Question

1. (5 pts) Perform topological sorting on the directed graph below. Show two orderings that can result, such that no letter is in the same position in each ordering: e.g., D cannot be in the 3rd position in both orderings; if the algorithm does not finish, show the part of the graph that remains unprocessed (and explain why it remains unprocessed). Order 1 Order 2

Answer 1

Topology Sort

Step   Visited       Sorted

10      I             D
9       D             I    
8       H            H
7       C             J
6       F             A
5       A             F
4       G             C
3       B             E
2       E             G
1       J             B

PoP From Up to Down From Sorted Stack

So Sorted List for order 1 is --> D I H J A F C E G B

Step         Visited      Sorted

10               H           H
9               E           D
8               J           J
7               D           E         
6               A           I
5               I           A
4               B           F
3               G           G
2               F           B             
1               C           C

PoP From Up to Down From Sorted Stack

So Sorted List for order 2 is --> H D J E I A F G B C