Algorithmic COMP108 Foundations Tutorial 10
18 April 2008
Note: If youve spent 10 minutes on a question without any clue of how to proceed, talk to the demonstrator. 1. Suppose there are two assembly lines each with 4 stations, Si,j . The assembly time is given in the circle representing the station and the transfer time is given next to the arrow from one station to another.
S1,1 30 40 0 S1,2 50 10 10 20 S2,2 0 40 S2,3 0 S1,3 40 20 0 S1,4 10
start
30 30 S2,1 0 30 0 50 S2,4
nish
(a) Using dynamic programming, ll in the table of the minimum time fi [j] needed to get through station Si,j . You should also show all the intermediate steps in computing these j values. f1 [j] 1 2 3 4 (c) Which stations should be chosen? 2. Consider the following recurrence. T (n) = 1 T (n 1) + T (n 3) if 0 n 2 if n > 2 f2 [j]
(b) What is the minimum time f needed to get through the assembly line?
(a) Design and write a pseudo code for a recursive procedure to compute T (n). (b) Draw the execution tree for T (7). (c) Using the concept of dynamic p...