Write and explain the linear search algorithm and discuss its best and worstcase time complexity. Show the working of the linear search algorithm for the data: 12, 11, 3, 9, 15, 20, 18, 19, 13, 8, 2, 1, 16.
### Linear Search Algorithm Linear search is a simple searching algorithm used to find an element in a list. It works by checking each element in the list sequentially until the target element is found or the end of the list is reached. #### Algorithm (Step-by-Step) 1. Start from the first element of the array. 2. Compare the current element with the target element. 3. If the current element matches the target, return the index. 4. If the target is not found, move to the next ___ _____ __________ _____ ____ ________ _________ ____ ________.
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What is a Greedy Approach to Problem-solving? Formulate the fractional Knapsack Problem as an optimisation problem and write a greedy algorithm to solve this problem. Solve the following fractional Knapsack problem using this algorithm. Show all the steps. Suppose there is a knapsack of capacity 15 Kg and 6 items are to packed in it. The weight and profit of the items are as under:
(p1, p2,…, p6) = (3, 2, 4, 5, 1, 6)
(w1, w2,…, w6) = (2, 1, 2, 1, 5, 1)
Using Horner's rule, evaluate the polynomialAnalyse the computation time required for polynomial evaluation using Horner’s rule against the Brute force method.
Vertex cover problem
Graph Colouring Problem
Expalin the Partition procedure of the Quick Sort algorithm. Use this procedure and quick sort algorithm to sort the following array of size 8: [12, 9, 17, 15, 23, 19, 16, 24]. Compute the worst case and best case complexity of Quick sort algorithm.
Explain the divide and conquer apprach of multiplying two matrices of large size. Also, explain the Strassen’s matric multiplication algorithm. Find the time complexity of both these approaches.