Show that any sequence of m MAKE-SET, FIND-SET, and LINK operations, where all the LINK operations appear before any of the FIND-SET operations, takes only O.m/ time if we use both path compression and union by rank. What happens in the same situation if we use only the path-compression heuristic?

I want the answer for number 4.

One way to avoid Runge's problem is to choose non-equally spaced data points. A particularly good set to choose are the so-called Chebyshev nodes. To use these, replace the equidistant points xk produced by xeq with xk = COS 2k+1 2n+2 for k=0,..., n. (3.4) Generate data points using (3.4) and (3.3), then plot the resulting Lagrange interpolating polynomial and, hence, show that using (3.4) solves the Runge problem.

10. Consider the union-find container given below and suppose you used path compression when implementing union-find. Item 1 3 4 6 7 8 10 Representative 1 8 1 5 4 6 10 I. After calling find on item 7, 4's representative would be 8. II. After calling find on item 6, 8's representative would be 5. III. Calling find on 3 would change one or more representatives in the table. IV. There are 2 disjoint sets represented here. V. After calling find on item 2, 6's representative would be 5. Which of the following is true given these 10 elements and their representatives? A. I only В. I, IV C. IV only D. I, III, IV Е. I, IV, V

Describe how to maintain the outcomes of the insertions and deletions made in the following ways in an incremental manner: Outside connection on the left

part f, part g, part h, part i. use python

If the sequence number space is k bits large, you should seriously consider using both the selective-repeat technique and the Go-Back-N strategy in your search for a solution. What is the maximum allowable size for the sender window that we are allowed to make use of?

Which method should I use while inserting, erasing, and finding nodes in a data structure to guarantee that each operation has a temporal complexity lower than O(n)?

This question is about disjoint set. A В D E F G H J K M N P Q R S T U V Y Suppose we do not have path compression and union by size, what is the result if а. we union S and T? b. Suppose we have path compression, but we don't have union by size, what is the result if we union S and T? C. Suppose we have union by size, but we don't have path compression, what is the result if we union S and T? d. Suppose we have both path compression and union by size, what is the result if we union Q and W? N

When looking for a solution, you should give careful consideration to using both the selective-repeat approach and the Go-Back-N strategy if the sequence number space is big enough to include k bits of information. What is the largest size that the sender window that we are permitted to utilise is permitted to be in its entirety?