Implementation: Tree CSP Solver (aimacode#434)

* Update csp.py

* Add test

Author: antmarakis

csp.py

@@ -85,7 +85,7 @@ def display(self, assignment):
         # Subclasses can print in a prettier way, or display with a GUI
         print('CSP:', self, 'with assignment:', assignment)
 
-    # These methods are for the tree- and graph-search interface:
+    # These methods are for the tree and graph-search interface:
 
     def actions(self, state):
         """Return a list of applicable actions: nonconflicting
@@ -308,15 +308,18 @@ def tree_csp_solver(csp):
     """[Figure 6.11]"""
     assignment = {}
     root = csp.variables[0]
-    root = 'NT'
     X, parent = topological_sort(csp, root)
+
+    csp.support_pruning()
     for Xj in reversed(X[1:]):
         if not make_arc_consistent(parent[Xj], Xj, csp):
             return None
-    for Xi in X:
-        if not csp.curr_domains[Xi]:
+
+    assignment[root] = csp.curr_domains[root][0]
+    for Xi in X[1:]:
+        assignment[Xi] = assign_value(parent[Xi], Xi, csp, assignment)
+        if not assignment[Xi]:
             return None
-        assignment[Xi] = csp.curr_domains[Xi][0]
     return assignment
 
 
@@ -361,7 +364,34 @@ def build_topological(node, parent, neighbors, visited, stack, parents):
 
 
 def make_arc_consistent(Xj, Xk, csp):
-    raise NotImplementedError
+    """Make arc between parent (Xj) and child (Xk) consistent under the csp's constraints,
+    by removing the possible values of Xj that cause inconsistencies."""
+    #csp.curr_domains[Xj] = []
+    for val1 in csp.domains[Xj]:
+        keep = False # Keep or remove val1
+        for val2 in csp.domains[Xk]:
+            if csp.constraints(Xj, val1, Xk, val2):
+                # Found a consistent assignment for val1, keep it
+                keep = True
+                break
+        
+        if not keep:
+            # Remove val1
+            csp.prune(Xj, val1, None)
+
+    return csp.curr_domains[Xj]
+
+
+def assign_value(Xj, Xk, csp, assignment):
+    """Assign a value to Xk given Xj's (Xk's parent) assignment.
+    Return the first value that satisfies the constraints."""
+    parent_assignment = assignment[Xj]
+    for val in csp.curr_domains[Xk]:
+        if csp.constraints(Xj, parent_assignment, Xk, val):
+            return val
+
+    # No consistent assignment available
+    return None
 
 # ______________________________________________________________________________
 # Map-Coloring Problems
@@ -389,8 +419,8 @@ def different_values_constraint(A, a, B, b):
 
 def MapColoringCSP(colors, neighbors):
     """Make a CSP for the problem of coloring a map with different colors
-    for any two adjacent regions.  Arguments are a list of colors, and a
-    dict of {region: [neighbor,...]} entries.  This dict may also be
+    for any two adjacent regions. Arguments are a list of colors, and a
+    dict of {region: [neighbor,...]} entries. This dict may also be
     specified as a string of the form defined by parse_neighbors."""
     if isinstance(neighbors, str):
         neighbors = parse_neighbors(neighbors)
@@ -400,9 +430,9 @@ def MapColoringCSP(colors, neighbors):
 
 def parse_neighbors(neighbors, variables=[]):
     """Convert a string of the form 'X: Y Z; Y: Z' into a dict mapping
-    regions to neighbors.  The syntax is a region name followed by a ':'
+    regions to neighbors. The syntax is a region name followed by a ':'
     followed by zero or more region names, followed by ';', repeated for
-    each region name.  If you say 'X: Y' you don't need 'Y: X'.
+    each region name. If you say 'X: Y' you don't need 'Y: X'.
     >>> parse_neighbors('X: Y Z; Y: Z') == {'Y': ['X', 'Z'], 'X': ['Y', 'Z'], 'Z': ['X', 'Y']}
     True
     """

tests/test_csp.py

@@ -338,6 +338,7 @@ 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)
@@ -351,5 +352,13 @@ def test_topological_sort():
     assert Parents['WA'] == 'SA'
 
 
+def test_tree_csp_solver():
+    australia_small = MapColoringCSP(list('RB'),
+                           'NT: WA Q; NSW: Q V')
+    tcs = tree_csp_solver(australia_small)
+    assert (tcs['NT'] == 'R' and tcs['WA'] == 'B' and tcs['Q'] == 'B' and tcs['NSW'] == 'R' and tcs['V'] == 'B') or \
+           (tcs['NT'] == 'B' and tcs['WA'] == 'R' and tcs['Q'] == 'R' and tcs['NSW'] == 'B' and tcs['V'] == 'R')
+
+
 if __name__ == "__main__":
     pytest.main()