Algorithms Answers

(For Questions 2 to 5)

Consider the function f(x) = x^3−2x^2−4x+ 2.

Question 3

Which of the following statements is true about the given function?

(1) The Intermediate Value Theorem does not hold between x = −1 and x = 1.

(2) The function has two roots in the interval [−2, 4].

(3) It will take at least 15 iterations of the bisection method to approximate the root between

x = −2/3 and x = 2 correct to 10^−4.

(4) It will take no more than 14 iterations for the bisection method to converge to the root between

x = −2/3 and x = 2 correct to 10^−5.

(5) The function has at least one singular point.

(For Questions 2 to 5)

Consider the function f(x) = x^3−2x^2−4x+ 2.

Question 2

Which of the following statements about the given function is FALSE?

(1) the graph of the function has one point of inflection and has two relative extrema.

(2) The function has no absolute extremum.

(3) The graph of the function has two roots in the interval [0, 3.5]

(4) The function has a point of inflection point at x = 0.

(5) The function has a relative maximum point at x =

−2

3

and relative minimum point at x = 2.

Question 1

To have an idea on whether we should apply the bisection method to determine the root of f(x) = 0

in a given interval, we may

(1) draw the graph of f(x) and observe the graphs then conclude

(2) check if f(x) and f'(x) are continuous then conclude

(3) apply the function f(x) to the endpoints of the given interval and check the sign of the corre-

sponding outputs.

(4) check if f(x) has a critical point in the given interval

(5) check if f(x) has a point of inflection in the given interval.

Find Matrix Chain multiplication for following four matrices (M1, M2, M3 and M4) using dynamic programming Technique. 

Matrix M1 M2 M3 M4

Order of Matrix 4 x 3 3 x 5 5 x 2 2 x 6

Consider two strings A and B. Take string A as your First name and Last name without space in-between (eg: TEJINDERTHIND) and string B as the name of your home town (eg: JALANDHARCITY). Now find the Longest Common Subsequence (LCS) common to strings A and B using Dynamic Programming

The Electoral Commission wants a computer program that can determine the eligibility of voters. The eligibility criteria are based on the age and the nationality of the voter. The commission wants to know whether an applicant is too young to vote, a foreigner and so cannot vote or eligible to vote. Write an algorithm and draw a corresponding flowchart to meet the commission's expectation.

Elucidate how A* algorithm is better than Best First Search algorithm with the help of a suitable example.