What is a recurrence relations? When are they used? Solve the following recurrence relations using the Master's method
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Expalin the PARTITION algorithm of the Quick Sort taking the last element as pivot. Demonstrate the use of Quick sort algorithm for sorting the following data of size 8: [1, 5, 8, 11, 16, 19, 29, 38]. Compute the complexity of the worst case of Quick Sort algorithm.
Differentiate between Quadratic-time and Exponential-time algorithms. Give example of one problem each for these two running times.
Explain the divide and conquer approach of multiplying two large matrices of size 16 x 16. Compute the time complexity of this approach.
Consider the following Graph:
Figure 1: A sample weighted Grари
a) Write the Kruskal's algorithm to find the minimum cost spanning tree of a graph. Also, find the time complexity of Kruskal's algorithm. Demonstrate the use of Kruskal's algorithm and Prim's algorithm to find the minimum cost spanning tree for the Graph given in Figure 1. Show all the steps.
Bellman-Ford's shortest path algorithm for the graph given in Figure 1. Show all the steps of computation.
search (where pi represents the probability that the search will be for the key node ki, whereas qi represents that the search is for dummy node di. Make suitable assumptions, if any)
Design and develop an efficient algorithm to find all the prime numbers in the range 2 to 10000.Access the complexity of this algorithm?
Write the Right to Left binary exponentiation algorithm. Demonstrate the use of this algorithm to compute the value of 523. Show all steps of the computation. Explain the worst-case complexity of this algorithm.
How can an optimisation problem be represented mathematically. Explain with the help of an example. Explain the steps of designing a Greedy solution for an optimisation problem. Also explain the concept of local and global optimal solutions. Solve the following fractional Knapsack problem using greedy approach. Show all the steps.
What is a recurrence relations? When are they used? Solve the following recurrence relations using the Master's method
Here are the equations from the image written in LaTeX format, along with a plain text version.$
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