public List <PointF> solve()
{
// This is the solving function.
// Over all we have O(|V|log|V|+|V|log|V|+|E|log|V|) which
// reduces to O((E+V)log|V|).
List <PointF> shortest = new List <PointF>();
List <data> queue = new List <data>();
List <double> distances = new List <double>();
List <int> possible = new List <int>();
data[] match = new data[points.Count];
// Make queue step. Takes O(|V|log(|V|)) because insert takes
// O(log|V|) and we are inserting |V| nodes.
for (int i = 0; i < points.Count; i++) // O(|V|)
{
possible.Add(i);
if (i == startNodeIndex)
{
distances.Add(0);
data temp = new data(points[i], 0, i, i);
match[i] = temp;
insert(ref queue, ref temp); // O(log|V|)
}
else
{
distances.Add(double.MaxValue);
data temp = new data(points[i], double.MaxValue, i, i);
match[i] = temp;
insert(ref queue, ref temp); // O(log|V|)
}
}
while (queue.Count > 0)
{
// This while loop takes O(|V|) because we pop one node off
// the queue at a time.
data u = deletemin(ref queue); // O(log|V|)
possible[u.original] = -1;
foreach (int v in adjacencyList[u.original])
{
// This step can take at worst O(|E|).
if (possible[v] == -1)
{
continue;
}
double e_dist = eucl_dist(points[v], u.point);
if (distances[v] > u.dist + e_dist)
{
int i_v = match[v].location;
if (i_v < 0)
{
continue;
}
queue[i_v].dist = u.dist + e_dist;
distances[v] = u.dist + e_dist;
if (final.ContainsKey(queue[i_v].point))
{
final[queue[i_v].point] = u.point;
}
else
{
final.Add(queue[i_v].point, u.point);
}
decrease_key(ref queue, i_v); // O(log|V|)
}
}
}
try
{
PointF start = points[stopNodeIndex];
PointF end = final[points[stopNodeIndex]];
shortest.Add(start);
shortest.Add(end);
while (end.X != points[startNodeIndex].X && end.Y != points[startNodeIndex].Y)
{
start = end;
end = final[start];
shortest.Add(end);
}
}
catch (KeyNotFoundException e)
{
return(new List <PointF>());
}
return(shortest);
}
public data deletemin(ref List <data> queue)
{
// This function allows user to delete minimum from dinary heap.
// Time complecity is a order of O(log|V|).
// This is proven by the fact that a binary heap bubbles down
// a value from a heap which is only log|V| deap.
if (queue.Count <= 1)
{
data temp = queue[0];
queue.RemoveAt(0);
return(temp);
}
data min = queue[0];
data last = queue[queue.Count - 1];
queue.RemoveAt(queue.Count - 1);
queue[0] = last;
queue[0].location = 0;
int index = 1;
int index_n;
while (true)
{
if ((2 * index) - 1 >= queue.Count)
{
break;
}
data child;
data left = queue[(2 * index) - 1];
if ((2 * index + 1) - 1 >= queue.Count)
{
child = left;
index_n = 2 * index;
}
else
{
data right = queue[(2 * index + 1) - 1];
if (left.dist <= right.dist)
{
child = left;
index_n = 2 * index;
}
else
{
child = right;
index_n = 2 * index + 1;
}
}
if (child.dist < queue[index - 1].dist)
{
data temp = queue[index_n - 1];
queue[index_n - 1] = queue[index - 1];
queue[index - 1] = temp;
queue[index - 1].location = index - 1;
queue[index_n - 1].location = index_n - 1;
index = index_n;
}
else
{
break;
}
}
return(min);
}