/// <summary>
/// Построение дерева штейнера алгоритмом Краскала
/// </summary>
/// <param name="points"> Опорные точки для построения </param>
/// <returns> Список рёбер дерева </returns>
public static dynamic Solve(List <T> points)
{
if (points.Count < 2)
{
return(null);
}
var pairs = new List <Tuple <Tuple <T, T>, double> >();
// составляем пары вершин
for (int i = 0; i < points.Count; i++)
{
for (int j = i + 1; j < points.Count; j++)
{
pairs.Add(new Tuple <Tuple <T, T>, double>(new Tuple <T, T>(points[i], points[j]), Dist.GetOrthogonalDist(points[i], points[j])));
}
}
// упорядочиваем пары вершин по длинам рёбер
pairs.Sort((t1, t2) => t1.Item2.CompareTo(t2.Item2));
var road = new List <Tuple <Tuple <T, T>, double> >();
double[,] matr = new double[points.Count, points.Count];
int[] parity = new int[points.Count];
for (int i = 0; i < pairs.Count; i++)
{
if (road.Count < 2)
{
int vert_1_ind = points.IndexOf(pairs[i].Item1.Item1);
int vert_2_ind = points.IndexOf(pairs[i].Item1.Item2);
road.Add(pairs[i]);
parity[vert_1_ind]++;
parity[vert_2_ind]++;
matr[vert_1_ind, vert_2_ind] = matr[vert_2_ind, vert_1_ind] = pairs[i].Item2;
}
// проверка на цикличность
else
{
int vert_1_ind = points.IndexOf(pairs[i].Item1.Item1);
int vert_2_ind = points.IndexOf(pairs[i].Item1.Item2);
parity[vert_1_ind]++;
parity[vert_2_ind]++;
matr[vert_1_ind, vert_2_ind] = matr[vert_2_ind, vert_1_ind] = pairs[i].Item2;
// проверка на наличие цикла
if (CyclesSearch(matr).Count > 0)
{
parity[vert_1_ind]--;
parity[vert_2_ind]--;
matr[vert_1_ind, vert_2_ind] = matr[vert_2_ind, vert_1_ind] = 0;
}
else
{
road.Add(pairs[i]);
}
}
// проверка на связность графа
bool[] visited = new bool[points.Count];
WidthSearch(points.IndexOf(pairs[0].Item1.Item1), matr, ref visited);
if (parity.ToList().IndexOf(0) == -1 && visited.ToList().IndexOf(false) == -1)
{
break;
}
}
var new_road = new List <Tuple <T, T> >();
for (int i = 0; i < road.Count; i++)
{
new_road.Add(new Tuple <T, T>
(new Point2D(road[i].Item1.Item1.X, road[i].Item1.Item1.Y) as T, new Point2D(road[i].Item1.Item1.X, road[i].Item1.Item2.Y) as T));
new_road.Add(new Tuple <T, T>
(new Point2D(road[i].Item1.Item1.X, road[i].Item1.Item2.Y) as T, new Point2D(road[i].Item1.Item2.X, road[i].Item1.Item2.Y) as T));
}
// вырожденный случай, когда все точки находятся на одной линии
if (points.FindAll(p => p.X == points[0].X).Count == points.Count ||
points.FindAll(p => p.Y == points[0].Y).Count == points.Count)
{
return(new_road);
}
for (int i = 0; i < new_road.Count; i++)
{
int ind_x = new_road.FindIndex(t => (!t.Item1.Equals(new_road[i].Item1) && !t.Item2.Equals(new_road[i].Item2)) &&
(t.Item1.Y == new_road[i].Item1.Y) && (t.Item2.Y == new_road[i].Item2.Y) && (t.Item1.Y == new_road[i].Item2.Y));
if (ind_x > -1)
{
if ((new_road[ind_x].Item1.X == new_road[i].Item1.X) &&
(new_road[ind_x].Item1.X <= new_road[i].Item2.X) &&
(new_road[ind_x].Item2.X <= new_road[i].Item2.X))
{
new_road[i] = new Tuple <T, T>
(new Point2D(new_road[ind_x].Item2.X, new_road[ind_x].Item2.Y) as T, new Point2D(new_road[i].Item2.X, new_road[i].Item2.Y) as T);
}
else if ((new_road[ind_x].Item2.X == new_road[i].Item2.X) &&
(new_road[ind_x].Item1.X <= new_road[i].Item2.X) &&
(new_road[ind_x].Item1.X <= new_road[i].Item1.X))
{
new_road[i] = new Tuple <T, T>
(new Point2D(new_road[ind_x].Item1.X, new_road[ind_x].Item1.Y) as T, new Point2D(new_road[i].Item2.X, new_road[i].Item2.Y) as T);
}
}
else
{
int ind_y = new_road.FindIndex(t => (!t.Item1.Equals(new_road[i].Item1) && !t.Item2.Equals(new_road[i].Item2)) &&
(t.Item1.X == new_road[i].Item1.X) && (t.Item2.X == new_road[i].Item2.X) && (t.Item1.X == new_road[i].Item2.X));
if (ind_y > -1)
{
if ((new_road[ind_y].Item1.Y == new_road[i].Item1.Y) &&
(new_road[ind_y].Item1.Y <= new_road[i].Item2.Y) &&
(new_road[ind_y].Item2.Y <= new_road[i].Item2.Y))
{
new_road[i] = new Tuple <T, T>
(new Point2D(new_road[ind_y].Item2.X, new_road[ind_y].Item2.Y) as T, new Point2D(new_road[i].Item2.X, new_road[i].Item2.Y) as T);
}
else if ((new_road[ind_y].Item2.Y == new_road[i].Item2.Y) &&
(new_road[ind_y].Item1.Y <= new_road[i].Item2.Y) &&
(new_road[ind_y].Item1.Y <= new_road[i].Item1.Y))
{
new_road[i] = new Tuple <T, T>
(new Point2D(new_road[ind_y].Item1.X, new_road[ind_y].Item1.Y) as T, new Point2D(new_road[i].Item2.X, new_road[i].Item2.Y) as T);
}
}
}
}
// разделяем все рёбра на линии, лежащие на одной оси
var solution = new List <Tuple <T, T> >();
for (int i = 0; i < new_road.Count; i++)
{
if ((new_road[i].Item1.X == new_road[i].Item2.X) || (new_road[i].Item1.Y == new_road[i].Item2.Y))
{
solution.Add(new_road[i]);
}
else
{
solution.Add(new Tuple <T, T>(
new Point2D(new_road[i].Item1.X, new_road[i].Item1.Y) as T,
new Point2D(new_road[i].Item1.X, new_road[i].Item2.Y) as T));
solution.Add(new Tuple <T, T>(
new Point2D(new_road[i].Item1.X, new_road[i].Item2.Y) as T,
new Point2D(new_road[i].Item2.X, new_road[i].Item2.Y) as T));
}
}
// отсортируем правильно все пары точек (чтобы первая точка была выше/правее второй)
for (int i = 0; i < solution.Count; i++)
{
if (solution[i].Item1.X == solution[i].Item2.X)
{
if (solution[i].Item1.Y <= solution[i].Item2.Y)
{
solution.Insert(i, new Tuple <T, T>(solution[i].Item2, solution[i].Item1));
solution.RemoveAt(i + 1);
}
}
else if (solution[i].Item1.Y == solution[i].Item2.Y)
{
if (solution[i].Item1.X <= solution[i].Item2.X)
{
solution.Insert(i, new Tuple <T, T>(solution[i].Item2, solution[i].Item1));
solution.RemoveAt(i + 1);
}
}
}
// разделяем накладывающиеся рёбра
int k = 0;
while (k < solution.Count)
{
if (solution[k].Item1.Equals(solution[k].Item2))
{
solution.RemoveAt(k);
}
if (solution[k].Item1.X == solution[k].Item2.X)
{
int ind = solution.FindLastIndex(edge => ((edge.Item1.X == edge.Item2.X) &&
(edge.Item1.Y == solution[k].Item1.Y || edge.Item2.Y == solution[k].Item2.Y)));
if (ind != -1 && ind != k)
{
if (solution[k].Item2.Equals(solution[ind].Item2))
{
if (solution[k].Item1.Y < solution[ind].Item1.Y)
{
solution.Add(new Tuple <T, T>(
new Point2D(solution[ind].Item1.X, solution[ind].Item1.Y) as T,
new Point2D(solution[k].Item1.X, solution[k].Item1.Y) as T));
solution.RemoveAt(ind);
k = -1;
}
else if (solution[k].Item1.Y > solution[ind].Item1.Y)
{
solution.Add(new Tuple <T, T>(
new Point2D(solution[k].Item1.X, solution[k].Item1.Y) as T,
new Point2D(solution[ind].Item1.X, solution[ind].Item1.Y) as T));
solution.RemoveAt(k);
k = -1;
}
else
{
solution.RemoveAt(k);
k = -1;
}
}
else if (solution[k].Item1.Equals(solution[ind].Item1))
{
if (solution[k].Item2.Y < solution[ind].Item2.Y)
{
solution.Add(new Tuple <T, T>(
new Point2D(solution[ind].Item2.X, solution[ind].Item2.Y) as T,
new Point2D(solution[k].Item2.X, solution[k].Item2.Y) as T));
solution.RemoveAt(k);
k = -1;
}
else if (solution[k].Item2.Y > solution[ind].Item2.Y)
{
solution.Add(new Tuple <T, T>(
new Point2D(solution[k].Item2.X, solution[k].Item2.Y) as T,
new Point2D(solution[ind].Item2.X, solution[ind].Item2.Y) as T));
solution.RemoveAt(ind);
k = -1;
}
else
{
solution.RemoveAt(k);
k = -1;
}
}
}
}
else if (solution[k].Item1.Y == solution[k].Item2.Y)
{
int ind = solution.FindLastIndex(edge => ((edge.Item1.Y == edge.Item2.Y) &&
(edge.Item1.X == solution[k].Item1.X || edge.Item2.X == solution[k].Item2.X)));
if (ind != -1 && ind != k)
{
if (solution[k].Item2.Equals(solution[ind].Item2))
{
if (solution[k].Item1.X < solution[ind].Item1.X)
{
solution.Add(new Tuple <T, T>(
new Point2D(solution[ind].Item1.X, solution[ind].Item1.Y) as T,
new Point2D(solution[k].Item1.X, solution[k].Item1.Y) as T));
solution.RemoveAt(ind);
k = -1;
}
else if (solution[k].Item1.X > solution[ind].Item1.X)
{
solution.Add(new Tuple <T, T>(
new Point2D(solution[k].Item1.X, solution[k].Item1.Y) as T,
new Point2D(solution[ind].Item1.X, solution[ind].Item1.Y) as T));
solution.RemoveAt(k);
k = -1;
}
else
{
solution.RemoveAt(k);
k = -1;
}
}
else if (solution[k].Item1.Equals(solution[ind].Item1))
{
if (solution[k].Item2.X < solution[ind].Item2.X)
{
solution.Add(new Tuple <T, T>(
new Point2D(solution[ind].Item2.X, solution[ind].Item2.Y) as T,
new Point2D(solution[k].Item2.X, solution[k].Item2.Y) as T));
solution.RemoveAt(k);
k = -1;
}
else if (solution[k].Item2.X > solution[ind].Item2.X)
{
solution.Add(new Tuple <T, T>(
new Point2D(solution[k].Item2.X, solution[k].Item2.Y) as T,
new Point2D(solution[ind].Item2.X, solution[ind].Item2.Y) as T));
solution.RemoveAt(ind);
k = -1;
}
else
{
solution.RemoveAt(k);
k = -1;
}
}
}
}
k++;
}
return(solution);
}
