(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)
Carefully explain any difficulties your previous (Program 2.1) program would have if the assumption about distinct x-coordinates is
Carefully explain what changes you made in your Program 2.1 to overcome such
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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