Using the recursive method in problem 3 and assuming n is the length of the array. 1. Modify the recursion tree from the previous problem to show the amount of work on each activation and the row sums.
2. Determine the initial conditions and recurrence equation.
3. Determine the critical exponent.
4. Apply the Little Master Theorem to solve that equation.
5. Explain whether this algorithm optimal.

Write a method that takes in an array of point2d objects, and then analyzes the dataset to find points that are close together. be sure to review the point2d api. in your method, if the distance between any pair of points is less than 10, display the distance and the (x,y)s of each point. for example, "the distance between (3,5) and (8,9) is 6.40312." the complete api for the point2d adt may be viewed at ~pf/sedgewick-wayne/algs4/documentation/point2d.html (links to an external site.)links to an external site.. try to write your program directly from the api - do not review the adt's source code.

When making changes to optimize part of a processor, it is often the case that speeding up one type of instruction comes at the cost of slowing down something else. for example, if we put in a complicated fast floating-point unit, that takes space, and something might have to be moved farther away from the middle to accommodate it, adding an extra cycle in delay to reach that unit. the basic amdahl's law equation does not take into account this trade-off. a. if the new fast floating-point unit speeds up floating-point operations by, on average, 2ă—, and floating-point operations take 20% of the original program's execution time, what is the overall speedup (ignoring the penalty to any other instructions)? b. now assume that speeding up the floating-point unit slowed down data cache accesses, resulting in a 1.5ă— slowdown (or 2/3 speedup). data cache accesses consume 10% of the execution time. what is the overall speedup now? c. after implementing the new floating-point operations, what percentage of execution time is spent on floating-point operations? what percentage is spent on data cache accesses?

Why is it uncommon for users to perform searches directly in database tables? a.)users are discouraged from interacting directly with tables because they might confuse tables with spreadsheets. b.) users are discouraged from interacting directly with tables because this may result in unintended changes to source data. c.)users do not have the technical skills required to perform searches directly in database tables. d.)users do not have the permissions required to perform searches directly in database tables.