/// <summary>
/// <paramref name="Indices"/> splits into three lists.
/// </summary>
/// <param name="SeqUniqObjs"> The sequence of the unique objectives. </param>
/// <param name="Indices"> The indices of the <paramref name="SeqUniqObjs"/>. </param>
/// <param name="SplitValue"> A value for the splitting. </param>
/// <param name="IndexOfValue"> The index of the value in the objectives, for the split. </param>
/// <param name="LessSplitValue">
/// The indices, where the <paramref name="IndexOfValue"/> th value of the objectives is less
/// than <paramref name="SplitValue"/>.
/// </param>
/// <param name="EqualSplitValue">
/// The indices, where the <paramref name="IndexOfValue"/> th value of the objectives are
/// equal to <paramref name="SplitValue"/>.
/// </param>
/// <param name="GreaterSplitValue">
/// The indices, where the <paramref name="IndexOfValue"/> th value of the objectives is
/// greater than <paramref name="SplitValue"/>.
/// </param>
private void SplitBy(IReadOnlyList <TObj>[] SeqUniqObjs, LinkedList <int> Indices, TObj SplitValue, int IndexOfValue,
out LinkedList <int> LessSplitValue, out LinkedList <int> EqualSplitValue, out LinkedList <int> GreaterSplitValue)
{
LessSplitValue = new LinkedList <int>();
EqualSplitValue = new LinkedList <int>();
GreaterSplitValue = new LinkedList <int>();
ResComp resComp;
foreach (int index in Indices)
{
resComp = ConverterResCmp.ConvertToResCmp(_objCmp(SeqUniqObjs[index][IndexOfValue], SplitValue));
if (resComp == ResComp.LE)
{
LessSplitValue.AddLast(index);
}
else if (resComp == ResComp.EQ)
{
EqualSplitValue.AddLast(index);
}
else
{
GreaterSplitValue.AddLast(index);
}
}
}
/// <summary>
/// <para>
/// Compare <paramref name="LeftSeq"/> and <paramref name="RightSeq"/> in the
/// lexicographical order.
/// </para>
/// <para>
/// <paramref name="LeftSeq"/> is lexicographically less than
/// <paramref name="RightSeq"/>, if and only if <paramref name="LeftSeq"/>[i] <
/// <paramref name="RightSeq"/>[i], for first i in {0,1,...,len(
/// <paramref name="LeftSeq"/>)-1}, where <paramref name="LeftSeq"/>[i] != <paramref name="RightSeq"/>[i].
/// </para>
/// <para>
/// <paramref name="LeftSeq"/> is equal to <paramref name="RightSeq"/>, if and only if
/// <paramref name="LeftSeq"/>[i] == <paramref name="RightSeq"/>[i], for all i in
/// {0,1,...,len( <paramref name="LeftSeq"/>)-1}.
/// </para>
/// <para>
/// In other cases, <paramref name="LeftSeq"/> is lexicographically greater than <paramref name="RightSeq"/>.
/// </para>
/// </summary>
/// <remarks>
/// <para>
/// <paramref name="LeftSeq"/> and <paramref name="RightSeq"/> must have the same lengths.
/// </para>
/// </remarks>
/// <param name="LeftSeq"></param>
/// <param name="RightSeq"></param>
/// <returns>
/// -1, if <paramref name="LeftSeq"/> is lexicographically less than <paramref name="RightSeq"/>.
/// 0, if <paramref name="LeftSeq"/> is equal to <paramref name="RightSeq"/>,. 1, otherwise.
/// </returns>
/// <exception cref="ArgumentNullException">
/// If <paramref name="LeftSeq"/> or <paramref name="RightSeq"/> is null.
/// </exception>
/// <exception cref="ArgumentException">
/// <para>
/// If <paramref name="LeftSeq"/> and <paramref name="RightSeq"/> have no the same length.
/// </para>
/// <para> If <paramref name="LeftSeq"/> and <paramref name="RightSeq"/> are empty. </para>
/// </exception>
public int Compare(IReadOnlyList <T> LeftSeq, IReadOnlyList <T> RightSeq)
{
if (LeftSeq == null)
{
throw new ArgumentNullException(nameof(LeftSeq));
}
if (RightSeq == null)
{
throw new ArgumentNullException(nameof(RightSeq));
}
if (LeftSeq.Count != RightSeq.Count)
{
throw new ArgumentException($"{nameof(LeftSeq)} and {nameof(RightSeq)} must have the same length.");
}
else if (LeftSeq.Count == 0)
{
throw new ArgumentException($"{nameof(LeftSeq)} and {nameof(RightSeq)} are empty.");
}
int res = 0;
ResComp resComp;
for (int i = 0; i < LeftSeq.Count; i++)
{
resComp = ConverterResCmp.ConvertToResCmp(_cmp(LeftSeq[i], RightSeq[i]));
if (resComp == ResComp.LE)
{
res = -1;
break;
}
else if (resComp == ResComp.GR)
{
res = 1;
break;
}
}
return(res);
}
/// <summary>
/// Two-objective sorting. It attributes front's index to the lexicographically ordered
/// elements in the <paramref name="SeqUniqObjs"/>, with the indices in the
/// <paramref name="Indices"/>, based on the first two values of the objectives using a
/// line-sweep algorithm.
/// </summary>
/// <param name="SeqUniqObjs"> The sequence of the unique objectives. </param>
/// <param name="Fronts"> The values of the fronts. </param>
/// <param name="Indices"> The indices of the <paramref name="SeqUniqObjs"/>. </param>
private void SweepA(IReadOnlyList <TObj>[] SeqUniqObjs, int[] Fronts, LinkedList <int> Indices)
{
HashSet <int> initInd = new HashSet <int>();
LinkedList <int> indicesWhereSecondValuesLessOrEqual = new LinkedList <int>();
using (IEnumerator <int> listEnumer = Indices.GetEnumerator())
{
listEnumer.MoveNext();
initInd.Add(listEnumer.Current);
int index = 0, maxFront = -1;
ResComp resComp;
while (listEnumer.MoveNext())
{
index = listEnumer.Current;
indicesWhereSecondValuesLessOrEqual.Clear();
foreach (int initIndex in initInd)
{
resComp = ConverterResCmp.ConvertToResCmp(_objCmp(SeqUniqObjs[initIndex][1], SeqUniqObjs[index][1]));
if (resComp == ResComp.LE || resComp == ResComp.EQ)
{
indicesWhereSecondValuesLessOrEqual.AddLast(initIndex);
}
}
if (indicesWhereSecondValuesLessOrEqual.Count != 0)
{
maxFront = indicesWhereSecondValuesLessOrEqual.Max(idx => Fronts[idx]);
Fronts[index] = Math.Max(Fronts[index], maxFront + 1);
}
initInd.RemoveWhere(idx => Fronts[idx] == Fronts[index]);
initInd.Add(index);
}
}
}
/// <summary>
/// Two-objective sorting. It attributes front's index to elements in the
/// <paramref name="SeqUniqObjs"/>, with the indices in the <paramref name="AssignIndices"/>,
/// based on the first two values of the objectives, by comparing them to elements in the
/// <paramref name="SeqUniqObjs"/>, with the indices in the <paramref name="CompIndices"/>,
/// using a line-sweep algorithm.
/// </summary>
/// <param name="SeqUniqObjs"> The sequence of the unique objectives. </param>
/// <param name="Fronts"> The values of the fronts. </param>
/// <param name="CompIndices"> The indices for comparing. </param>
/// <param name="AssignIndices"> The indices for assign front. </param>
private void SweepB(IReadOnlyList <TObj>[] SeqUniqObjs, int[] Fronts, LinkedList <int> CompIndices, LinkedList <int> AssignIndices)
{
HashSet <int> initInd = new HashSet <int>();
bool isMoveNext = true;
int compIndex = 0, maxFront = -1;
TObj[] rightObjs = new TObj[2];
TObj[] leftObjs = new TObj[2];
ResComp resComp;
LinkedList <int> listIndicesWithLessOrEqValue = new LinkedList <int>();
using (IEnumerator <int> compListEnum = CompIndices.GetEnumerator())
{
isMoveNext = compListEnum.MoveNext();
foreach (int assignIndex in AssignIndices)
{
if (isMoveNext)
{
rightObjs[0] = SeqUniqObjs[assignIndex][0];
rightObjs[1] = SeqUniqObjs[assignIndex][1];
}
while (isMoveNext)
{
compIndex = compListEnum.Current;
leftObjs[0] = SeqUniqObjs[compIndex][0];
leftObjs[1] = SeqUniqObjs[compIndex][1];
resComp = ConverterResCmp.ConvertToResCmp(_lexCmp.Compare(leftObjs, rightObjs));
if (resComp == ResComp.LE || resComp == ResComp.EQ)
{
var indicesWithLessValueAndEqualFront = from index in initInd
where Fronts[index] == Fronts[compIndex] && ConverterResCmp.ConvertToResCmp(_objCmp(SeqUniqObjs[index][1], SeqUniqObjs[compIndex][1])) == ResComp.LE
select index;
if (indicesWithLessValueAndEqualFront.Count() == 0)
{
initInd.RemoveWhere(idx => Fronts[idx] == Fronts[compIndex]);
initInd.Add(compIndex);
}
isMoveNext = compListEnum.MoveNext();
}
else
{
break;
}
}
listIndicesWithLessOrEqValue.Clear();
var indicesWithLessOrEqValue = (from index in initInd
let locResComp = ConverterResCmp.ConvertToResCmp(_objCmp(SeqUniqObjs[index][1], SeqUniqObjs[assignIndex][1]))
where locResComp == ResComp.EQ || locResComp == ResComp.LE
select index);
foreach (int index in indicesWithLessOrEqValue)
{
listIndicesWithLessOrEqValue.AddLast(index);
}
if (listIndicesWithLessOrEqValue.Count != 0)
{
maxFront = listIndicesWithLessOrEqValue.Max(idx => Fronts[idx]);
Fronts[assignIndex] = Math.Max(Fronts[assignIndex], maxFront + 1);
}
}
}
}
/// <summary>
/// Recursive procedure. It attributes a front's index to all elements in the
/// <paramref name="SeqUniqObjs"/>, with the indices in the <paramref name="AssignIndices"/>,
/// for the first for the first <paramref name="CountOfObjs"/> values of the objectives, by
/// comparing them to elements in the <paramref name="SeqUniqObjs"/>, with the indices in the <paramref name="CompIndices"/>.
/// </summary>
/// <param name="SeqUniqObjs"> The sequence of the unique objectives. </param>
/// <param name="Fronts"> The values of the fronts. </param>
/// <param name="CompIndices"> The indices for comparing. </param>
/// <param name="AssignIndices"> The indices for assign front. </param>
/// <param name="CountOfObjs">
/// The number of the values from the objectives, for the sorting.
/// </param>
private void NdHelperB(IReadOnlyList <TObj>[] SeqUniqObjs, int[] Fronts, LinkedList <int> CompIndices, LinkedList <int> AssignIndices, int CountOfObjs)
{
if (CompIndices.Count == 0 || AssignIndices.Count == 0)
{
return;
}
else if (CompIndices.Count == 1 || AssignIndices.Count == 1)
{
foreach (int assignIndex in AssignIndices)
{
var hv = SeqUniqObjs[assignIndex].Take(CountOfObjs);
foreach (int compIndex in CompIndices)
{
var lv = SeqUniqObjs[compIndex].Take(CountOfObjs);
if (Stools.IsDominate(lv, hv, _objCmp) || lv.CmpSeqEqual(hv, _objCmp))
{
Fronts[assignIndex] = Math.Max(Fronts[assignIndex], Fronts[compIndex] + 1);
}
}
}
}
else if (CountOfObjs == 2)
{
SweepB(SeqUniqObjs, Fronts, CompIndices, AssignIndices);
}
else
{
var uniqValuesObjFromCompIndices = (from index in CompIndices
select SeqUniqObjs[index][CountOfObjs - 1]).Distinct();
var uniqValuesObjFromAssignIndices = (from index in AssignIndices
select SeqUniqObjs[index][CountOfObjs - 1]).Distinct();
TObj minUniqValueObjFromCompIndices, maxUniqValueObjFromCompIndices;
TObj minUniqValueObjFromAssignIndices, maxUniqValueObjFromAssignIndices;
uniqValuesObjFromAssignIndices.MinMax(out minUniqValueObjFromAssignIndices, out maxUniqValueObjFromAssignIndices, _objCmp);
uniqValuesObjFromCompIndices.MinMax(out minUniqValueObjFromCompIndices, out maxUniqValueObjFromCompIndices, _objCmp);
ResComp resComp;
resComp = ConverterResCmp.ConvertToResCmp(_objCmp(maxUniqValueObjFromCompIndices, minUniqValueObjFromAssignIndices));
if (resComp == ResComp.LE || resComp == ResComp.EQ)
{
NdHelperB(SeqUniqObjs, Fronts, CompIndices, AssignIndices, CountOfObjs - 1);
}
else
{
resComp = ConverterResCmp.ConvertToResCmp(_objCmp(minUniqValueObjFromCompIndices, maxUniqValueObjFromAssignIndices));
if (resComp == ResComp.LE || resComp == ResComp.EQ)
{
TObj median = Stools.FindLowMedian(uniqValuesObjFromAssignIndices.Union(uniqValuesObjFromCompIndices).ToArray(), _objCmp);
LinkedList <int> lessMedian1, equalMedian1, greaterMedian1, lessMedian2, equalMedian2, greaterMedian2;
SplitBy(SeqUniqObjs, CompIndices, median, CountOfObjs - 1, out lessMedian1, out equalMedian1, out greaterMedian1);
SplitBy(SeqUniqObjs, AssignIndices, median, CountOfObjs - 1, out lessMedian2, out equalMedian2, out greaterMedian2);
LinkedList <int> lessAndEqualMedian1 = MergeLists(lessMedian1, equalMedian1);
NdHelperB(SeqUniqObjs, Fronts, lessMedian1, lessMedian2, CountOfObjs);
NdHelperB(SeqUniqObjs, Fronts, lessMedian1, equalMedian2, CountOfObjs - 1);
NdHelperB(SeqUniqObjs, Fronts, equalMedian1, equalMedian2, CountOfObjs - 1);
NdHelperB(SeqUniqObjs, Fronts, lessAndEqualMedian1, greaterMedian2, CountOfObjs - 1);
NdHelperB(SeqUniqObjs, Fronts, greaterMedian1, greaterMedian2, CountOfObjs);
}
}
}
}