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## Question:

1.Context: Graph and Graph Algorithms

b.i)Using Dijkstra’s shortest path algorithm determine the shortest path to all other nodes in the following graph, starting from node A. Show all the steps with the values of distance and predecessor for each node.

ii)Mention one problem with Dijkstra’s shortest path algorithm.

iii)How can this problem be solved?

c.i.What is a minimum spanning tree (MST) of a graph?

ii.Using prims algorithm find the MST for the following graph rooted at node 0. Show all the steps.

2.Greedy Algorithm and Dynamic Programming

a.i)State the fractional knapsack problem.

ii)Write an algorithm to solve the problem using a greedy approach.

b.i)What is memoization?

ii)Write a bottom up algorithm to calculate the nth Fibonacci number using dynamic programming.

iii)In class we discussed about an algorithm to find the longest common substring between two strings using dynamic programming. Using the algorithm complete the following table for the strings “LCLC” and “CLCL”.

 C L C L L C L C

a.i) What is a convex hull for a N points in a 2-dimensional spaces?

ii) Given two lines with a common end point (i.e. AB and AC) in a 2-dimensional space, how can we determine the orientation (Clock wise, counter clock-wise, co-linearity) of the uncommon end-points (i.e. B and C) with respect to each other? Assume the co-ordinates for A, B, C is (x1,y1), (x2,y2), and (x3,y3).

b.For a single ended linked list, describe (do not write any code) the required steps to insert a new node:

i.At the beginning of the list

ii.At a particular position in the list

iii.At the end of the list

4. Context: Dictionary ADT and hashing

a.i) What is pre-hashing?

ii) What is the advantage of using a hash value of the key to find the index for value in the hash table over directly using the key as an index?

iii) When do we have a collision in a hash table?

iv) What is the basic difference between open addressing and closed addressing collision resolution policies?

b.Say, we have the following keys to be stored in a dictionary.

keys = {2,3,9,6,11,13,7,12}

The hash table for contains 10 slots, and the index to the hash table is given by the following hash function

H(k) = ((pre-hash(k) mod m), where m is the size of the hash table Pre-hash(k) = 2*k + 3

For resolving collision, we are using closed addressing with quadratic probing. Fill the following table and hash table with correct key values.

5. Context: Algorithm Analysis:

a. Define the asymptotic upper bound (Big O), Asymptotic Tight Bound (Big ϴ) of a function f(n).

6. Context: Heaps and Sorting

a.Construct a max heap from the following array. Draw the heap (tree), before and after each iteration of the build-max-heap algorithm. Circle the node on which you are currently calling max-heapify on and subtree.

A = [15,17,20,1,7,9,45,3,9,5,11]

b.Show the contents of the array after all the required number of passes for sorting the following array using radix sort

A = [0109,  0221, 1723, 0034, 0324, 1211, 0659, 1222]

### CIS223-Computer Science

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## More CIS223 CIS223-Computer Science: Questions & Answers

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Question: Upon successful completion of this unit students should be able to: Understand the common terms and definitions of cloud computing models, architectures and technologies Critically analyse the technical capabilities and business benefits of virtualisation and cloud computing Evalua ...

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### Management

We have already given an assignment before for this subject which is based on the topic "e-commerce security" please use the same the topic for the rest of the assignment. i attached a file of the previous assignment, please continue and do the assignment on the same topic. also there is another ass ...

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### CO4509: Computer Security

Question: WidgetsInc has contracted Benny Vandergast Inc to develop their new webbased store. Benny Vandergast Inc has provided a VMware virtual machine for testing. WidgetsInc have decided to give you the job of evaluating the security of the system provided by Benny Vandergast Inc. You should p ...

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