private List <Problem <Hypergraph.EdgeAnnotation> > GenerateBackwardProblems(List <GroundedClause> goalClauses,
Pebbler.HyperEdgeMultiMap <Hypergraph.EdgeAnnotation> edgeDatabase)
{
// System.Diagnostics.Debug.WriteLine("Backward");
List <int> clauseIndices = AcquireGoalIndices(goalClauses);
// The resultant structure of problems; graph size dictates associated array size in hashMap; number of givens is a limiting factor the size of problems
// Problem generation limits the number of givens in BACKWARD problems to 4 (or the constant in the HashMap structure)
ProblemHashMap <Hypergraph.EdgeAnnotation> problems = new ProblemHashMap <Hypergraph.EdgeAnnotation>(edgeDatabase, graph.vertices.Count);
// Generate all the problems based on the node indices
foreach (int goalNode in clauseIndices)
{
if (Utilities.PROBLEM_GEN_DEBUG)
{
System.Diagnostics.Debug.WriteLine("Template node; will generate problems (" + goalNode + "): " + graph.vertices[goalNode].data.ToString());
}
pathGenerator.GenerateProblemsUsingBackwardPathToLeaves(problems, edgeDatabase, goalNode);
}
// Filter backward problems so that only problems with goal being the original figure givens persist.
return(FilterBackwardProblems(clauseIndices, FilterForMinimalAndRedundantProblems(problems.GetAll())));
}
//
// COMPELTE POWERSET implementation
//
// Time consuming, but complete.
//
//
// From this node, generate all problems backward.
// Do so by generating simple problems first (in a depth-first manner)
//
private List <Problem <Hypergraph.EdgeAnnotation> > GenerateAllProblemsFrom(ProblemHashMap <Hypergraph.EdgeAnnotation> memoizedProblems,
HyperEdgeMultiMap <Hypergraph.EdgeAnnotation> edgeDatabase, int node)
{
// If we have already generated problems, no need to regenerate
if (memoizedProblems.HasNodeBeenGenerated(node))
{
return(memoizedProblems.Get(node));
}
// For all edges, create base problems and add them all to the database
List <PebblerHyperEdge <Hypergraph.EdgeAnnotation> > forwardEdges = edgeDatabase.GetBasedOnGoal(node);
// If there are no edges, this is a 'root' node (has no predecessors)
if (forwardEdges == null || !forwardEdges.Any())
{
// We've successfully generated all the problems for this node: zero problems
memoizedProblems.SetGenerated(node);
return(new List <Problem <Hypergraph.EdgeAnnotation> >());
}
//
// Create all the base problems consisting of only one edge and add to the database
List <Problem <Hypergraph.EdgeAnnotation> > baseProblems = new List <Problem <Hypergraph.EdgeAnnotation> >();
foreach (PebblerHyperEdge <Hypergraph.EdgeAnnotation> edge in forwardEdges)
{
baseProblems.Add(new Problem <Hypergraph.EdgeAnnotation>(edge));
}
memoizedProblems.PutUnchecked(baseProblems);
// For all of the base problems, generate backward
foreach (Problem <Hypergraph.EdgeAnnotation> baseProblem in baseProblems)
{
GenerateAllProblemsFromSingleEdge(memoizedProblems, edgeDatabase, baseProblem);
}
// We've successfully generated all the problems for this node
memoizedProblems.SetGenerated(node);
// Return all the generated problems
return(memoizedProblems.Get(node));
}
//
// For all given nodes in this problem, generate the single maximal problem
//
// This is done is a convluted way to speed up execution since we need to combine in the size of the powerset of cardinality of givens
//
private void GenerateMaximalProblemFromSingleEdge(ProblemHashMap <Hypergraph.EdgeAnnotation> memoizedProblems,
HyperEdgeMultiMap <Hypergraph.EdgeAnnotation> edgeDatabase,
Problem <Hypergraph.EdgeAnnotation> baseProblem)
{
// Create all simple problems by pursuing only a single path backward in the givens: append
// all problems from a given to the base problem
//
// |
// v
// given __
// | |
// v | baseProblem
// goal __|
//
// Acquire all of the problems for the singleton sets of the powerset for all of the givens of this problem
List <Problem <Hypergraph.EdgeAnnotation> >[] singletonMapToNewProblems = new List <Problem <Hypergraph.EdgeAnnotation> > [baseProblem.givens.Count];
List <Problem <Hypergraph.EdgeAnnotation> >[] singletonMapToOriginalProblems = new List <Problem <Hypergraph.EdgeAnnotation> > [baseProblem.givens.Count];
bool generatedNewProblems = false;
for (int g = 0; g < baseProblem.givens.Count; g++)
{
// Acquire the original problems and save them
singletonMapToOriginalProblems[g] = GenerateAllMaximalProblemsFrom(memoizedProblems, edgeDatabase, baseProblem.givens[g]);
if (singletonMapToOriginalProblems[g] == null)
{
singletonMapToOriginalProblems[g] = new List <Problem <Hypergraph.EdgeAnnotation> >();
}
// Using the original problems, append them to the base problem
singletonMapToNewProblems[g] = new List <Problem <Hypergraph.EdgeAnnotation> >();
// Append all of these given problems to the base problem
foreach (Problem <Hypergraph.EdgeAnnotation> problem in singletonMapToOriginalProblems[g])
{
Problem <Hypergraph.EdgeAnnotation> baseProblemCopy = new Problem <Hypergraph.EdgeAnnotation>(baseProblem);
baseProblemCopy.Append(graph, edgeDatabase, problem);
//memoizedProblems.Put(baseProblemCopy);
singletonMapToNewProblems[g].Add(baseProblemCopy);
generatedNewProblems = true;
}
}
if (baseProblem.goal == 98)
{
//Debug.WriteLine("98NO-OP");
}
// If we did not perform any appending, we have reached a maximal situation
// Add the maximal problem to the database
if (!generatedNewProblems)
{
// Determine suppression now to mitigate number of problems added
baseProblem.DetermineSuppressedGivens(graph);
memoizedProblems.Put(baseProblem);
return;
}
//
// Stitch together all of the possible combinations of maximal problems
//
// | | |
// | | |
// v v v
// g_1 g_2 ... g_n __
// | | baseProblem
// v |
// target __|
//
//
// We are looking for the maximal set of problems; therefore, we don't need all combinations.
// What we do require is the combining of all generated problems with the base problem.
//
// Find all the sets of populated new problems
List <int> populatedIndices = new List <int>();
for (int index = 0; index < singletonMapToNewProblems.Length; index++)
{
if (singletonMapToNewProblems[index].Any())
{
populatedIndices.Add(index);
}
}
List <Problem <Hypergraph.EdgeAnnotation> > maximalProblems = new List <Problem <Hypergraph.EdgeAnnotation> >(singletonMapToNewProblems[populatedIndices[0]]);
populatedIndices.RemoveAt(0);
foreach (int index in populatedIndices)
{
//int count = 0;
List <Problem <Hypergraph.EdgeAnnotation> > tmpMaximalProbs = new List <Problem <Hypergraph.EdgeAnnotation> >();
foreach (Problem <Hypergraph.EdgeAnnotation> singleton in singletonMapToOriginalProblems[index])
{
foreach (Problem <Hypergraph.EdgeAnnotation> problem in maximalProblems)
{
//if (baseProblem.goal == 98)
//{
// Debug.WriteLine(count++);
//}
Problem <Hypergraph.EdgeAnnotation> problemCopy = new Problem <Hypergraph.EdgeAnnotation>(problem);
// It is possible for a problem to have been created which deduced further information with an additional edge;
// that is, a given node was pushed into the path of the problem. Hence, no need to append in this situation
if (problem.givens.Contains(singleton.goal))
{
problemCopy.Append(graph, edgeDatabase, singleton);
}
tmpMaximalProbs.Add(problemCopy);
}
}
maximalProblems = tmpMaximalProbs;
}
// Add all the maximal problems to the database
foreach (Problem <Hypergraph.EdgeAnnotation> problem in maximalProblems)
{
// Determine suppression now to mitigate number of problems added
problem.DetermineSuppressedGivens(graph);
memoizedProblems.Put(problem);
}
}
//
// For all given nodes in this problem, generate all problems
//
// This is done is a convluted way to speed up execution since we need to combine in the size of the powerset of cardinality of givens
//
private void GenerateAllProblemsFromSingleEdge(ProblemHashMap <Hypergraph.EdgeAnnotation> memoizedProblems,
HyperEdgeMultiMap <Hypergraph.EdgeAnnotation> edgeDatabase,
Problem <Hypergraph.EdgeAnnotation> baseProblem)
{
// Create all simple problems by pursuing only a single path backward in the givens: append
// all problems from a given to the base problem
//
// |
// v
// given __
// | |
// v | baseProblem
// goal __|
//
// Acquire all of the problems for the singleton sets of the powerset for all of the givens of this problem
List <Problem <Hypergraph.EdgeAnnotation> >[] singletonMapToNewProblems = new List <Problem <Hypergraph.EdgeAnnotation> > [baseProblem.givens.Count];
List <Problem <Hypergraph.EdgeAnnotation> >[] singletonMapToOriginalProblems = new List <Problem <Hypergraph.EdgeAnnotation> > [baseProblem.givens.Count];
for (int g = 0; g < baseProblem.givens.Count; g++)
{
// Acquire the original problems and save them
singletonMapToOriginalProblems[g] = GenerateAllProblemsFrom(memoizedProblems, edgeDatabase, baseProblem.givens[g]);
if (singletonMapToOriginalProblems[g] == null)
{
singletonMapToOriginalProblems[g] = new List <Problem <Hypergraph.EdgeAnnotation> >();
}
// Using the original problems, append them to the base problem
singletonMapToNewProblems[g] = new List <Problem <Hypergraph.EdgeAnnotation> >();
// Append all of these given problems to the base problem
foreach (Problem <Hypergraph.EdgeAnnotation> problem in singletonMapToOriginalProblems[g])
{
Problem <Hypergraph.EdgeAnnotation> baseProblemCopy = new Problem <Hypergraph.EdgeAnnotation>(baseProblem);
baseProblemCopy.Append(graph, edgeDatabase, problem);
memoizedProblems.Put(baseProblemCopy);
singletonMapToNewProblems[g].Add(baseProblemCopy);
}
}
// If there was only 1 given, we need to perform a powerset combining
if (baseProblem.givens.Count == 1)
{
return;
}
//
// Stitch together all of the possible combinations of problems that will result;
// note this is a POWERSET construction of all possible problems; hence, note exponential explosion in number of problems
//
// | |
// | |
// v v
// g_1 g_2 ... g_n __
// | | baseProblem
// v |
// target __|
//
// | |
// | |
// v v
// g_1 g_2 ... g_n __
// | | baseProblem
// v |
// target __|
//
// | | |
// | | |
// v v v
// g_1 g_2 ... g_n __
// | | baseProblem
// v |
// target __|
//
// Acquire an encoded list of subsets: the powerset for the number of givens in this problem
List <string> powerset = Utilities.ConstructPowerSetStringsWithNoEmpty(baseProblem.givens.Count, baseProblem.givens.Count); // <-- We avoid generating singleton sets
// Maps a subset string representation (from the powerset) to the list of problems that it results in.
Dictionary <string, List <Problem <Hypergraph.EdgeAnnotation> > > powersetMapToProblems = new Dictionary <string, List <Problem <Hypergraph.EdgeAnnotation> > >(powerset.Count);
//
// For every combination of possible problems (a subset of the powerset), we combine problems
//
// Note, the Utilities generated the powerset in the specific sorted ordering of lower cardinality sets first (also values in subset are increasing)
// So a typical subset string is given by 012 or 023
foreach (string subset in powerset)
{
// Break the subset string into its constituent elements: <Arbitrary subset, singleton>
KeyValuePair <string, int> splitSubset = Utilities.SplitStringIntoKnownToProcess(subset);
// Subset Problems; given the subset {012}: {01}
List <Problem <Hypergraph.EdgeAnnotation> > subsetProblems;
if (!powersetMapToProblems.TryGetValue(splitSubset.Key, out subsetProblems))
{
// Use the singleton list; ASCII conversion of char to int
subsetProblems = singletonMapToNewProblems[Convert.ToInt32(splitSubset.Key)];
}
// Singleton tails; given the subset {012}: {2}
List <Problem <Hypergraph.EdgeAnnotation> > singletonProblems = singletonMapToOriginalProblems[splitSubset.Value];
// Combine the precomputed powerset subset (.Key) guiding the appending of the singleton (.Value) problems
List <Problem <Hypergraph.EdgeAnnotation> > combinedSubsetProblems = new List <Problem <Hypergraph.EdgeAnnotation> >();
foreach (Problem <Hypergraph.EdgeAnnotation> subsetProblem in subsetProblems)
{
foreach (Problem <Hypergraph.EdgeAnnotation> singletonProb in singletonProblems)
{
// It is possible for a problem to have been created which deduced further information with an additional edge;
// that is, a given node was pushed into the path of the problem. Hence, no need to append in this situation
if (subsetProblem.givens.Contains(singletonProb.goal))
{
// Combine the two problems and record
Problem <Hypergraph.EdgeAnnotation> subsetProblemCopy = new Problem <Hypergraph.EdgeAnnotation>(subsetProblem);
subsetProblemCopy.Append(graph, edgeDatabase, singletonProb);
memoizedProblems.Put(subsetProblemCopy);
combinedSubsetProblems.Add(subsetProblemCopy);
}
}
}
// We have calculated the problems for this subset, keep track of them
powersetMapToProblems.Add(subset, combinedSubsetProblems);
}
}
//
// Given a start node, construct a path using reachability analysis to construct a path from start template node back to leaves.
// Forward problems are generated by following forward edges in reverse
//
// A multimap of all pebbled edges (from pebbling)
public void GenerateProblemsUsingBackwardPathToLeaves(ProblemHashMap <Hypergraph.EdgeAnnotation> memoizedProblems,
HyperEdgeMultiMap <Hypergraph.EdgeAnnotation> edgeDatabase, int goalNode)
{
// Although this returns the set of problems, we can still acquire them through the ProblemHashMap
GenerateAllMaximalProblemsFrom(memoizedProblems, edgeDatabase, goalNode);
}