//
// Given the problems with at least one assumption, construct ALL such combinations to form (I, G).
//
private void CalculateKnonStrictCardinalities(GeometryTutorLib.ProblemAnalyzer.InterestingProblemCalculator interestingCalculator,
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > problems,
StatisticsGenerator.ProofProblemFigureStatisticsAggregator figureStats)
{
// K-G container: index 0 is 1-G, index 1 is 2-G, etc.
List <List <GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > > KmgProblems = new List <List <GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > >();
//
// Create the new set of multigoal problems each with 1 goal: 1-G
//
List <GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > mgProblems = new List <GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation> >();
foreach (GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> problem in problems)
{
GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation> new1GProblem = new GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation>();
new1GProblem.AddProblem(problem);
mgProblems.Add(new1GProblem);
}
// Add the 1-G problems to the K-G problem set.
KmgProblems.Add(mgProblems);
// Construct all of the remaining
CalculateKnonStrictCardinalities(KmgProblems, problems, ProofProblemFigureStatisticsAggregator.MAX_K);
//
// Now that we have 1, 2, ..., MAX_K -G multigoal problems, we must filter them.
// That is, are the problems strictly interesting?
//
// Filtered K-G container: index 0 is 1-G, index 1 is 2-G, etc.
List <List <GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > > filteredKmgProblems = new List <List <GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > >();
foreach (List <GeometryTutorLib.ProblemAnalyzer.MultiGoalProblem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > originalKgProblems in KmgProblems)
{
filteredKmgProblems.Add(interestingCalculator.DetermineStrictlyInterestingMultiGoalProblems(originalKgProblems));
}
// Calculate the final numbers: counts of the k-G Strictly interesting problems.
StringBuilder str = new StringBuilder();
for (int k = 1; k <= ProofProblemFigureStatisticsAggregator.MAX_K; k++)
{
figureStats.kGcardinalities[k] = filteredKmgProblems[k - 1].Count;
str.AppendLine(k + "-G: " + figureStats.kGcardinalities[k]);
}
Debug.WriteLine(str);
if (GeometryTutorLib.Utilities.PROBLEM_GEN_DEBUG)
{
Debug.WriteLine(str);
}
}
// Returns: <number of interesting problems, number of original problems generated>
public ProofProblemFigureStatisticsAggregator AnalyzeFigure()
{
ProofProblemFigureStatisticsAggregator figureStats = new ProofProblemFigureStatisticsAggregator();
// For statistical analysis, count the number of each particular type of implicit facts.
CountIntrisicProperties(figureStats);
// Start timing
figureStats.stopwatch.Start();
// Precompute all coordinate-based interesting relations (problem goal nodes)
// These become the basis for the template-based problem generation (these are the goals)
Precompute();
// Handle givens that strengthen the intrinsic parts of the figure; modifies if needed
givens = DoGivensStrengthenFigure();
// Use a worklist technique to instantiate nodes to construct the hypergraph for this figure
ConstructHypergraph();
// Create the integer-based hypergraph representation
ConstructPebblingHypergraph();
// Pebble that hypergraph
Pebble();
// Analyze paths in the hypergraph to generate the pair of <forward problems, backward problems> (precomputed nodes are goals)
KeyValuePair<List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>>,
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>>> problems = GenerateTemplateProblems();
// Combine the problems together into one list
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>> candidateProbs = new List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>>();
candidateProbs.AddRange(problems.Key);
//candidateProbs.AddRange(problems.Value); // converse
figureStats.totalBackwardProblemsGenerated = problems.Value.Count;
figureStats.totalProblemsGenerated = candidateProbs.Count;
// Determine which, if any, of the problems are interesting (using definition that 100% of the givens are used)
interestingCalculator = new GeometryTutorLib.ProblemAnalyzer.InterestingProblemCalculator(graph, figure, givens, goals);
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>> interestingProblems = interestingCalculator.DetermineInterestingProblems(candidateProbs);
figureStats.totalInterestingProblems = interestingProblems.Count;
// Explicit number of facts: hypergraph size - figure facts
figureStats.totalExplicitFacts = graph.vertices.Count - figure.Count;
// Validate that the original book problems were generated.
Validate(interestingProblems, figureStats);
// Stop timing before we generate all of the statistics
figureStats.stopwatch.Stop();
List<GeometryTutorLib.ProblemAnalyzer.Problem<GeometryTutorLib.Hypergraph.EdgeAnnotation>> strictlyInteresting = GetStrictlyInteresting(interestingProblems);
// Construct partitions based on different queries
// GenerateStatistics(interestingProblems, figureStats, strictlyInteresting);
//
// Is this figure complete? That is, do the assumptions define the figure completely?
//
figureStats.isComplete = templateProblemGenerator.DefinesFigure(precomputer.GetPrecomputedRelations(), precomputer.GetStrengthenedClauses());
// Debug.WriteLine("Explicit Complete: " + figureStats.isComplete);
// Construct the K-goal problems
// CalculateKnonStrictCardinalities(interestingCalculator, interestingProblems, figureStats);
return figureStats;
}
// Returns: <number of interesting problems, number of original problems generated>
public ProofProblemFigureStatisticsAggregator AnalyzeFigure()
{
ProofProblemFigureStatisticsAggregator figureStats = new ProofProblemFigureStatisticsAggregator();
// For statistical analysis, count the number of each particular type of implicit facts.
CountIntrisicProperties(figureStats);
// Start timing
figureStats.stopwatch.Start();
// Precompute all coordinate-based interesting relations (problem goal nodes)
// These become the basis for the template-based problem generation (these are the goals)
Precompute();
// Handle givens that strengthen the intrinsic parts of the figure; modifies if needed
givens = DoGivensStrengthenFigure();
// Use a worklist technique to instantiate nodes to construct the hypergraph for this figure
ConstructHypergraph();
// Create the integer-based hypergraph representation
ConstructPebblingHypergraph();
// Pebble that hypergraph
Pebble();
// Analyze paths in the hypergraph to generate the pair of <forward problems, backward problems> (precomputed nodes are goals)
KeyValuePair <List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> >,
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > > problems = GenerateTemplateProblems();
// Combine the problems together into one list
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > candidateProbs = new List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> >();
candidateProbs.AddRange(problems.Key);
//candidateProbs.AddRange(problems.Value); // converse
figureStats.totalBackwardProblemsGenerated = problems.Value.Count;
figureStats.totalProblemsGenerated = candidateProbs.Count;
// Determine which, if any, of the problems are interesting (using definition that 100% of the givens are used)
interestingCalculator = new GeometryTutorLib.ProblemAnalyzer.InterestingProblemCalculator(graph, figure, givens, goals);
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > interestingProblems = interestingCalculator.DetermineInterestingProblems(candidateProbs);
figureStats.totalInterestingProblems = interestingProblems.Count;
// Explicit number of facts: hypergraph size - figure facts
figureStats.totalExplicitFacts = graph.vertices.Count - figure.Count;
// Validate that the original book problems were generated.
Validate(interestingProblems, figureStats);
// Stop timing before we generate all of the statistics
figureStats.stopwatch.Stop();
List <GeometryTutorLib.ProblemAnalyzer.Problem <GeometryTutorLib.Hypergraph.EdgeAnnotation> > strictlyInteresting = GetStrictlyInteresting(interestingProblems);
// Construct partitions based on different queries
// GenerateStatistics(interestingProblems, figureStats, strictlyInteresting);
//
// Is this figure complete? That is, do the assumptions define the figure completely?
//
figureStats.isComplete = templateProblemGenerator.DefinesFigure(precomputer.GetPrecomputedRelations(), precomputer.GetStrengthenedClauses());
// Debug.WriteLine("Explicit Complete: " + figureStats.isComplete);
// Construct the K-goal problems
// CalculateKnonStrictCardinalities(interestingCalculator, interestingProblems, figureStats);
return(figureStats);
}
