEMssSfAVyViSsQ8SFQIgFclyXCpCoI1EwAg6xm4GU2x4i4TJrUBYE8COC6zEOP9KJ9BDDIEtY5rsqElYfoEKiIAAO1isBSLQQqJoBBVjHgqqrHVVkVWeqFQPoEcF2mr0N60D4CGGQJ6pwRcIJKQ2QI1EwA12XNwGkOAgUJYJAVBNjE7bgqm6BOmxBIiwADt7T0hbQQwCBL7BnAVZmYwhAXAg0SwHXZIHyahkCXBDDIugTW5OWMeJukT9sQSJMArss09YbU7SOAQZaQznFVJqQsRIVAJAR6Gcg9/fTT7pe//KVbvHix0/1PPfWUe9aznuWGDRvmXvCCF7jtt98+/DuSLiIGBLIggEGWiBpxVSaiKMSEQIQEBnNdyuD69re/7fSeue2229z8+fPdBhts4EaNGuXWW289t/baa7t///vfwTi777773O9+9zu37bbbuh133NG98pWvdPvvv79bf/31I+w5IsVMwHvvnnzySbfmmmu6tdZaK2ZRa5ENg6wGzEuWLHEPPvig++c//+n+85//hJHlhhtu6EaOHOnWWGONQSXoZYQ7aKVcAAEItIrA6lyXDz/8sDv33HPd+eef70aMGOH23HNPN27cuPBfX19fv3z+8pe/BMNNxtt1113nfv7zn7sDDzzQHXPMMcFQ6/dGTrSWwD333ONuueWWZc/NggUL3NKlS5fxeMYznuE233xzt8MOOwRDX8/hTjvtFAYGyy7K/B8YZBUoWFP911xzjbv11lvDw/fAAw+4zTbbzK2zzjphJKARwWOPPeY0OtDDpwfvVa96ldt7771XO0rAVVmBkqgSAi0jsPzAbvfdd3fTpk1z3/nOd9yECROCIaWZrl7Lvffe62bNmuVmz54d3mlnnHGGGzNmTK/VcV8mBPTMXXTRRe6ss85yDz30UDC0NKuqb97LX/5yt9FGG4UJCk1UaMLi/vvvX/bdlLEvl/l+++3npkyZEp6rTLD03w0zCiglELDpfP/Nb37T77LLLt5mv7yNFv0Xv/hF/9Of/tTbQ7naFuxh89/4xje8vRj92LFj/SabbOKnT5/u7cFddr25Grw9tN5cBMuO8Q8IQAACvRC4/vrrvRlgfuONN/Y2Y+YfeeSRXqrp956///3v/jOf+Yw396U/5ZRTvN6LlPYRsAkHf9xxx4Vv12tf+1o/Z86cnp4Fm8zwH/7wh/1zn/tc/4pXvMJffvnlWcPULA2lIAEbFXqbavXbbbedt+l/b9OwPdVo0/7+oIMO8rZmIxh0ehi32morf8EFF/RUHzdBAAIQ6BCQ8fWWt7zFb7nlll6GWZXlV7/6lTd3k7eZEG8egyqbou7ICNisqzePkH/729/u77rrrlKks9mz8B00t7q39Yr+T3/6Uyn1xlYJBlkBjfzhD39Y9oIzF2WBmla89Y9//KM//PDDw6hAfykQgAAEihCwhfjedkf6I4880msWq45iOzX9qaeeGjwGmumn5E3A1kr7Qw45xD//+c/3V155ZSWdVRuHHnpoaOOKK66opI0mK8Ug65G+HgZNox511FE9z4gN1vTcuXP98OHD/aRJk/wTTzwx2OWchwAEILAKgY4xJhdiE0VLObSMA6OsCfr1tKnZV9uR6229l//zn/9ceaOahdt0002DwV95YzU2wKL+/pfX9XvmkksucZMnT3a2/suNHz++3+vKOPH444+H3UvaCKAFuOuuu24Z1VIHBCDQAgK/+c1v3K677uqOOOIIN2PGjMZ6fNlll7l3v/vd7qqrrnK2pqgxOWi4fALm0QnP2G677eZmzpxZfgP91KgF/3q2jz76aHfCCSf0c1VahzHIutRXxxj73ve+F+LvdHl7T5crRpB2mtgsGUZZTwS5CQLtI6CQAgrgevDBBzdqjHXId4wy7Z6ztbGdw/xNmEBTxlgHWW5GGQZZR7ND+GtuSmdrulydxlhHrI5Rpm3ECqmhQHoUCEAAAv0RsOUUzta5OlvP098ltR/XLJ1tKHDz5s1zijtFSZeAQlVotlPhKxTypKmiQMWS48wzz3RvfetbmxKjlHYxyIaI8fe//72zXZTO1kO4N7zhDUO8q9zLZJTpwbOdUs7CY5RbObVBAALZELj22mvdO9/5TveLX/zC2SLraPqlaP+KQ6VZu/e///3RyIUg3RM47bTTnIWzCEGBn/nMZ3ZfQYl3aJLiXe96V3jen/e855VYc71VYZANkfdee+3lXvSiF9XqI1+daLadPLhKleJk9OjRq7uEYxCAQIsJ/O1vf3Mve9nL3Omnn+7e9ra3RUfCQiE4i9cYorZvs8020cmHQIMTuPvuu0Mwc4uzGZ61we+o/gqtUVQGiW9961vVN1ZRCxhkQwD7la98xVmww5DfLYZF9Z/97Gfd17/+9RDRWAl/KRCAAAQ6BD75yU+6m2++Oaw37RyL7a9m+OVq0sYoSnoELEirmzhxorOgrdEIb+FcghdLM3cHHHBANHJ1IwgG2SC05Ca0+D3hxfH6179+kKvrOf3f//435PjS7pLDDjusnkZpBQIQiJ6Axf4KOXI1YHvd614XrbxaDK6F/Uq5ZKF9opUTwVYl8KMf/SispZZBHdta5osvvthpwuKOO+5YVfAEjmCQDaIkvdgsBVKYjRrk0lpPp/7g1QqLxiDQEgLayWjxxpwSNxcpyr/75S9/2Vl8Kffoo486rf3SZqYyi9a4vfjFL3Ynn3xymdVSV8UElPtUuZePP/74ilvqvno9p5pA0f8Hr371q7uvoOE7MMgGUYAS7mq3khahxlQ6D5785TvvvHNMoiELBCDQEAHN4svQsYj8hSSQy/PTn/50WOelnZpa6/XrX/+6UJ0r3/yzn/3M7bvvvu7BBx90LL1YmU6cv2Wov/SlL3X6+5znPKcUIbVR7phjjglGVBkx6j760Y+GmVeFqEqtYJANoDHFy9lzzz2dJfZ2a6+99gBXdndKbtC11lqru5tWc7UePMVhueiii1ZzlkMQgECbCDz88MNu6623dpbnr7QA0lOmTHFnnXVWMPDOO++80nFqY5LW5+o9S4mfgMKW6Hto+ZVLE1YbUCzfqZMBZfkvC9erAYQ24P32t791qe24xCAbQP2a+tdLrowX0T333ONOOumk4Pq0RKmur6/P7bHHHuGYJRMfQIr+T6lOTR1rZwkFAhBoNwHFSfzc5z7nfvKTn5QGQjGm5s+fHwZ9mnkru8j7YImo3Uc+8pGyq6a+CghoBkvhSjSzWUaxNEtuk002UQrHYOjpu1hGkWfrxBNPDCGiyqivrjowyAYgrXhf+k9pR4oUTc3L+FLQujPOOMNttNFGYW3G2LFjnfzxZ599dk/V6yFWXbfffjuRr3siyE0QyIeAPkAa7H3+858vpVMa6GmGQZuINCtS1sdyeeG++tWvOhmSSgtHiZuAAsFusMEGTqGXRowYUYqwl19+efguakZr0aJFpdSpSjSza/lT3cc//vHS6qylohrzZibXlI3c/J133llY7nHjxvktt9zS2w6oZXUp4a4p2NvCw2XHevmH5fLytnW8l1u5BwIQyIjA7rvv7m0TUmk9MkMpvKNsN2Rpda5ckcUkC0miVz7O7/gILFy40FuQ4VIFmzp1anjGLIZYqfV+7Wtf82984xtLrbOOypgh68fsVWR+We0KslgkCrHWc2hKVtGytXi1s3ZM674UskLpHooswP3Qhz4UpnsVBJICAQi0l8DGG2/sNBtfVrDVY489Nuww13tKsRg1Q2IfpULvw5W1ozrXX3/9sAi7ihm4ldvjd+8EzMgJmWrmzp3bcyXSt7xCf/3rX0MdyiTx+OOPh52RL3zhC90aa6wRlvHY4KLnNnSj1qRpg4u+vykVDLJ+tKUIxDKUpNgiRQ+edqPoQdxiiy3CokXFB9J/Ms6KxnHR1vSrr7467FApIif3QgAC6RLQRiFtPHriiSdKW9CvxOSKqq/1XXJT/fjHP3ZLlixxNvMQFvrrfVZGUTyySy+91O2www5lVEcdFRHQmmqt+Zo5c2ahFuSi1kSH6po2bVqo69xzz3XDhg0L+U3Hjx9fON3Xk08+6dZZZx2n3M/6m0rBIOtHUz/84Q9DFGLttCxalL5EL5zly8iRI51iiWnxYZGiOjRyiSlicpH+cC8EINA9ARlk2qmo9V6aZShaHnvssbB+TDNiKlr7qtQ0Msy0sFtriBQGo+iAUnVrl50+yK95zWv0kxIpAa1R1MSCdsWWURSyab/99qskpIrkU/J6PcdaZ51KwSDrR1OadfrYxz4WUpD0c8mQDytmmF44V155ZUjEqlGsil5qcmMWKYrhosjEeiFTIACBdhJ49rOf7W666abwwSyDgGYxtJNOHzWlN9p///2XVavZ/RtuuCG4R4sOKFWpdnJqI4JcTJR4CWh5jOLFKTVXGUWxx2bNmuXe+973unPOOaeMKleoQx4obUbRkqFkSh0L1VJs47rrrvNjxowpJLpNyXotjF1+Mf/SpUu9bU0PCxntIfGWfqJQG7Nnz/a2E7RQHdwMAQikTUDvFb1PbGBWSkdsl1qob9KkSavUpwXYastcWKuc6+WArXnztvatl1u5p0YCFrbJf+ADHyitRQswG56jKjal6ZurZ9SWDJUmbx0VaZEmZTUELBeWtxQMqzkztEN6MZplHh6K888/f5WbZOyZa8HbmoxVznVzwEaW/sADD+zmFq6FAAQyI2CupPA+sVAVpfRsu+22C++uCy+8cJX6zDUazr3jHe9Y5VwvB2wxv9duS0rcBMxV6Q8//PBShLRcpuEZktFkgVxLqXP5SsxV6W1215t3avnD0f8bg6wfFVk8H2/Ts16zXL0UC84YHjg9FPPmzVuhCstKH4y1vffee4Xjvfw46KCDvO2w7OVW7oEABDIi8JKXvMRff/31hXsko06DRX0sLdr5KvVZbLJw7hOf+MQq57o9oLb0nrXF193eyvU1E7Bcpt42XpTSqq2pDs+QntkqiiVA95qBS61gkA2gMdtl5G0t2QBX9H9KhpxeaJaYfIWLdHyvvfYK8Vws0v4K53r5MWrUKC/3KgUCEGg3Ac2UazlE0XLNNdeEd5etcV2lKgtTEM7p3aYPdNHygx/8oPDSkKIycP/QCFiSeW/rsrztYBzaDQNcNXny5PAc2fqxFa76/ve/v8LvXn9YHlZv+ad7vb2x+zDIBkCvtRIW6XeAKwY+ZdGnvcVW8TvuuKPXWgxLcxRmxrTmq4xpWs20WYw0b1uIBxaEsxCAQPYENPizXICF+2nR88PH8oADDlilrk996lPhnEVs9xY/apXz3R6wBeLeMqF0exvXN0RA37NbbrmlcOu2kSM8R3PmzFlW13e/+11voVSW/S7yD9u96S0Ha5EqGrkXg2wA7Bbjy++2224DXDH4KS0utFhmXiPBu+++22utR1lFI9QUp2XL6j/1QAAC/yNgsRO9BbP+34Ee/6Vo/5oBO/7441eoQe8yuZh07gtf+MIK53r9MXHiRG870Hu9nftqJiBDx+KQFW7VYoOF58hyRYe6tOZa66otAHHhui30i9fs7s0331y4rrorwCAbgLgW3Nt2cn/vvfcOcFVzp9785jf70047rTkBaBkCEIiGgNa9Wv4+L7dikaIZEBldK7uTpk+fHo5b3LBSFktrhl8zbRbPrIi43FsjgUsuucRrKU/R0pkhs0j6/l//+lfYmPamN73Jy5gqWjT5oZm8Mic/iso01PuJQ2ZvnoGKYqQogrCNCAe6rPZz999/vxs9erR74IEHnFKmUCAAAQgo3ZF94ArHdbLZipDSRqltlNpI8Q7NHerGjh3rzLVUOJK6NHX22Wc7BQe1BdgoLhECiqlpxk4IdF4kkK+eIcW2s928IWq/sjQo0byyTRQttiQoBBlW3LTUCgbZIBrTC0mRqRVgbr311hvk6vpOf/CDH3S2QynkmKuvVVqCAARiJrBo0aKQguihhx5yNvvUs6jmFXC2+Si8YxRY0zYjhajqiti/7rrr9lzv8jfacosQZFS5DSnpEDj55JNDxgYFDC5SlGfSEpaHwMBlRdO3XcEh84MCrqc4UYFBNoQnSrnbNDI89dRTh3B19ZdodkzRrW+88cYwwqi+RVqAAARSIaAUSnvssYfTbFmRojRMtg4npEeyjUkhan+R+pa/V7NiFtPKWWDsUtIvLV83/66WwCOPPOJsraKbP39++Ftta93Vruj/yl+p2bYUCwbZELQmA0gGmW0HdzvttNMQ7qjuEvNFu1133dXZjk1nO56qa4iaIQCBJAlce+21zrb8O9tMFGUeP+VDlLtLLiuL/J4k47YLrYTzSjavFFpKrxVDkSyabV2wYIHbfPPNYxCpaxkwyIaITLkobVu5u/POO8OasiHeVvplksF2f7rbb7/dKVcXBQIQgMDKBCxgtDZsOdsxufKpxn8rOfVll10WcmFa2J7G5UGA7gloLZkmJyz2nTvuuOO6r6DkO5QfWmuqZShqMJJqwSDrQnPjx493luYjTIdaJOsu7iznUsv35uQ+tUCwYcaunFqpBQIQyI2AxQgLa2ksFpOz0BLRdE+zdjvvvHMwxrbddtto5EKQ7gloJkrrq/VdalqXRx99dFjnfdVVV3XfkYjuwCDrQhmWH8tZXDI3btw4Z/kpXZ1GmR56S7UUdiZptxMFAhCAwEAELE6hO/TQQ8Nan80222ygS2s5ZxHeg6vSAs66FHfA1QIpsUYUfUAbPTRJsNVWWzUivQUXduedd56zcC1u0003bUSGshrFIOuSZBNGGcZYl0ricghAIBDQbmyFGNAHs8mPlYwxhSOQi9IymLCQP6Pns2MQNWGUNdl2FSrEIOuBasco0wvOIgu74cOH91DL4LdoDcg555zjTjzxRKc1bMyMDc6MKyAAgRUJaLelNiQ1ZZQtb4xdccUVpcSaWrGH/GqaQMcwsqCszrI5VC6Ovo2nnHJK+P42YQhW1UEMsh7JamvtCSecEBbNatpWi2jLLIqjcthhhznLeelmz54d3KRl1k9dEIBAewh0jDLtwKxzB9rSpUvdvvvuG2bGMMbyft7kupSRpDhlU6dOrWxJj4Kh69uo8BtaM9aUq7QSbZqlSSlAwKxzP3LkSG8L/v3VV19dOPWDBaD1M2bMCClQzN3gbXRZQDpuhQAEIPD/BGym3VuwTG8DvFqQWFiEkCxa+Q95j9WCvPFG7rjjDm/R9/0uu+ziLcZc6fLY2u3wbbQ1iFk+U+SyLOGRUU62008/PRhm22yzjbfQFN6s9yHXrFxeMuwsLo+3bAB+0qRJ3sJaDPl+LoQABCAwFALz5s0L76l99tmnq3fUUOruXGMhCLwF6AzG34UXXtg5zN+WEND3TMa/vmXmOfLKjVqk2Cyrt6U7XjlUt956a3/TTTcVqS7qe3FZljjvqMjWc+fOdbNmzXL24nNKOaIdmYpyrcjGluE+TN1bEuCQkkSxxG699daQPkLr0LQj6sgjjywlT1yJ3aIqCEAgIwJyI06bNi3EAnvPe97jjjrqqFLcmEuWLAkhgc4880w3atSoEC+xqvW1Gakj264ofZfWQCtu5hZbbOGOOOKIENBcITLWXHPNAfutZ+m2225z2il8wQUXOOVWVRR+BX7NOXYdBtmAj0XvJ5966qlgaOmhktGlNWEyxJ5++ulgmCnP3Pbbbx+MNRltMt4oEIAABOoioPfSzJkzndZ2Kb6hPnjmauo68vpdd90VwvFcfPHFIS7VlClTnNI3USAgAkp2f+mll7o5c+aEb6GCuOrbp+w3G264Yfge6ruo76Oy4nS+lzLq9Txq0GCzY62AiUHWCjXTSQhAAAKrJ/Doo4+GuIpf+tKXnHaQK0+uBon6T7MZSiY+bNgwp0GmPpqLFy8OsxcabGqW33xAITr65MmTo8ttuPoec7RJApo507MjQ96W+4RnSrNe8iAp8Lo8SjLY9LttBYOsbRqnvxCAAAT6IaCZ/M6svv4uWrQofDA1y6FUbTLMRowYsWxmXx9PW9dT2Y66fsTkMASyJIBBlqVa6RQEIAABCEAAAikRwCBLSVvICgEIQAACEIBAlgQwyLJUK52CAAQgAAEIQCAlAhhkKWkLWSEAAQhAAAIQyJIABlmWaqVTEIAABCAAAQikRACDLCVtISsEIAABCEAAAlkSwCDLUq10CgIQgAAEIACBlAhgkKWkLWSFAAQgAAEIQCBLAhhkWaqVTkEAAhCAAAQgkBIBDLKUtIWsEIAABCAAAQhkSQCDLEu10ikIQAACEIAABFIigEGWkraQFQIQgAAEIACBLAlgkGWpVjoFAQhAAAIQgEBKBDDIUtIWskIAAhCAAAQgkCUBDLIs1UqnIAABCEAAAhBIiQAGWUraQlYIQAACEIAABLIkgEGWpVrpFAQgAAEIQAACKRHAIEtJW8gKAQhAAAIQgECWBDDIslQrnYIABCAAAQhAICUCGGQpaQtZIQABCEAAAhDIkgAGWZZqpVMQgAAEIAABCKREAIMsJW0hKwQgAAEIQAACWRLAIMtSrXQKAhCAAAQgAIGUCGCQpaQtZIUABCAAAQhAIEsCGGRZqpVOQQACEIAABCCQEgEMspS0hawQgAAEIAABCGRJAIMsS7XSKQhAAAIQgAAEUiKAQZaStpAVAhCAAAQgAIEsCWCQZalWOgUBCEAAAhCAQEoEMMhS0hayQgACEIAABCCQJQEMsizVSqcgAAEIQAACEEiJAAZZStpCVghAAAIQgAAEsiSAQZalWukUBCAAAQhAAAIpEcAgS0lbyAoBCEAAAhCAQJYEMMiyVCudggAEIAABCEAgJQL/B3WGi3PqoNvgAAAAAElFTkSuQmCC)\n", "\n", " This graph has 2 connected components - $\\{s,a,b\\}$ and $\\{t\\}$ since all vertices $s,a,b$ are connected to each other while vertex $t$ is not connected to either of them and is in a connected component alone.\n", "\n", "\n", "How can we modify the code of $dfs$ to count the number of connected components in $G$?\n", "\n", "Try to think of how $dfs$ behaves on graphs with 1 connected component vs graphs with multiple connected components.\n" ], "metadata": { "id": "OQMrogVwkrFj" } } ] }