Using Horner's rule, evaluate the polynomialAnalyse the computation time required for polynomial evaluation using Horner’s rule against the Brute force method.
### Step 1: Understanding Horner’s Rule Horner’s rule is an efficient way to evaluate polynomials by reducing the number of multiplications and additions. It rewrites a polynomial in nested form to minimize operations. Given the polynomial: \[ p(x) = 2x^5 - 5x^4 - 3x^2 + 15 \] we need to evaluate it at \( x = 2 \). ### Step 2: Rewriting Using Horner’s Rule Rearrange the polynomial: \[ p(x) = 2x^5 - 5x^4 + 0x^3 - 3x^2 + 0x + 15 \] Now, ________ __________ _____ ______ ___ ______.
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What are NP-Hard and NP-Complete problem? What is the role of reduction? Explain with the help of an example.
Consider the following Graph:
Figure 1: Graph for Problem 3(a) and 3(b)
a) Write the Kruskal’s algorithm and Prim’s algorithm to find the minimum cost
spanning tree of the graph given in Figure 1. Show all the steps of computation.
Also, compute the time complexity of both the algorithms.
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path algorithm. Show all the steps of computation. Also, find the time complexity
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dynamic programming approach to find the optimal sequence of chain
multiplication of the following matrices:
| Matrix | Dimension |
| A1 | 5 × 10 |
| A2 | 10 × 20 |
| A3 | 20 × 15 |
| A4 | 15 × 8 |
| A5 | 8 × 10 |
Using Horner's rule, evaluate the polynomial p(x)= 2x5 -5x4 -3x2+15 at x=2. Analyse the computation time required for polynomial evaluation using Horner’s rule against the Brute force method.
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.
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