class CSP(search.Problem):\n",
+ " """This class describes finite-domain Constraint Satisfaction Problems.\n",
+ " A CSP is specified by the following inputs:\n",
+ " variables A list of variables; each is atomic (e.g. int or string).\n",
+ " domains A dict of {var:[possible_value, ...]} entries.\n",
+ " neighbors A dict of {var:[var,...]} that for each variable lists\n",
+ " the other variables that participate in constraints.\n",
+ " constraints A function f(A, a, B, b) that returns true if neighbors\n",
+ " A, B satisfy the constraint when they have values A=a, B=b\n",
+ "\n",
+ " In the textbook and in most mathematical definitions, the\n",
+ " constraints are specified as explicit pairs of allowable values,\n",
+ " but the formulation here is easier to express and more compact for\n",
+ " most cases. (For example, the n-Queens problem can be represented\n",
+ " in O(n) space using this notation, instead of O(N^4) for the\n",
+ " explicit representation.) In terms of describing the CSP as a\n",
+ " problem, that's all there is.\n",
+ "\n",
+ " However, the class also supports data structures and methods that help you\n",
+ " solve CSPs by calling a search function on the CSP. Methods and slots are\n",
+ " as follows, where the argument 'a' represents an assignment, which is a\n",
+ " dict of {var:val} entries:\n",
+ " assign(var, val, a) Assign a[var] = val; do other bookkeeping\n",
+ " unassign(var, a) Do del a[var], plus other bookkeeping\n",
+ " nconflicts(var, val, a) Return the number of other variables that\n",
+ " conflict with var=val\n",
+ " curr_domains[var] Slot: remaining consistent values for var\n",
+ " Used by constraint propagation routines.\n",
+ " The following methods are used only by graph_search and tree_search:\n",
+ " actions(state) Return a list of actions\n",
+ " result(state, action) Return a successor of state\n",
+ " goal_test(state) Return true if all constraints satisfied\n",
+ " The following are just for debugging purposes:\n",
+ " nassigns Slot: tracks the number of assignments made\n",
+ " display(a) Print a human-readable representation\n",
+ " """\n",
+ "\n",
+ " def __init__(self, variables, domains, neighbors, constraints):\n",
+ " """Construct a CSP problem. If variables is empty, it becomes domains.keys()."""\n",
+ " variables = variables or list(domains.keys())\n",
+ "\n",
+ " self.variables = variables\n",
+ " self.domains = domains\n",
+ " self.neighbors = neighbors\n",
+ " self.constraints = constraints\n",
+ " self.initial = ()\n",
+ " self.curr_domains = None\n",
+ " self.nassigns = 0\n",
+ "\n",
+ " def assign(self, var, val, assignment):\n",
+ " """Add {var: val} to assignment; Discard the old value if any."""\n",
+ " assignment[var] = val\n",
+ " self.nassigns += 1\n",
+ "\n",
+ " def unassign(self, var, assignment):\n",
+ " """Remove {var: val} from assignment.\n",
+ " DO NOT call this if you are changing a variable to a new value;\n",
+ " just call assign for that."""\n",
+ " if var in assignment:\n",
+ " del assignment[var]\n",
+ "\n",
+ " def nconflicts(self, var, val, assignment):\n",
+ " """Return the number of conflicts var=val has with other variables."""\n",
+ " # Subclasses may implement this more efficiently\n",
+ " def conflict(var2):\n",
+ " return (var2 in assignment and\n",
+ " not self.constraints(var, val, var2, assignment[var2]))\n",
+ " return count(conflict(v) for v in self.neighbors[var])\n",
+ "\n",
+ " def display(self, assignment):\n",
+ " """Show a human-readable representation of the CSP."""\n",
+ " # Subclasses can print in a prettier way, or display with a GUI\n",
+ " print('CSP:', self, 'with assignment:', assignment)\n",
+ "\n",
+ " # These methods are for the tree and graph-search interface:\n",
+ "\n",
+ " def actions(self, state):\n",
+ " """Return a list of applicable actions: nonconflicting\n",
+ " assignments to an unassigned variable."""\n",
+ " if len(state) == len(self.variables):\n",
+ " return []\n",
+ " else:\n",
+ " assignment = dict(state)\n",
+ " var = first([v for v in self.variables if v not in assignment])\n",
+ " return [(var, val) for val in self.domains[var]\n",
+ " if self.nconflicts(var, val, assignment) == 0]\n",
+ "\n",
+ " def result(self, state, action):\n",
+ " """Perform an action and return the new state."""\n",
+ " (var, val) = action\n",
+ " return state + ((var, val),)\n",
+ "\n",
+ " def goal_test(self, state):\n",
+ " """The goal is to assign all variables, with all constraints satisfied."""\n",
+ " assignment = dict(state)\n",
+ " return (len(assignment) == len(self.variables)\n",
+ " and all(self.nconflicts(variables, assignment[variables], assignment) == 0\n",
+ " for variables in self.variables))\n",
+ "\n",
+ " # These are for constraint propagation\n",
+ "\n",
+ " def support_pruning(self):\n",
+ " """Make sure we can prune values from domains. (We want to pay\n",
+ " for this only if we use it.)"""\n",
+ " if self.curr_domains is None:\n",
+ " self.curr_domains = {v: list(self.domains[v]) for v in self.variables}\n",
+ "\n",
+ " def suppose(self, var, value):\n",
+ " """Start accumulating inferences from assuming var=value."""\n",
+ " self.support_pruning()\n",
+ " removals = [(var, a) for a in self.curr_domains[var] if a != value]\n",
+ " self.curr_domains[var] = [value]\n",
+ " return removals\n",
+ "\n",
+ " def prune(self, var, value, removals):\n",
+ " """Rule out var=value."""\n",
+ " self.curr_domains[var].remove(value)\n",
+ " if removals is not None:\n",
+ " removals.append((var, value))\n",
+ "\n",
+ " def choices(self, var):\n",
+ " """Return all values for var that aren't currently ruled out."""\n",
+ " return (self.curr_domains or self.domains)[var]\n",
+ "\n",
+ " def infer_assignment(self):\n",
+ " """Return the partial assignment implied by the current inferences."""\n",
+ " self.support_pruning()\n",
+ " return {v: self.curr_domains[v][0]\n",
+ " for v in self.variables if 1 == len(self.curr_domains[v])}\n",
+ "\n",
+ " def restore(self, removals):\n",
+ " """Undo a supposition and all inferences from it."""\n",
+ " for B, b in removals:\n",
+ " self.curr_domains[B].append(b)\n",
+ "\n",
+ " # This is for min_conflicts search\n",
+ "\n",
+ " def conflicted_vars(self, current):\n",
+ " """Return a list of variables in current assignment that are in conflict"""\n",
+ " return [var for var in self.variables\n",
+ " if self.nconflicts(var, current[var], current) > 0]\n",
+ "