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### write a program to solve the Closest Points problem for an input file that contains duplicate x- coordinate values

INSTRUCTIONS TO CANDIDATES

(8 pts)    write a program to solve the Closest Points problem for an input file that contains duplicate x- coordinate values. As an extreme case, the data file could look like this:

5 6.7

5 7.1

5 4.2

5 5.7

5 4.9

(6 pts)        In addition (on paper for the TA)

1. Carefully explain any difficulties your previous (Program 2.1) program would have if the assumption about distinct x-coordinates is

1. Carefully explain what changes you made in your Program 2.1 to overcome such

1. In the previous version of this problem (with no duplicate x-values), the algorithm used had the following recurrence relation: T(n) = 2T(n/2) + Q(n) plus the time to presort, Q(n lg n).

this term includes Q(n) to divide + Q(n) to find Y' + Q(n) to search Y' for points + Q(1) for final comparison

So T(n) = Q(n lg n) (recurrence relation we have seen before) + Q(n lg n) (presort), therefore overall T(n) = Q(n lg n).

How do the changes in part (b) affect the overall order-of-magnitude of the algorithm?

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