Sierpinski Triangle - Polynomial Time Algorithm - BFT over DFT - Dynamic Programming - IT Assignment Help

Assignment Task:

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Week 6. Think.

1. Often programs need to manipulate collections of information, e.g., a list of student names, a list of numbers or a collection of records. For example, you have a list of names you want to sort – what is the first thing required before you can manipulate the data? How does Python support
the representation of collections?

2. Write an iterative algorithm and a recursive algorithm to sum the numbers in a list.

3. Write a recursive algorithm to sort the numbers in a list.

4. Compare mergesort and insertion sort of this list [2,9,1,6,3,2]: how many comparisons are needed in each?

5. Consider the following problem. Write pseudocode for an algorithm (that uses recursion) to solve it.

Week 7. Think.

1. What does it mean to say that a function T(n) = O(n log n) ?

2. If the time complexity of mergesort is O(n log n) and insertion sort isO(n2), where n is the input size, how much faster is mergesort?

3. What does a polynomial time algorithm mean, i.e. an algorithm in class P?

4. What does non-deterministic polynomial time algorithm mean, i.e. an algorithm in class NP?

5. Give an example of an algorithm that is in NP?

6. Is P=NP?

7. Consider the following directed graph represented by adjacency lists:
A: [B,C]
B: [D]
C: [E,F,G]
D: []
E: []
F: []
G: []
Do a BFT and a DFT of the graph.

8. What is the advantage of BFT over DFT when searching over an infinite sized graph?

Week 8. Think.

1. What is dynamic programming? Why does it usually work faster?

2. Using the dynamic programming solution for the knapsack problem, compute a solution to this knapsack problem: Weight value
2 16
3 19
4 23
5 28
total number of items = 4
capacity of the knapsack = 7

3. Suppose that the similarity between an object O and 6 other objects in the database A,B,C,D,E and F are as follows:
sim(A,O) = 0.1
sim(B,O) = 0.3
sim(C,O) = 0.85
sim(D,O) = 0.8
sim(E,O) = 0.9
sim(F,O) = 0.6
Also, suppose objects A, B and C are in class 1 and D,E and F are in class 2.
With k=4, what class should O be in, using the kNN algorithm?
With k=2, what class should O be in, using the kNN algorithm?

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