For the Gregory-Leibniz expression, compute the absolute value of the error (that is, abs (pi_gl( ath.pi)) for n = 1 to 500. Store these errors in a list (say, pi_gl_error), and repeat this for other two series, storing the errors in new lists. Plot a graph with the errors pi_gl_error, i_nik_error pi_wallis_error on the y-axis, against the range (1,500) on the x-axis. (Yo hould plot all three lines on the same graph. Be sure to label axes and data. You should choose f

EXM.1.AHL.TZ0.37 IB [Maximum mark: 8] In this part, marks will only be awarded if you show the correct application of the required algorithms, and show all your working. In an offshore drilling site for a large oil company, the distances between the planned wells are given below in metres. 1 2 3 4 5 6 7 8 9 10 2 30 3 40 60 4 90 190 130 5 80 200 10 160 6 70 40 20 40 40 130 7 60 120 50 90 30 60 8 50 140 90 70 70 140 70 40 9 40 170 140 60 50 90 50 70 10 200 200 80 150 110 90 30 190 90 100 11 150 30 200 120 190 120 60 190 150 200 + It is intended to construct a network of paths to connect the different wells in a way that minimises the sum of the distances between them. Use Prim's algorithm, starting at vertex 3, to find a network of paths of minimum total length that can span the whole site. [8]

The benefits and disadvantages of weighted graphs against adjacency lists should be compared.

Improve Luby’s MIS algorithm coded in Python by selecting a vertex at random,finding its neighbors and then finding the vertex with the minimum assignedrandom value to be included in the MIS.