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Algorithms MCQ - Algorithm Design Techniques

41 Consider the polynominal p(x) = a₀ + a₁x + a₂x² + a₃x³, where a₁ ≠ 0, ∀i. The minimum number of multiplcations needed to evaluate p on an input x is

p(x) = a₀ + a₁x + a₂x² + a₃x³
p(x) = a₀ + (Ca₃x + a₂)x + a)x
t = cl₃* x
t = t + a₂
t = t * x
t = t + a₁
t = t * x
t = t + a₀
So minimum 3 multiplication are needed to e valuate P.

42 The characters a to h have the set of frequencies based on the first 8 Fibonacci numbers as follows: a : 1, b : 1, c : 2, d : 3, e : 5, f: 8, g : 13, h : 21 A Huffman code is used to represent the characters. What is the sequence of characters corresponding to the following code?
110111100111010

43 Which of the follovving is the Huffman code for the letters a, b, c, d, e?

44 What is the average length of the correct answer to above question?

45 Which of the following statement(s) is/are correct regarding Bellman-Ford shortest path algorithm?
P. Alvvays finds a negative weighted cycle, if one exists.
Q. Finds whether any negative weighted cycle is reachable from the source

I n Bellman Ford shortest path algorithm, we choose a node first and then we find any negative weighted cycle is reachable from source.

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Question:

What is the minimum possible weight of a path P from vertex 1 to vertex 2 in this graph such that P contains at most 3 edges?

A. 7
B. 8
C. 9
D. 10

Correct answer: B

Explanation:

Path from vertex 1 to 2 is (1 – 0) + (0 – 4) + (4 – 2) 1 + 4 + 3 = 8

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