2.2 topological sort 02

Definition
 A topological sort of a Directed Acylic Graph
(DAG) is a linear ordering of all its vertices such
that if there is a path from vi to vk then vi appears
before vk in the ordering.

Algorithm for finding a topological sort
Initialize TSArray to null
for (i=1; i<=numofvertices; i++)
 v = find vertex of degree zero
 if v is null
 Graph has a cycle. Exit
 else
 add v to TSArray
 remove v and all its outgoing vertices
Print TSArray

Algorithm for enumerating all topological sorts
TopologicalSorts()
compute the indegree count array, Indegree[ ]
initialize TSArray[ ] to null
for each vertex v
if indegree[v] == zero
push Indegree[ ], TSArray[ ], v
while (stack not empty)
pop Indegree[ ], TSArray[ ], v
add v to TSArray
for each x adjacent to v, Indegree[x]--
for each vertex v
if indegree[v] == zero
push Indegree[ ], TSArray[ ], v

Find out the ordering
1 2
4
6 7
53

Solution
•1 2 5 4 3 7 6
•1 2 5 4 7 3 6
•Find out other possibilities.

How many squares can you create in this figure by connecting any 4
dots (the corners of a square must lie upon a grid dot?
TRIANGLES:
How many triangles are located in the image below?

There are 11 squares total; 5 small, 4 medium, and 2 large.
27 triangles. There are 16 one-cell triangles, 7 four-cell triangles, 3 nine-cell triangles, and
1 sixteen-cell triangle.

2.2 topological sort 02

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2.2 topological sort 02