Question1) Explain the result of the following sequence of UNION operations using union-by-weight with the following assumptions Unions are executed on the representatives on the sets that have the arguments. If the sets contain the same weight, make the representative of the second argument point to the representative of the first argument. The universe of elements is the integers 0 - 16
a. Union( 3, 5 )
b. Union( 1, 7 )
c. Union( 14, 15 )
d. Union( 8, 9 )
e. Union( 1, 8 )
f. Union( 3, 10 )
g. Union( 3, 11 )
h. Union( 3, 12 )
i. Union( 3, 13 )
j. Union( 3, 6 )
k. Union( 16, 0 )
l. Union( 14, 16)
m. Union( 1, 3 )
n. Union (1, 14 )
Question2) Answer the questions regarding the graph given below.
a) Name one cycle which begins and ends at B.
b) True/False – the graph is strongly connected. If not, explain why not.
c) Find the shortest weighted paths from A to all other vertices. Your answer must include a list of all the vertices in order starting from A in each path and the weight of each path.