CS1102 Tut 10 Graphs

1
CS1102 Tut 10 Graphs

• Max Tan
• tanhuiyi_at_comp.nus.edu.sg
• S15-03-07 Tel[phone]http//www.comp.nus.edu.sg
  /tanhuiyi

2
Groups Assignment

• Question 1 Group 1
• Question 2 Group 2
• Question 3 Group 3
• Question 4 Group 4
• Question 5 Group 1
• Question 6 Group 2

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Groups Assignment

• Question 1 Group 2
• Question 2 Group 3
• Question 3 Group 1
• Question 4 Group 2
• Question 5 Group 3
• Question 6 Group 1

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First 15 minutes

• Breadth first search
• Depth first search
• Topological Sort
• Shortest path

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First 15 minutes BFS

• Breadth first search is like ripples in a pond,
  the ripples spread outwards
• Breadth first search is like level order
  traversal in a tree
• Difference is in a tree, once a root is traversed
  it will never be reached again

Hence, you need to remember which node has been
traveled before otherwise you will go into an
infinite loop!
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First 15 minutes

• Algorithm
• 1) Dequeue. If I encounter a node Ive never seen
  before, I print it and enqueue its adj nodes.
• 2) Remember that I have seen the node before.
• 3) Repeat 1 until queue is empty

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First 15 minutes DFS

• Depth first search is like solving a maze
• Travel as far as you can before you reach a dead
  end, then go back to the last junction and try a
  different route (which you have not explored).
• Routes may intersect!

There may be cycles, so your depth first search
must be careful
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First 15 minutes

• Algorithm
• 1) Peek node from top of stack (this is the last
  junction traveled)
• 2) If there is an unexplored route, try that
  route, otherwise pop from stack (try previous
  junction)

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First 15 minutes

• Algorithm
• 1) Peek node from top of stack (this is the last
  junction traveled)
• 2) If there is an unexplored route, try that
  route, otherwise pop from stack (try previous
  junction)

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First 15 minutes TSORT

• Topological sort is to obtain the solution to
  take modules which fulfills pre-req requirements
• Idea is, Nodes with incoming edges has pre-reqs
• Choose nodes with NO prereqs first
• After node is taken, remove the node AND all its
  corresponding outgoing edges

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First 15 minutes

• Topological sort is to obtain the solution to
  take modules which fulfills pre-req requirements
• Idea is, Nodes with incoming edges has pre-reqs
• Choose nodes with NO prereqs first
• After node is taken, remove the node AND all its
  corresponding outgoing edges

cs2103
cs1101
cs2105
cs1104
CS1101
CS1102
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First 15 minutes Dijkstras

• Dijkstras algorithm is a shortest path algorithm
• It is a greedy algorithm (pick the smallest each
  time) and it is optimum (gives the best answer)

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Question 1

• Give the adjacency matrix and the adjacency list
  for the following directed graph.

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Question 1
15
Question 1
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Question 2

• Assume that there is a method that will return
  the index of a vertex in the adjacency matrix and
  the adjacency list in O(1) time.
• Discuss the pros and cons of using adjacency
  matrix and adjacency list to represent graphs and
  the running times of the operations
• To insert a vertex (together with all its edges)
• To delete a vertex (together with all its edges),
  and
• To check whether a vertex is adjacent to another
  vertex.

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Question 2

• List vs Matrix
• Matrix needs O(V2) space
• List needs O(V E) space
• Complete graph O(V2) for both
• Sparse graph (only 1 or 2 edges per vertex),
  wastage of space in a matrix representation!

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Question 2

• Run time
• InsertionMatrix O(k), where k is total number
  of vertices affectedList O(k), where k is
  total number of vertices affected

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Question 2

• Run time
• DeletionMatrix O(v) (just set rowi and columni
  to 0)List O(E), Have to scan all the lists to
  find v and remove from list. Total is O(E) time

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Question 2

• Run time
• Check adjacencyMatrix O(1) List O(k), Scan
  through the list of B to determine if A is in the
  list

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Question 3

• Use both the depth-first strategy and the
  breadth-first strategy to traverse the following
  graph beginning with vertex a. List the vertices
  in the order in which each traversal visits them.

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Question 3 - DFS

• A B C D H F G E I
• A B C E I G D H F

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Question 3 - BFS

• A B C D E F H I G
• A D C B H F E G I

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Question 4

• List down the in-degrees of all the vertices in
  the graph given in Question 3. What do you obtain
  when you add up the in-degrees of all the
  vertices?

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Question 4

• Total is equals to the number of edges!

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Question 5

• Write two topological orders of the vertices for
  the graph.
• a, b, c, d, h, f, e, g, i
• a, b, c, d, f, h, e, g, i

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Question 6 Shortest path

• A 0
• B 8 ? 2
• C 8 ? 4
• D 8 ? 6

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Question 6 Shortest path

• A 0
• B 2
• C 4 ? 3
• D 6

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Question 6 Shortest path

• A 0
• B 2
• C 3
• D 6 ? 4
• E 8 ? 5

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Question 6 Shortest path

• A 0
• B 2
• C 3
• D 4
• E 5
• F 8 ? 7
• H 8 ? 8

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Question 6 Shortest path

• A 0
• B 2
• C 3
• D 4
• E 5
• F 7
• H 8
• G 8 ? 10
• I 8 ? 8

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Question 6 Shortest path

• A 0
• B 2
• C 3
• D 4
• E 5
• F 7
• H 8
• G 10 ? 9
• I 8

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Question 6 Shortest path

• A 0
• B 2
• C 3
• D 4
• E 5
• F 7
• H 8
• G 9
• I 8

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Question 6 Shortest path

• A 0
• B 2
• C 3
• D 4
• E 5
• F 7
• H 8
• G 9
• I 8

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Question 6 Shortest path

• A 0
• B 2
• C 3
• D 4
• E 5
• F 7
• H 8
• G 9
• I 8

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Question 6
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End

• Good luck for your exams!