Implemented Topological Sort (aimacode#401)

* Implement Topological Sort

- Implemented topological_sort
- Added auxiliary function build_topological
- Updated call to topological_sort

* Use defaultdict to build visited

* Added test

* Update csp.py

Skip first item of iteration

Author: antmarakis

csp.py

@@ -14,12 +14,13 @@
 class CSP(search.Problem):
     """This class describes finite-domain Constraint Satisfaction Problems.
     A CSP is specified by the following inputs:
-        variables        A list of variables; each is atomic (e.g. int or string).
+        variables   A list of variables; each is atomic (e.g. int or string).
         domains     A dict of {var:[possible_value, ...]} entries.
         neighbors   A dict of {var:[var,...]} that for each variable lists
                     the other variables that participate in constraints.
         constraints A function f(A, a, B, b) that returns true if neighbors
                     A, B satisfy the constraint when they have values A=a, B=b
+    
     In the textbook and in most mathematical definitions, the
     constraints are specified as explicit pairs of allowable values,
     but the formulation here is easier to express and more compact for
@@ -29,7 +30,7 @@ class CSP(search.Problem):
     problem, that's all there is.
 
     However, the class also supports data structures and methods that help you
-    solve CSPs by calling a search function on the CSP.  Methods and slots are
+    solve CSPs by calling a search function on the CSP. Methods and slots are
     as follows, where the argument 'a' represents an assignment, which is a
     dict of {var:val} entries:
         assign(var, val, a)     Assign a[var] = val; do other bookkeeping
@@ -307,8 +308,9 @@ def tree_csp_solver(csp):
     """[Figure 6.11]"""
     assignment = {}
     root = csp.variables[0]
-    X, parent = topological_sort(csp.variables, root)
-    for Xj in reversed(X):
+    root = 'NT'
+    X, parent = topological_sort(csp, root)
+    for Xj in reversed(X[1:]):
         if not make_arc_consistent(parent[Xj], Xj, csp):
             return None
     for Xi in X:
@@ -318,8 +320,43 @@ def tree_csp_solver(csp):
     return assignment
 
 
-def topological_sort(xs, x):
-    raise NotImplementedError
+def topological_sort(X, root):
+    """Returns the topological sort of X starting from the root.
+
+    Input:
+    X is a list with the nodes of the graph
+    N is the dictionary with the neighbors of each node
+    root denotes the root of the graph.
+
+    Output:
+    stack is a list with the nodes topologically sorted
+    parents is a dictionary pointing to each node's parent
+
+    Other:
+    visited shows the state (visited - not visited) of nodes
+
+    """
+    nodes = X.variables
+    neighbors = X.neighbors
+
+    visited = defaultdict(lambda: False)
+
+    stack = []
+    parents = {}
+
+    build_topological(root, None, neighbors, visited, stack, parents)
+    return stack, parents
+
+def build_topological(node, parent, neighbors, visited, stack, parents):
+    """Builds the topological sort and the parents of each node in the graph"""
+    visited[node] = True
+
+    for n in neighbors[node]:
+        if(not visited[n]):
+            build_topological(n, node, neighbors, visited, stack, parents)
+
+    parents[node] = parent
+    stack.insert(0,node)
 
 
 def make_arc_consistent(Xj, Xk, csp):

tests/test_csp.py

@@ -274,6 +274,18 @@ def test_universal_dict():
 def test_parse_neighbours():
     assert parse_neighbors('X: Y Z; Y: Z') == {'Y': ['X', 'Z'], 'X': ['Y', 'Z'], 'Z': ['X', 'Y']}
 
+def test_topological_sort():
+    root = 'NT'
+    Sort, Parents = topological_sort(australia,root)
+    
+    assert Sort == ['NT','SA','Q','NSW','V','WA']
+    assert Parents['NT'] == None
+    assert Parents['SA'] == 'NT'
+    assert Parents['Q'] == 'SA'
+    assert Parents['NSW'] == 'Q'
+    assert Parents['V'] == 'NSW'
+    assert Parents['WA'] == 'SA'
+
 
 if __name__ == "__main__":
     pytest.main()