/**
* Creates the backtrace table. This is magic. The basic idea is that the penalty table contains a set of penalty
* values based on some strategically selected numbers. I'm not quite sure what they are, but they help determine
* the backtrace table values. The backtrace table contains information used to help determine if words matched
* (OK), were inserted (INSERTION), substituted (SUBSTITUTION), or deleted (DELETION).
*
* @param referenceItems the ordered list of reference words
* @param hypothesisItems the ordered list of hypothesis words
* @return the backtrace table
*/
int[,] CreateBacktraceTable <T>(LinkedList <T> referenceItems, LinkedList <T> hypothesisItems, IComparator comparator)
{
int[,] penaltyTable;
int[,] backtraceTable;
int penalty;
int minPenalty;
penaltyTable = new int[referenceItems.Count + 1, hypothesisItems.Count + 1];
backtraceTable = new int[referenceItems.Count + 1, hypothesisItems.Count + 1];
// Initialize the penaltyTable and the backtraceTable. The
// rows of each table represent the words in the reference
// string. The columns of each table represent the words in
// the hypothesis string.
//
penaltyTable[0, 0] = 0;
backtraceTable[0, 0] = Ok;
// The lower left of the tables represent deletions. If you
// think about this, a shorter hypothesis string will have
// deleted words from the reference string.
//
for (var i = 1; i <= referenceItems.Count; i++)
{
penaltyTable[i, 0] = DeletionPenalty * i;
backtraceTable[i, 0] = Deletion;
}
// The upper right of the tables represent insertions. If
// you think about this, a longer hypothesis string will have
// inserted words.
//
for (var j = 1; j <= hypothesisItems.Count; j++)
{
penaltyTable[0, j] = InsertionPenalty * j;
backtraceTable[0, j] = Insertion;
}
// Row-by-row, column-by-column, fill out the tables.
// The goal is to keep the penalty for each cell to a
// minimum.
//
for (var i = 1; i <= referenceItems.Count; i++)
{
for (var j = 1; j <= hypothesisItems.Count; j++)
{
minPenalty = MaxPenalty;
// First assume that this represents a deletion.
//
penalty = penaltyTable[i - 1, j] + DeletionPenalty;
if (penalty < minPenalty)
{
minPenalty = penalty;
penaltyTable[i, j] = penalty;
backtraceTable[i, j] = Deletion;
}
// If the words match, we'll assume it's OK.
// Otherwise, we assume we have a substitution.
//
if (comparator.IsSimilar(referenceItems.ElementAt(i - 1), (hypothesisItems.ElementAt(j - 1))))
{
penalty = penaltyTable[i - 1, j - 1];
if (penalty < minPenalty)
{
minPenalty = penalty;
penaltyTable[i, j] = penalty;
backtraceTable[i, j] = Ok;
}
}
else
{
penalty = penaltyTable[i - 1, j - 1] + SubstitutionPenalty;
if (penalty < minPenalty)
{
minPenalty = penalty;
penaltyTable[i, j] = penalty;
backtraceTable[i, j] = Substitution;
}
}
// If you've made it this far, it should be obvious I
// have no idea what the heck this code is doing. I'm
// just doing a transliteration.
//
penalty = penaltyTable[i, j - 1] + InsertionPenalty;
if (penalty < minPenalty)
{
minPenalty = penalty;
penaltyTable[i, j] = penalty;
backtraceTable[i, j] = Insertion;
}
}
}
return(backtraceTable);
}