#### lab11

Skidmore, CS 206
Excerpt: ... Lab 11 Tuesday, April 7, 2009 CS206 - Introduction to Computer Science II Skidmore College Instructor: Michael Eckmann This lab will serve a few purposes 1. designing and writing code for Graphs with Adjacency lists = 1. Work on Program 4. Note well: I added another instance variable to Vertex which represents the index number it is in in the Graph's vertexList array. This made it easier for me to search the adjacency list of a vertex using just the vertex numbers. Remember that the adjacency list stores information about the edges in the graph. So, think about what data will need to be stored in each node of the linked lists for the adjacency lists . = Nothing needs to be submitted for lab 11. ...

#### Lecture14

Lehigh, IE 170
Excerpt: ... class Edge{ public: Edge(int i, int j): v(i), w(j) {} ~Edge(); int v, w; }; class Vertex{ private: / Imlementation dependend code public: int getIndex() const; Vertex const * getNext() const; } IE170 Lecture 14 5 A Client Function for Printing a Graph Here's an example of a standard way in which the graph interface class is used. Here, we print out a graph by enumerating all the edges incident to each vertex. void printGraph(const Graph& G) { for (int s = 0; s < G.V(); s+){ cout < s < ":"; for (Vertex* t = G.getFirst(s); t != 0; t = t->getNext(){ cout < Vertex->getIndex() < ":"; } } } IE170 Lecture 14 6 Graph Data Structures To support these basic graph operations, we need a data structure to store the graph. As with many previous data structures, there are basically two different ways to compactly represent a graph. Ajacency matrix: An implementation based on arrays. Adjacency lists : An implementation based on linked lists. We have to analyze the tradeoffs between ...

#### Lecture 13

Seattle Pacific, CSC 2431
Excerpt: ... Page 1 of 1 Lecture 13 June 2, 2006 The Final Exam is Tuesday, June 6, 2006 from 10:30AM 12:30PM A final exam study guide is posted The topic for today is Graphs and Graph Algorithms Graphs o Cartesian graphs Not o Are sets of (vertex, arc) pairs The arcs may be directed (digraph) or undirected (graph) The arcs may have weights or costs assigned to them o Store as array or as a linked structure What would this look like? How is it different for graphs and digraphs? Use either adjacency matrices or adjacency lists Some useful graph algorithms o Shortest path Dijkstra's algorithm o Depthfirst search Similar to preorder traversal o Breadthfirst search Similar to level order traversal o Number of paths of length n (number of hops) from one node to another Matrix multiplication ...

#### hw3

Lehigh, CS 383
Excerpt: ... Assignment 3 CS383: Algorithms, Boston College Due on Sept. 28th in class This is a "collaboration-forbidden" assignment, which means collaboration of any kind is a violation of academic regulations. But you can always consult course staff and cours ...

#### hw4final

Georgia Tech, CS 3510
Excerpt: ... 9-8-04 CS 3510 A Design and Analysis of Algorithms Homework 4 Due: Friday, 9-17-04 at the start of class Problem 1: Feedback (10 points) The professor is under the impression that you might need a little bit more incentive to immerse yourselves in ...

#### lecture-graphs

East Los Angeles College, COMP 523
Excerpt: ... Lectures on Graph Algorithms: searching, testing and sorting COMP 523: Advanced Algorithmic Techniques Lecturer: Dariusz Kowalski Graph Algorithms 1 Overview Previous lectures: Recursive method (searching, sorting, ) This lecture: algorithms on g ...

#### lecture10

East Los Angeles College, COMP 523
Excerpt: ... Lecture 10 Graph algorithms: testing graph properties COMP 523: Advanced Algorithmic Techniques Lecturer: Dariusz Kowalski Lecture 10: Testing Graph Properties 1 Overview Previous lectures: Representation of graphs (adjacency matrix or list) Bre ...

#### lecture10

East Los Angeles College, COMP 523
Excerpt: ... Lecture 10 Graph algorithms: testing graph properties COMP 523: Advanced Algorithmic Techniques Lecturer: Dariusz Kowalski Lecture 10: Testing Graph Properties 1 Overview Previous lectures: Representation of graphs (adjacency matrix or list) Bre ...

#### Quiz13

Clemson, CS 212
Excerpt: ... CPSC 212-1Name: _ Quiz #13March 28, 2002 Closed books. Closed Notes. Calculators OK. 20 points. 10 minutes. Weight of each question in parentheses. Please use a pencil. If you need more space, use the back of the sheet. 1.Conside ...

#### quiz15

Alabama, CS 511
Excerpt: ... CS 511 Quiz 15 1. Show both the adjacency matrix and adjacency lists representations for this graph. (Each adjacency list should be arranged in alphabetical order.) A B C D E F G H 2. Show both the adjacency matrix and adjacency lists representations for this digraph. (Each adjacency list should be arranged in alphabetical order.) A B C D E F G H Everybody did well on this quiz, so there is no need to provide solutions. ...

#### WtGraph.h

Eastern Washington University, CSCD 327
Excerpt: ... graph { return Nnodes; } int N_Edges(void) / Total undirected edges { return Nedges; } void Dump(void); / Debug: dump out the graph info. void VertexList(void); / List vertices with their flags int DepthRecur(void); / Recursive depth-first traversal void FlipLists(void); / Invert all adjacency lists int Depth1st(void); / Depth-first traversal - non-recursive int Breadth1st(void); / Breadth-first traversal int Prim(void); / Prim's minimum spanning tree private: int Find (char Value); / Subscript of vertex in Node array void ClearFlags(void); / Clear all the .Flag fields int Depth1st(VertPtr Parent, VertPtr Node); int Nnodes, / Number of vertices in the graph Nedges; / Number of edges in the graph int ID; / In traversals, order of visit Vertex *Node, / Dynamic array of Vertices *Curre ...

#### WtGraph.h

Eastern Washington University, CSCD 327
Excerpt: ... rsive depth-first traversal void FlipLists(void); / Invert all adjacency lists int Depth1st(void); / Depth-first traversal - non-recursive int Breadth1st(void); / Breadth-first traversal int Prim(void); / Prim's minimum spanning tree private: int Find (char Value); / Subscript of vertex in Node array void ClearFlags(void); / Clear all the .Flag fields int Depth1st(VertPtr Parent, VertPtr Node); int Nnodes, / Number of vertices in the graph Nedges; / Number of edges in the graph int ID; / In traversals, order of visit Vertex *Node, / Dynamic array of Vertices *Current; / Available pointer to a node static const VertPtr Dmy; / Parent for unconnected component }; / Note: the adjacency list's underlying struct can also be / used for the stack/queue in traversals. / That means we have to provide a dummy "weight" each tim ...

#### Lecture15-4

UWO, CS 2210
Excerpt: ... is referenced in the adjacency list of u and v How to Improve Edge List Structure? v u Graph Representation: Adjacency List Structure w z v (u,v) (v,w) (u,v) (u,w) (u,w) (v,w) (w,z) u w (w,z) z v u w z v u w z (u,v) (v,w) (u,w) (w,z) (u,v) (v,w) (u,w) (w,z) The problem with edge list structure is that each vertex does not know which edges are incident on it Solution: put pointers (reference) from each vertex to the edge object incident on this vertex Each vertex can have lots of edges incident on it Thus we need a sequence of incident vertices this sequence is called Adjacency List, because its usually implemented as a list Space requirement: O(n) for the vertex sequence, O(m) for the edge sequence For vertex v, O(deg(v) for the adjacency list of v. For all adjacency lists , O(v deg(v) ) = 2m = O(m) by property 1 from the beginning of lecture For the back links O(m) Thus total space is O(n + m) 8 2 Adjacency List Structure (u,v) (v,w) (u,v) (u,w) (u,w) (v,w) (w,z) (w,z) G ...

Lehigh, IE 170

#### finalreview

Willamette, CS 343
Excerpt: ... CS 343 Analysis of Algorithms, Spring 2004 1 Review for Final Exam The exam will be closed notes, closed book, and no calculators. Exam may include true/false, multiple choice, short answer, and short proofs. When doing proofs, you must explain all of your steps. Suggestion: carefully review lab problems and class notes. Reread relevant sections in text. This exam will include problems from the previous two exams so please study these. New Material 1. Greedy Algorithms What is a greedy algorithm? Why use non-optimal greedy algorithms? What is the greedy choice property and how do you prove that a problem satisfies it? What is the optimal substructure and how do you argue that a problem satisfies it? Applications: cheapest path, hill climbing, activity selection, Huffman codes, fractional knapsack problem 2. Graphs Definitions Data structures for storing graphs: edge lists, adjacency lists , adjacency matrices. Breadth First Search Trees Depth First Search Trees Topological Sorting Thes ...

#### WtGraphA.h

Eastern Washington University, CSCD 327
Excerpt: ... /* Weighted Graph Routines Author: Timothy Rolfe loosely based on Robert Sedgewick's Algorithms in C+ The graph is represented by an array of structs representing the vertices. Each vertex contains its designator, a int flag ...

#### exercise_7

Ill. Chicago, CS 201
Excerpt: ... Exercise 6 for Trees & Graphs 1. In Figure1 a) Which node is the root? b) Which nodes are leaves? c) Name the parent node of J; d) List the siblings of H; e) List the left child of node E; 2. In Figure 1 a) Give the level of node I; b) Give the depth ...

#### quiz7

Siena, CSIS 385
Excerpt: ... CSIS-385: Quiz 7 Given the following graph: AEDB BECA CFB DGA EIHFBA FEC GD HJIE IHE JH Name_ #1. Draw the graph. Assume the graph is undirected #2. Do a Depth-first search starting at vertex A. Process each adjacency list in the order given. Note ...

#### h5

FIU, CIS 5407
Excerpt: ... he n adjacency lists of a given simple undirected graph G(V, E). Hint: Use radix sort with n buckets. 35. (Regular) In an undirected graph, the adjacency list representation consists of n linked lists of edge objects. For each undirected edge of the form e = {vi , vj }, the adjacency list representation contains two edge objects. One edge object is in the list Adj[i] containing the source index i and the destination index j, while the other edge object is in the list Adj[j] containing the source index j and the destination index i. Since an undirected edge can be thought of as being composed of two directed edges, we could think of one edge object as representing the edge e = (vi , vj ), with the other referring to the edge e = (vj , vi ). We also say that the two directed edges e = (vi , vj ) and e = (vj , vi ) are partners of each other. In general, for a given edge e, it takes O(n) time to locate its partner edge object, unless we can store in each edge object a pointer to its partner edg ...

#### lecture9

East Los Angeles College, COMP 523
Excerpt: ... Lecture 9 Graph algorithms: BFS and DFS search COMP 523: Advanced Algorithmic Techniques Lecturer: Dariusz Kowalski Overview Previous lectures: Greedy algorithms Minimum spanning tree - many greedy approaches (Prims and Kruskals algorithms) Prior ...

#### HW4

Delaware, CISC 320
Excerpt: ... CISC 320 Introduction to Algorithms (Spring 2009) Homework 4 Handed out: April 23, 2009 Due date: March 5, 2009 (Due in class on that day - sketches of the solutions will be handed out at that time) Your handwriting must be legible, and your answers ...

#### lecture9

East Los Angeles College, COMP 523
Excerpt: ... Lecture 9 Graph algorithms: BFS and DFS search COMP 523: Advanced Algorithmic Techniques Lecturer: Dariusz Kowalski Overview Previous lectures: Greedy algorithms Minimum spanning tree - many greedy approaches (Prims and Kruskals algorithms) Prior ...

#### SWAT06

Princeton, COS 521
Excerpt: ... topological order 7 for u B {u} u v in increasing topological order 8 Reorder(u ,v ) Fig. 1. Our algorithm 2.1 Data structure We store the current topological order, as a set of two arrays, storing the bijective mapping T and its inverse. This ensures that nding T (i) and T 1 (u) are constant time operations. The graph itself is stored as an array of vertices. For each vertex we maintain two adjacency lists , which keep the incoming and outgoing edges separately. Each adjacency list is stored as an array of buckets of vertices. Each bucket contains at most t nodes for a xed t. Depending on the concrete implementation of the buckets, the parameter t is later chosen to be approximately n0.75 so as to balance the number of inserts and deletes from the buckets and the extra edges touched by the algorithm. The i-th bucket (i 0) of a node u contains all adjacent nodes v with i t < d(u, v) (i + 1) t. The nodes of a bucket are stored with node index (and not topological order) ...