/// <summary>
/// Graph consists of only one part
/// </summary>
/// <param name="dynamic"></param>
/// <param name="graph"></param>
private static void SolveSinglePart(ResultPair[] dynamic, int[] graph)
{
int last = graph.Length - 1;
bool wasReverted = false;
List<bool> labeling = new List<bool>();
int count = 0;
if (graph[0] == 2 && graph[last] == 2)
{//only egos 2
int i = 0;
ChooseEverySecondTwo(graph, labeling, ref count, ref i, 0);
if (labeling.Count != graph.Length)
{
labeling.Add(true);
count++;
}
dynamic[last] = new ResultPair
{
Optimum = count,
Labeling = labeling,
Ending = Ending.DoubleTwo,
};
return;
}
if (graph[last] == 2)
{//two only at the end => reverse and so two at the beginning
graph = graph.Reverse().ToArray();
wasReverted = true;
}
if (graph[0] == 2)
{//2 at the beginning, maybe reversed
int i = 0;
ChooseEverySecondTwo(graph, labeling, ref count, ref i, 0);
if (graph.Length - labeling.Count > 1)
labeling.Add(!labeling.Last());
//choose last one
if (labeling.LastOrDefault())
labeling.Add(false);
else
{
labeling.Add(true);
count++;
}
if (wasReverted)
{
graph = graph.Reverse().ToArray();
labeling.Reverse();
}
dynamic[last] = new ResultPair
{
Optimum = count,
Labeling = labeling,
Ending = Ending.SingleTwo,
};
return;
}
//start and ends with ego 1
//length of the graph is odd => starter 12 at the beginning (e.g.)
if (graph.Length % 2 == 1)
{
labeling.Add(true);
labeling.Add(true);
count = 2;
int i = 2;
ChooseEverySecondTwo(graph, labeling, ref count, ref i, 1);
//choose last one
if (labeling.LastOrDefault())
labeling.Add(false);
else
{
labeling.Add(true);
count++;
}
dynamic[last] = new ResultPair
{
Optimum = count,
Labeling = labeling,
Ending = Ending.SingleTwo,
};
return;
}
//legth of the graph is even => starter first 22, legth is at least 4 (or 11 => not possible)
labeling.Add(false);
labeling.Add(true);
labeling.Add(true);
count = 2;
int j = 3;
ChooseEverySecondTwo(graph, labeling, ref count, ref j, 0);//choose last one
if (labeling.LastOrDefault())
labeling.Add(false);
else
{
labeling.Add(true);
count++;
}
dynamic[last] = new ResultPair
{
Optimum = count,
Labeling = labeling,
Ending = Ending.SingleTwo,
};
}
/// <summary>
/// Solve a middle part (start and ends with one, part before exists and is solved)
/// </summary>
/// <param name="dynamic"></param>
/// <param name="graph"></param>
/// <param name="l"></param>
private static void SolveMiddlePart(ResultPair[] dynamic, int[] graph, int l)
{
ResultPair lastEnd = dynamic[l];
if (lastEnd.Ending == Ending.TwoOne)
{//last chosen is 1
//starter 12, 1 is already chosen
List<bool> labeling = new List<bool>();
int count = 0;
int i = l + 1;
ChooseEverySecondTwo(graph, labeling, ref count, ref i, 1);
SetDynamic(dynamic, i, l, count, labeling, i == l + 1 ? Ending.TwoOneTwo : Ending.SingleTwo);
//starter 22
i = l + 1;
while (graph[i] == 2 && graph[i + 1] == 2)
{
labeling = new List<bool>();
labeling.Add(true);
labeling.Add(true);
count = 2;
ChooseEverySecondTwoDown(labeling, ref count, i -1,l,2-i);
int j = i + 2;
ChooseEverySecondTwo(graph, labeling, ref count, ref j, 1 - i);
SetDynamic(dynamic, j, l, count, labeling,j == i + 1 ? Ending.DoubleTwo : Ending.SingleTwo);
i++;
}
//starter 21
i = l + 1;
while (graph[i] != 2 || graph[i + 1] != 1)
{
i++;
}
labeling = new List<bool>();
labeling.Add(true);
labeling.Add(true);
count = 2;
ChooseEverySecondTwoDown(labeling, ref count, i - 1, l + 1, 2 - i);
SetDynamic(dynamic, i + 1, l, count, labeling, Ending.TwoOne);
}//Ending.TwoOne
else
{
//starter 12
int i = l + 1;
List<bool> labeling = new List<bool>();
int count = 1;
if (graph[i] == 2)
{
i++;
labeling.Add(false);
}
//nyní graph[i] == 1
labeling.Add(true);
int onePosition = i;
i++;
ChooseEverySecondTwo(graph, labeling, ref count, ref i, 1 - onePosition);
SetDynamic(dynamic, i,l,count,labeling,i == onePosition + 1
? (onePosition == l + 1 ? Ending.TwoOneTwo : Ending.OneTwo)
: Ending.SingleTwo);
//starter 22
i = l + 1;
bool twoBeforeOne = false;
if (graph[i] == 2)
{
twoBeforeOne = true;
i++;
}
i++;
bool makeGap = false;
if (lastEnd.Ending == Ending.DoubleTwo ||
lastEnd.Ending == Ending.TwoOneTwo)
{//make a gap 21 if it is possible
makeGap = true;
}
while (graph[i] == 2 && graph[i + 1] == 2)
{
labeling = new List<bool>();
labeling.Add(true);
labeling.Add(true);
count = 2;
ChooseEverySecondTwoDown(labeling, ref count, i - 1, onePosition + 1, 2 - i);
labeling.Reverse();
//ćonnect to the previous part
if (twoBeforeOne)
{
if (!makeGap)
{
labeling.Add(true);
count++;
labeling.Add(false);
}
else
{
if (!labeling.Last())
{
labeling[labeling.Count - 1] = true;
count++;
}
labeling.Add(false);
labeling.Add(false);
}
}
else
{
if (i == onePosition + 2)
{
labeling.Add(false);
}
else
{
if (!labeling.Last())
{
labeling[labeling.Count - 1] = true;
count++;
}
labeling.Add(false);
}
}
labeling.Reverse();
int j = i + 2;
ChooseEverySecondTwo(graph, labeling, ref count, ref j, 1 - i);
SetDynamic(dynamic, j, l, count, labeling, j == i + 1 ? Ending.DoubleTwo : Ending.SingleTwo);
i++;
}
//starter 21
i = l + 1;
if (twoBeforeOne)
i++;
i++;
while (graph[i] != 2 || graph[i + 1] != 1)
{
i++;
}
labeling = new List<bool>();
labeling.Add(true);
labeling.Add(true);
count = 2;
ChooseEverySecondTwoDown(labeling, ref count, i - 1, onePosition + 1, 2 - i);
labeling.Reverse();
//connect to the previous part
if (twoBeforeOne)
{
if (!makeGap)
{
labeling.Add(true);
count++;
labeling.Add(false);
}
else
{
if (!labeling.Last())
{
labeling[labeling.Count - 1] = true;
count++;
}
labeling.Add(false);
labeling.Add(false);
}
}
else
{
if (i == onePosition + 2)
{//want to make a gap 12, so must create 212 and solve the next part
if (i + 2 < graph.Length)
{
bool[] helpLabeling = new bool[labeling.Count];
labeling.CopyTo(helpLabeling);
List<bool> innerLabeling = helpLabeling.ToList();
innerLabeling.Add(false);
innerLabeling.Reverse();
innerLabeling.Add(true);
int innerCount = count + 1;
int m = i + 3;
ChooseEverySecondTwo(graph, innerLabeling, ref innerCount, ref m, i + 2);
SetDynamic(dynamic, m, l, innerCount, innerLabeling,
m == i + 2 ? Ending.TwoOneTwo : Ending.SingleTwo);
}
}
//try also not prolonged version
if (!labeling.Last())
{
labeling[labeling.Count - 1] = true;
count++;
}
labeling.Add(false);
}
labeling.Reverse();
SetDynamic(dynamic, i + 1, l, count, labeling, Ending.TwoOne);
}
}
/// <summary>
/// Solve one part, it is not single or first part
/// </summary>
/// <param name="dynamic"></param>
/// <param name="graph"></param>
/// <param name="l"></param>
private static void SolveOnePart(ResultPair[] dynamic, int[] graph, int l)
{
if (IsEnd(dynamic[l].Ending, graph, l))
SolveEndPart(dynamic, graph, l);
else
SolveMiddlePart(dynamic, graph, l);
}
private static void SolveFirstPart(int[] graph, ResultPair[] dynamic)
{
int i = 0;
if (graph[0] == 2)
{
int count = 0;
List<bool> labeling = new List<bool>();
ChooseEverySecondTwo(graph, labeling, ref count, ref i, 0);
dynamic[i] = new ResultPair
{
Optimum = count,
Labeling = labeling,
Ending = i == 0 ? Ending.DoubleTwo : Ending.SingleTwo
};
}
else
{//unchosen one at the beginning
//starter 12
int count = 2;
i = 2;
List<bool> labeling = new List<bool>();
labeling.Add(true);
labeling.Add(true);
ChooseEverySecondTwo(graph, labeling, ref count, ref i, 1);
if (dynamic[i] == null || dynamic[i].Optimum > count)
dynamic[i] = new ResultPair
{
Optimum = count,
Labeling = labeling,
Ending = i == 1 ? Ending.OneTwo : Ending.SingleTwo,
};
//starters 22
i = 1;
while (i < graph.Length && graph[i] == 2 && graph[i + 1] == 2)
{
labeling = new List<bool>();
count = 2;
labeling.Add(true);
labeling.Add(true);
ChooseEverySecondTwoDown(labeling, ref count, i - 1, 0, 2 - i);
int j = i + 2;
ChooseEverySecondTwo(graph, labeling, ref count, ref j, 1 - i);
if (dynamic[j] == null || dynamic[j].Optimum > count)
dynamic[j] = new ResultPair
{
Optimum = count,
Labeling = labeling,
Ending = j == i + 1 ? Ending.DoubleTwo : Ending.SingleTwo,
};
i++;
}
//starter 21
i = 1;
while (graph[i] != 2 || graph[i + 1] != 1)
{
i++;
}
labeling = new List<bool>();
labeling.Add(true);
labeling.Add(true);
count = 2;
ChooseEverySecondTwoDown(labeling, ref count, i - 1, 0, 2 - i);
if (dynamic[i + 1] == null || dynamic[i + 1].Optimum > count)
dynamic[i + 1] = new ResultPair
{
Optimum = count,
Labeling = labeling,
Ending = Ending.TwoOne,
};
}
}
private static void SolveEndPart(ResultPair[] dynamic, int[] graph, int l)
{
if (l == graph.Length - 1)
return;
ResultPair lastEnd = dynamic[l];
int i = 0;
int count = 0;
List<bool> labeling = new List<bool>();
if (graph[graph.Length - 1] == 2)
{
if (lastEnd.Ending == Ending.TwoOne)
{
i = graph.Length - 1;
labeling = new List<bool>();
labeling.Add(true);
count = 1;
ChooseEverySecondTwoDown(labeling, ref count, i - 1, l + 1, 2 - i);
SetDynamic(dynamic, i, l, count, labeling, Ending.SingleTwo);
i++;
}
//starter last 2
count = 1;
labeling = new List<bool>();
labeling.Add(true);
bool twoBeforeOne = false;
i = l + 1;
if (graph[i] == 2)
{
twoBeforeOne = true;
i++;
}
int onePosition = i;
i = graph.Length - 1;
bool makeGap = false;
if (lastEnd.Ending == Ending.DoubleTwo ||
lastEnd.Ending == Ending.TwoOneTwo)
{//make a gap 21 if it is possible
makeGap = true;
}
ChooseEverySecondTwoDown(labeling, ref count, i - 1, onePosition + 1, 2 - i);
labeling.Reverse();
//connect to the previous part
//maybe make a gap 21
if (twoBeforeOne)
{
if (!makeGap)
{
labeling.Add(true);
count++;
labeling.Add(false);
}
else
{
if (!labeling.Last())
{
labeling[labeling.Count - 1] = true;
count++;
}
labeling.Add(false);
labeling.Add(false);
}
}
else
{
if (i == onePosition + 2)
{
labeling.Add(false);
}
else
{
if (!labeling.Last())
{
labeling[labeling.Count - 1] = true;
count++;
}
labeling.Add(false);
}
}
labeling.Reverse();
SetDynamic(dynamic, i, l, count, labeling, Ending.DoubleTwo);
return;
}
SolveMiddlePart(dynamic, graph, l);
//if there is 1 at the end, it is solved by standart method and finished here
if (graph[graph.Length - 3] == 1)
{//the last part ..121, already started
if (dynamic[graph.Length - 1] == null || dynamic[graph.Length - 1].Optimum > dynamic[graph.Length - 2].Optimum)
{//if the starter is 12 => last 1 is not chosen, propagate value only
labeling = new List<bool>();
labeling.Add(false);
dynamic[graph.Length - 1] = new ResultPair
{
Optimum = dynamic[graph.Length - 2].Optimum,
Labeling = dynamic[graph.Length - 2].Labeling.Concat(labeling).ToList(),
Ending = Ending.SingleTwo,//nonsens - technical only
};
}
return;
}
// last part, at least two 2 (..221)
if (dynamic[graph.Length - 3] != null)
{
if (dynamic[graph.Length - 1] == null || dynamic[graph.Length - 1].Optimum > dynamic[graph.Length - 3].Optimum + 1)
{
labeling = new List<bool>();
labeling.Add(false);
labeling.Add(true);
dynamic[graph.Length - 1] = new ResultPair
{
Optimum = dynamic[graph.Length - 3].Optimum + 1,
Labeling = dynamic[graph.Length - 3].Labeling.Concat(labeling).ToList(),
Ending = Ending.SingleTwo,//nonsens - technical only
};
}
}
if (dynamic[graph.Length - 2] != null)
{
if (dynamic[graph.Length - 1] == null || dynamic[graph.Length - 1].Optimum > dynamic[graph.Length - 2].Optimum)
{
labeling = new List<bool>();
labeling.Add(false);
dynamic[graph.Length - 1] = new ResultPair
{
Optimum = dynamic[graph.Length - 3].Optimum,
Labeling = dynamic[graph.Length - 3].Labeling.Concat(labeling).ToList(),
Ending = Ending.SingleTwo,//nonsens - technical only
};
}
}
}
private static void SetDynamic(ResultPair[] dynamic, int i, int l, int count, List<bool> labeling, Ending ending)
{
if (dynamic[i] == null || dynamic[i].Optimum > count + dynamic[l].Optimum ||
(dynamic[i].Optimum == count + dynamic[l].Optimum && IsStrong(ending)))
dynamic[i] = new ResultPair
{
Optimum = count + dynamic[l].Optimum,
Labeling = dynamic[l].Labeling.Concat(labeling).ToList(),
Ending = ending,
};
}
private static bool[] GetResultFromDynamic(ResultPair[] dynamic)
{
return dynamic[dynamic.Length - 1].Labeling.ToArray();
}
/// <summary>
/// Solve one graph with egos one or two, no consecutive ones
/// </summary>
/// <param name="graph"></param>
/// <returns></returns>
private static bool[] GetOptimalLabeling(int[] graph)
{
ResultPair[] dynamic = new ResultPair[graph.Length];
if (IsEnd(Ending.TwoOne, graph, 0))
{
SolveSinglePart(dynamic, graph);
return GetResultFromDynamic(dynamic);
}
SolveFirstPart(graph, dynamic);
//main loop of dynamic programming
for (int l = 0; l < dynamic.Length; l++)
{
if (dynamic[l] != null)
{
SolveOnePart(dynamic, graph, l);
// for testing only
for (int j = l; j < dynamic.Length; j++)
{
if (dynamic[j] != null && dynamic[j].Labeling.Count != j + 1)
{
throw new InvalidOperationException("nesprávně dlouhé labeling");
}
}
}
}
return GetResultFromDynamic(dynamic);
}
