Topological Sort Algorithm Assignment Help

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What is Topological Sort Algorithm?

A topological sort is an ordering of vertices in a directed acyclic graph G, such that if there is a path from vi to vj in G, then vj appears after vi in the ordering.

Topological_sort max,avg,min (V + E)
toposort_dfs(g, s)
1: l = new list
2: foreach v E V,then do
3: colour[v] = grey
4: depth_first_search_visit (s, l)
5: foreach v E V do
6:if (colour[ v ] == grey)then
7: depth_first_search_visit ( v, l )
8:return l

dfs_visit(u , l)
1: colour[u] = white
2:for each neighbor v of u do
3:if (colour[v] == grey)then
4: depth_first_search_visit (v, l)
5: colour[u] = black
6: push_front(lu)

Properties of an Algorithms

  1. Specified Input
  2. Specified Output
  3. Scope defination
  4. Definiteness
  5. Execution
  6. Effectiveness

There are various ways to classify algorithms. Some of the popular methodologies are:

  1. Logical
  2. Serial, parallel or distributed
  3. Deterministic or non-deterministic
  4. Exact or approximate
  5. Divide and conquer
  6. Search and enumeration
  7. Randomized algorithm
  8. Reduction of complexity
  9. Linear programming
  10. Dynamic programming
  11. The greedy method

Example 1: Find Topological order for this DAG:

Finding topological order for DAG
Valid topological sorts
s1 = {R, S, T, U, V, W, X, Y, Z}
s2 = {R, T, S, W, V, U, Y, X, Z}
s3 = {R, S, U, T, V, X, W, Y, Z}
s4 = {R, T, W, S, V, Y, U, X, Z}

Example 2:

Topological Order for this DAG
Valid   topological sorts
- 7, 5, 3, 11,   8, 2, 9, 10
- 3, 5, 7, 8,   11, 2, 9, 10
- 3, 7, 8, 5,   11, 10, 2, 9
- 5, 7, 3, 8,   11, 10, 9,2
- etc