Sort the following numbers using the Quick.Sort algorithm:

35,23,38,22,11,47

Consider the following binary search tree

<img src='./qimages/10172-1b.jpg'>

illustrate the steps of the algorithm BUILD-MAX-HEAP for the following data:

16, 14, 10, 18, 7

Also compute the running time of the BUILD-MAX-HEAP algorithm.

Explain, with steps, the algorithm for finding the longest common subsequence of the sequences X C and y using Dynamic programming.

Illustrate, with all the steps, the operation of COUNTING-SORT on the array

A

Find the minimum spanning tree for the following graph using Prim's algorithm,explaining all the steps

<img src='./qimages/10172-3b.jpg'>

illustrate the steps of the Rabin-Karp matcher algorithm on the text

3141592653589783

for the pattern P 26. Assume you are working with q 11. Indicate all the spurious hits.

Consider the knapsack instance with n with the cost array

P2, p3) 100, weight array
w2, w3) 20, 30).

The knapsack can hold a weight of 50 units..Solve the 0 knapsack problem and the fractional knapsack problem for
the data above with the most efficient algorithm.

You should also explain why your choice of algorithm is most efficient.

Compute the Discrete Fourier Transform.(DFT) of the vector 3).

Run the Bellman-Ford algorithm on the directed graph given below, using the vertex s as the source. Explain all your steps.

<img src='./qimages/10172-5b.jpg'>

6. Which of the following statements are True, and which are False? Justify your answers.

Merge Sort algorithm is a stable sorting algorithm.

Every binary heap is a B-tree.

In the dynamic programming approach, the value of an optimal solution of an optimisation problem is determined in a bottom-up fashion.

In any directed graph with negative weights, Dijkstra's algorithm can be used to find the shortest path.

For any integer k if a b bEN, and b Fk the call EUCLID makes fewer than k recursive calls, where Fk is the 1)th Fibonacci number.