Data Structures - Lecture 10 [Graphs]
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Graphs are data structures consisting of nodes and edges connecting nodes. They can be directed or undirected. Trees are special types of graphs. Common graph algorithms include depth-first search (DFS) and breadth-first search (BFS). DFS prioritizes exploring nodes along each branch as deeply as possible before backtracking, using a stack. BFS explores all nodes at the current depth before moving to the next depth, using a queue.
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2. The programmer then compiles the code, which converts it into an object file. If there are no errors, it is successfully compiled. Otherwise, errors are reported.
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[Please copy the link and paste it into any web browser to access the content.]
Video Link: https://youtu.be/kIEqwzhHJ54
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Photochemistry contributes to the development of sustainable energy solutions.
LAZY SUNDAY QUIZ "A GENERAL QUIZ" JUNE 2025 SMC QUIZ CLUB, SILCHAR MEDICAL CO...
LAZY SUNDAY QUIZ "A GENERAL QUIZ" JUNE 2025 SMC QUIZ CLUB, SILCHAR MEDICAL CO...Ultimatewinner0342 🧠 Lazy Sunday Quiz | General Knowledge Trivia by SMC Quiz Club – Silchar Medical College
Presenting the Lazy Sunday Quiz, a fun and thought-provoking general knowledge quiz created by the SMC Quiz Club of Silchar Medical College & Hospital (SMCH). This quiz is designed for casual learners, quiz enthusiasts, and competitive teams looking for a diverse, engaging set of questions with clean visuals and smart clues.
🎯 What is the Lazy Sunday Quiz?
The Lazy Sunday Quiz is a light-hearted yet intellectually rewarding quiz session held under the SMC Quiz Club banner. It’s a general quiz covering a mix of current affairs, pop culture, history, India, sports, medicine, science, and more.
Whether you’re hosting a quiz event, preparing a session for students, or just looking for quality trivia to enjoy with friends, this PowerPoint deck is perfect for you.
📋 Quiz Format & Structure
Total Questions: ~50
Types: MCQs, one-liners, image-based, visual connects, lateral thinking
Rounds: Warm-up, Main Quiz, Visual Round, Connects (optional bonus)
Design: Simple, clear slides with answer explanations included
Tools Needed: Just a projector or screen – ready to use!
🧠 Who Is It For?
College quiz clubs
School or medical students
Teachers or faculty for classroom engagement
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💡 Why Use This Quiz?
Ready-made, high-quality content
Curated with lateral thinking and storytelling in mind
Covers both academic and pop culture topics
Designed by a quizzer with real event experience
Usable in inter-college fests, informal quizzes, or Sunday brain workouts
📚 About the Creators
This quiz has been created by Rana Mayank Pratap, an MBBS student and quizmaster at SMC Quiz Club, Silchar Medical College. The club aims to promote a culture of curiosity and smart thinking through weekly and monthly quiz events.
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📣 Reuse & Credit
You’re free to use or adapt this quiz for your own events or sessions with credit to:
SMC Quiz Club – Silchar Medical College & Hospital
Curated by: Rana Mayank Pratap
Filipino 9 Maikling Kwento Ang Ama Panitikang Asiyano
Filipino 9 Maikling Kwento Ang Ama Panitikang Asiyanosumadsadjelly121997 Filipino 9 Maikling Kwento Ang Ama Panitikang Asiyano
YSPH VMOC Special Report - Measles Outbreak Southwest US 6-14-2025.pptx
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Data Structures - Lecture 10 [Graphs]
- 1. GRAPHS DATA STRUCTURES MUHAMMAD HAMMAD WASEEM 1
- 2. WHAT IS A GRAPH? • A data structure that consists of a set of nodes (vertices) and a set of edges that relate the nodes to each other • The set of edges describes relationships among the vertices 2
- 3. FORMAL DEFINITION OF GRAPHS • A graph G is defined as follows: G=(V,E) V(G): a finite, nonempty set of vertices E(G): a set of edges (pairs of vertices) 3
- 4. DIRECTED VS. UNDIRECTED GRAPHS • When the edges in a graph have no direction, the graph is called undirected. • When the edges in a graph have a direction, the graph is called directed (or digraph) 4 E(Graph2) = {(1,3) (3,1) (5,9) (9,11)
- 5. TREES VS. GRAPHS • Trees are special cases of graphs!! 5
- 6. GRAPH TERMINOLOGY • Adjacent nodes: two nodes are adjacent if they are connected by an edge • Path: a sequence of vertices that connect two nodes in a graph • Complete graph: a graph in which every vertex is directly connected to every other vertex • Degree of a vertex: The degree of a vertex in a graph is the number of edges that touch it. • The Size of a Graph: The size of a graph is the number of vertices that it has. 6 5 is adjacent to 7 7 is adjacent from 5
- 7. GRAPH TERMINOLOGY (CONT.) • What is the number of edges in a complete directed graph with N vertices? N * (N-1) 7 2 ( )O N
- 8. GRAPH TERMINOLOGY (CONT.) • What is the number of edges in a complete undirected graph with N vertices? N * (N-1) / 2 8 2 ( )O N
- 9. GRAPH TERMINOLOGY (CONT.) • Weighted graph: a graph in which each edge carries a value 9
- 10. GRAPH IMPLEMENTATION • Array-based implementation • A 1D array is used to represent the vertices • A 2D array (adjacency matrix) is used to represent the edges 10
- 12. GRAPH IMPLEMENTATION (CONT.) • Linked-list implementation • A 1D array is used to represent the vertices • A list is used for each vertex v which contains the vertices which are adjacent from v (adjacency list) 12
- 14. ADJACENCY MATRIX VS. ADJACENCY LIST REPRESENTATION • Adjacency matrix • Good for dense graphs --|E|~O(|V|2) • Memory requirements: O(|V| + |E| ) = O(|V|2 ) • Connectivity between two vertices can be tested quickly • Adjacency list • Good for sparse graphs -- |E|~O(|V|) • Memory requirements: O(|V| + |E|)=O(|V|) • Vertices adjacent to another vertex can be found quickly 14
- 15. GRAPH SEARCHING • Problem: find a path between two nodes of the graph (e.g., Austin and Washington) • Methods: Depth-First-Search (DFS) or Breadth- First-Search (BFS) 15
- 16. DEPTH-FIRST-SEARCH (DFS) • What is the idea behind DFS? • Travel as far as you can down a path • Back up as little as possible when you reach a "dead end" (i.e., next vertex has been "marked" or there is no next vertex) • DFS can be implemented efficiently using a stack 16
- 17. DEPTH-FIRST-SEARCH (DFS) (CONT.)Set found to false stack.Push(startVertex) DO stack.Pop(vertex) IF vertex == endVertex Set found to true ELSE Push all adjacent vertices onto stack WHILE !stack.IsEmpty() AND !found IF(!found) Write "Path does not exist" 17
- 19. 19
- 20. 20
- 21. BREADTH-FIRST-SEARCHING (BFS) • What is the idea behind BFS? • Look at all possible paths at the same depth before you go at a deeper level • Back up as far as possible when you reach a "dead end" (i.e., next vertex has been "marked" or there is no next vertex) 21
- 22. BREADTH-FIRST-SEARCHING (BFS) (CONT.) • BFS can be implemented efficiently using a queue Set found to false queue.Enqueue(startVertex) DO queue.Dequeue(vertex) IF vertex == endVertex Set found to true ELSE Enqueue all adjacent vertices onto queue WHILE !queue.IsEmpty() AND !found • Should we mark a vertex when it is enqueued or when it is dequeued ? 22 IF(!found) Write "Path does not exist"
- 24. next: 24
- 25. 25
- 26. SINGLE-SOURCE SHORTEST- PATH PROBLEM • There are multiple paths from a source vertex to a destination vertex • Shortest path: the path whose total weight (i.e., sum of edge weights) is minimum • Examples: • Austin->Houston->Atlanta->Washington: 1560 miles • Austin->Dallas->Denver->Atlanta->Washington: 2980 miles 26
- 27. SINGLE-SOURCE SHORTEST- PATH PROBLEM (CONT.) • Common algorithms: Dijkstra's algorithm, Bellman-Ford algorithm • BFS can be used to solve the shortest graph problem when the graph is weightless or all the weights are the same (mark vertices before Enqueue) 27
- 28. SIMPLE SEARCH ALGORITHM Let S be the start state 1. Initialize Q with the start node Q=(S) as only entry; set Visited = (S) 2. If Q is empty, fail. Else pick node X from Q 3. If X is a goal, return X, we’ve reached the goal 4. (Otherwise) Remove X from Q 5. Find all the children of node X not in Visited 6. Add these to Q; Add Children of X to Visited 7. Go to Step 2 28
- 29. DEPTH FIRST SEARCH(DFS) • Expand deepest unexpanded node • Implementation: • fringe = LIFO queue, i.e., put successors at front • Properties of DFS • Complete: No, fails in infinite-depth spaces, spaces with loops • Modify to avoid repeated states along path • Complete in finite spaces • Time: O(bm): terrible if m is much larger than d • but if solutions are dense, may be much faster than breadth-first • Space: O(bm), i.e., linear space! 29
- 30. DFS: EXAMPLE Q Visited 1 2 3 4 5 30 S BA E FDC G H
- 31. DFS: EXAMPLE Q Visited 1 S S 2 3 4 5 31 S BA E FDC G H
- 32. DFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 4 5 32 S BA E FDC G H
- 33. DFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 C,D,B S,A,B,C,D 4 5 33 S BA E FDC G H
- 34. DFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 C,D,B S,A,B,C,D 4 G,H,D,B S,A,B,C,D,G,H 5 34 S BA E FDC G H
- 35. DFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 C,D,B S,A,B,C,D 4 G,H,D,B S,A,B,C,D,G,H 5 H,D,B S,A,B,C,D,G,H 35 S BA E FDC G H
- 36. DFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 C,D,B S,A,B,C,D 4 G,H,D,B S,A,B,C,D,G,H 5 H,D,B S,A,B,C,D,G,H 6 D,B S,A,B,C,D,G,H 36 S BA E FDC G H
- 37. DFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 C,D,B S,A,B,C,D 4 G,H,D,B S,A,B,C,D,G,H 5 H,D,B S,A,B,C,D,G,H 6 D,B S,A,B,C,D,G,H 37 S BA E FDC G H
- 38. BREADTH FIRST SEARCH(BFS) • Expand shallowest unexpanded node • Implementation: • fringe = FIFO queue, i.e., New successors go at end • Properties of DFS • Complete: Yes(if b is finite) • Time: 1+b+b2+b3+… +bd + b(bd-1) = O(bd+1) • Space: O(bd+1) (keeps every node in memory) • Imagine searching a tree with branching factor 8 and depth 10. Assume a node requires just 8 bytes of storage. The breadth first search might require up to: = (8)10 nodes = (23)10 X 23 = 233 bytes = 8,000 Mbytes = 8 Gbytes • Optimal: Yes (if cost = 1 per step) 38
- 39. BFS: EXAMPLE Q Visited 1 2 3 4 5 39 S BA E FDC G H
- 40. BFS: EXAMPLE Q Visited 1 S S 2 3 4 5 40 S BA E FDC G H
- 41. BFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 4 5 41 S BA E FDC G H
- 42. BFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 B,C,D S,A,B,C,D 4 5 42 S BA E FDC G H
- 43. BFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 B,C,D S,A,B,C,D 4 5 43 S BA E FDC G H
- 44. BFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 B,C,D S,A,B,C,D 4 C,D,E,F S,A,B,C,D,E,F 5 44 S BA E FDC G H
- 45. BFS: EXAMPLE Q Visited 2 A,B S,A,B 3 B,C,D S,A,B,C,D 4 C,D,E,F S,A,B,C,D,E,F 5 D,E,F,G,H S,A,B,C,D,E,F,G,H 6 45 S BA E FDC G H
- 46. BFS: EXAMPLE Q Visited 3 B,C,D S,A,B,C,D 4 C,D,E,F S,A,B,C,D,E,F 5 D,E,F,G,H S,A,B,C,D,E,F,G,H 6 E,F,G,H S,A,B,C,D,E,F,G,H 7 46 S BA E FDC G H
- 47. BFS: EXAMPLE Q Visited 4 C,D,E,F S,A,B,C,D,E,F 5 D,E,F,G,H S,A,B,C,D,E,F,G,H 6 E,F,G,H S,A,B,C,D,E,F,G,H 7 F,G,H S,A,B,C,D,E,F,G,H 8 47 S BA E FDC G H
- 48. BFS: EXAMPLE Q Visited 5 D,E,F,G,H S,A,B,C,D,E,F,G,H 6 E,F,G,H S,A,B,C,D,E,F,G,H 7 F,G,H S,A,B,C,D,E,F,G,H 8 G,H S,A,B,C,D,E,F,G,H 9 48 S BA E FDC G H
- 49. BFS: EXAMPLE Q Visited 6 E,F,G,H S,A,B,C,D,E,F,G,H 7 F,G,H S,A,B,C,D,E,F,G,H 8 G,H S,A,B,C,D,E,F,G,H 9 H S,A,B,C,D,E,F,G,H 10 49 S BA E FDC G H
- 50. BFS: EXAMPLE Q Visited 6 E,F,G,H S,A,B,C,D,E,F,G,H 7 F,G,H S,A,B,C,D,E,F,G,H 8 G,H S,A,B,C,D,E,F,G,H 9 S,A,B,C,D,E,F,G,H 10 S,A,B,C,D,E,F,G,H 50 S BA E FDC G H
- 51. BFS: EXAMPLE Q Visited 1 S S 2 A,B S,A,B 3 B,C,D S,A,B,C,D 4 C,D,E,F S,A,B,C,D,E,F 5 D,E,F,G,H S,A,B,C,D,E,F,G,H 6 E,F,G,H S,A,B,C,D,E,F,G,H 7 F,G,H S,A,B,C,D,E,F,G,H 8 G,H S,A,B,C,D,E,F,G,H 9 H S,A,B,C,D,E,F,G,H 10 S,A,B,C,D,E,F,G,H 51 S BA E FDC G H
- 52. THANKS • Implement DFS and BFS in lab and submit softcopy at [email protected] 52