Data structures and algorithms lab7
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This document summarizes a lab on data structures and algorithms related to graphs. It introduces graphs and their representations, as well as graph traversal algorithms like depth-first search (DFS) and breadth-first search (BFS). It also discusses bipartite graphs. The lab objectives are to learn about graphs, DFS, BFS, and bipartite graphs. Various exercises are provided to apply these graph concepts.
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![GRAPHS: REPRESENTATION
Adjacency Matrix
A V x V matrix, with AdjacencyMatrix[i][j] storing whether
there is an edge between the ith vertex and the jth vertex or
not
Linked List of Neighbours
One linked list per vertex, each storing directly reachable vertices
!! What are the advantages and disadvantages of each of
them?](https://image.slidesharecdn.com/datastructuresandalgorithms-lab7-140330060452-phpapp02/85/Data-structures-and-algorithms-lab7-7-320.jpg)
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Vaibhav Gupta
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boundaryml/baml
Imagine if every API call you made
failed only 5% of the time
boundaryml/baml
Imagine if every LLM call you made
failed only 5% of the time
boundaryml/baml
Imagine if every LLM call you made
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boundaryml/baml
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but now everything must be
fault tolerant
boundaryml/baml
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think about these systems
Aaron Villalpando
Cofounder @ Boundary
Boundary
Combinator
boundaryml/baml
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boundaryml/baml
But now we do this:
boundaryml/baml
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boundaryml/baml
Problems web dev had:
Strings. Strings everywhere.
boundaryml/baml
Problems web dev had:
Strings. Strings everywhere.
State management was impossible.
boundaryml/baml
Problems web dev had:
Strings. Strings everywhere.
State management was impossible.
Dynamic components? forget about it.
boundaryml/baml
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Strings. Strings everywhere.
State management was impossible.
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Strings. Strings everywhere.
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boundaryml/baml
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Changing one thing breaks another.
New models come out all the time.
Iteration loops take minutes.
Low engineering rigor
boundaryml/baml
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boundaryml/baml
<show don’t tell>
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Chris
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Data structures and algorithms lab7
- 1. DATA STRUCTURES AND ALGORITHMS LAB 7 Bianca Tesila FILS, March 2014
- 2. OBJECTIVES Graphs DFS BFS Bipartite Graphs
- 3. GRAPHS: INTRODUCTION Pair of sets: G = (V, E) V = the set of vertices E = the set of edges; E ⊆ V x V
- 4. GRAPHS: INTRODUCTION Directed/ Undirected
- 5. GRAPHS: INTRODUCTION Weighted/ Unweighted
- 6. GRAPHS: INTRODUCTION Cyclic/ Acyclic
- 7. GRAPHS: REPRESENTATION Adjacency Matrix A V x V matrix, with AdjacencyMatrix[i][j] storing whether there is an edge between the ith vertex and the jth vertex or not Linked List of Neighbours One linked list per vertex, each storing directly reachable vertices !! What are the advantages and disadvantages of each of them?
- 8. GRAPHS: TRAVERSALS Depth-First Search - Go as far as you can (if you have not visited that node yet), otherwise, go back and try another way There is no source vertex All the vertices are traversed DFS (vertex u) { mark u as visited for each vertex v directly reachable from u if v is unvisited DFS (v) } !! Initially, all the vertices are marked as unvisited.
- 9. GRAPHS: TRAVERSALS !! Exercise: Emily wants to distribute candies to N students, one by one, with a rule that if student A is teased by B, A can receive the candy before B. Given the lists of students teased by each student, find a possible sequence to give the candies.
- 10. GRAPHS: TRAVERSALS Breadth-First Search - Instead of going as far as possible, BFS tries to search all paths. Uses a start vertex for the traversal: s Determine the minimum number of edges (shortest path considering that all the edges have the same weight = 1) between the source s and all the other vertices of the graph Not all the vertices are traversed BFS makes use of a queue to store visited (but not dead) vertices, expanding the path from the earliest visited vertices while queue Q not empty dequeue the first vertex u from Q for each vertex v directly reachable from u if v is unvisited enqueue v to Q mark v as visited !! Initially, all the vertices, except for the start vertex, are marked as unvisited and the queue contains only the start vertex .
- 11. GRAPHS: TRAVERSALS !! Exercise: Let’s consider un undirected graph, representing a social network. Given an user, display all his friends (or information about them) having the degree <=N (N is given). A is friend with B if there is an edge between A and B; we say that the degree of friendship is 1. Friends of friends have the degree of friendship 2.
- 12. GRAPHS: BIPARTITE GRAPHS A graph whose vertices can be divided into two disjoint sets such that every edge connects a vertex in U to one in V.
- 13. GRAPHS: BIPARTITE GRAPHS !! Exercise: Check if a graph is bipartite and if so, display the components of those two sets U and V. The graph will be represented by the lists of neighbors. Check your code for the following graphs: G1=({ 1,2,3,4,5,6,7,8,9},{ 12, 13, 45, 56, 75, 24, 58, 79, 43, 89}) G2=({ 1,2,3,4,5,6,7,8,9},{ 12, 13, 45, 56, 75, 24, 58, 79, 43, 89,47})
- 14. HOMEWORK Finish all the lab assignments.