//Time: O(|v|^2)
//Space: O(V)
//The main function for doing dijkstra's algorithm and resurning the results.
public List <double> dijkstras()
{
//Console.WriteLine("Inside array dijkstras");
int max = Int32.MaxValue;
//We start by adding all values to infinity
for (int i = 0; i < points.Count; i++)
{
//Insert
//Time: O(1) Beacuse your doing it for one point.
//Space: O(1) Beacuse your making the queue.
distance.Add(max);
previous.Add(max);
queue.Add(max);
}
distance[startIndex] = 0;
queue[startIndex] = 0;
int minIndex = startIndex;
//to compare and change indexes
int minusOnes = 0;
EuclideanDistanceImplementation edi = new EuclideanDistanceImplementation();
while (minusOnes < queue.Count)
{
double minValue = max;
//Console.WriteLine("minusOnes " + minusOnes);
//the deleteMin function
//Time: O(|v|) Because you have to iterate over every point to find the minimum.
//Space: O(1) Nothing changed.
for (int i = 0; i < queue.Count; i++)
{
//Console.WriteLine("Dist is " + queue[i]);
if (queue[i] != -1 && queue[i] < minValue)
{
minIndex = i;
minValue = queue[i];
//Console.WriteLine("min index is " + i + " of " + queue[i]);
}
}
//Console.WriteLine("The current min Index is " + minIndex);
//previous.Add(points[minIndex]);
queue[minIndex] = -1;//set the value to -1 to take it out, basically
//update the distances of each of this node's directed edges. O(3)
for (int i = 0; i < adjacencyList[minIndex].Count; i++)
{
int currAdj = adjacencyList[minIndex].ElementAt(i);
//Console.WriteLine("currAdj is " + currAdj + " of " + adjacencyList[minIndex]);
double dist = edi.calculate(points[minIndex], points[currAdj]);
//Console.WriteLine("dist path of " + currAdj +" is " + distance[currAdj] + " versus " + (distance[minIndex] + dist));
if (distance[currAdj] > distance[minIndex] + dist)
{
distance[currAdj] = distance[minIndex] + dist;
//Console.WriteLine("Add " + currAdj + " from point " + minIndex);
//previous.Add(minIndex);
previous[currAdj] = minIndex;
//decreaseKey
//Time: O(1) Because you can directly access the index.
//Space: O(1) Because you change only one thing.
queue[currAdj] = distance[currAdj];
}
}
minusOnes++;
}
previous.Add(endIndex);
return(previous);
}
private void solveButton_Clicked()
{
// *** Implement this method, use the variables "startNodeIndex" and "stopNodeIndex" as the indices for your start and stop points, respectively ***
//Here we define the data objects we'll be using
String s = sourceNodeBox.Text;
int startIndex = Int32.Parse(s);
s = targetNodeBox.Text;
int endIndex = Int32.Parse(s);
EuclideanDistanceImplementation edi = new EuclideanDistanceImplementation();
Font arialFont = new Font("Arial", 11);
Pen p = new Pen(Color.Black, 1);
double totalDistance = 0;
DateTime startTime;
double arrayTime = 0;
double heapTime = 0;
double elapsedMillisecondsTime = 0;
if (arrayCheckBox.Checked == true)
{
//start the timer
startTime = DateTime.Now;
//compute dijkstra's algorithm with the data we have.
ArrayImplementation ai = new ArrayImplementation(startIndex, endIndex, points, adjacencyList);
List <double> previous = ai.dijkstras();//returns previous with all the indexes till the endIndex.
int currIndex = endIndex;
//Draw the shortest path with the costs backwards
//Time: O(|v|) Because you may have to draw each point at worst.
//Space: O(1) Beacuse you only change one point.
while (currIndex != startIndex)
{
//Console.WriteLine("Here");
//Console.WriteLine("Prev " + previous.ElementAt(currIndex));
//make sure that we can actually reach this thing
if (previous.ElementAt(currIndex) == 2147483647)
{
this.pathCostBox.Text = "unreachable";
return;
}
//draw the line
graphics.DrawLine(p, points[currIndex], points[(int)previous.ElementAt(currIndex)]);
//get and display length for every line drawn
double dist = edi.calculate(points[currIndex], points[(int)previous.ElementAt(currIndex)]);
totalDistance = totalDistance + dist;
string str = Convert.ToString((int)dist);
//calculation for the slope of the line and put it in the middle
RectangleF rectf = new RectangleF(70, 90, 80, 80);//x, y, width, height
rectf.X = Math.Abs(points[(int)previous.ElementAt(currIndex)].X + points[currIndex].X) / 2;
rectf.Y = Math.Abs(points[(int)previous.ElementAt(currIndex)].Y + points[currIndex].Y) / 2;
graphics.DrawString(str, arialFont, Brushes.Black, rectf);
currIndex = (int)previous.ElementAt(currIndex);
//Stop the timer and write the values to the forms
this.pathCostBox.Text = Convert.ToString(totalDistance);
elapsedMillisecondsTime = (DateTime.Now - startTime).TotalMilliseconds;
arrayTime = elapsedMillisecondsTime / 10000;
this.arrayTimeBox.Text = Convert.ToString(arrayTime);
}
}
//Now do the same thing with a Heap
//O(log |v|))
//start the timer
startTime = DateTime.Now;
HeapImplementation heapQueue = new HeapImplementation(points.Count);
//ArrayQueue
List <double> dist1 = new List <double>();
List <int> prev1 = new List <int>();
List <double> dist2 = new List <double>();
List <int> prev2 = new List <int>();
totalDistance = 0;
for (int u = 0; u < points.Count; u++)
{
dist1.Add(Int16.MaxValue);
prev1.Add(-1);
dist2.Add(Int16.MaxValue);
prev2.Add(-1);
}
dist1[startNodeIndex] = 0;
dist2[startNodeIndex] = 0;
//Heap implementation
for (int u = 0; u < dist2.Count; u++)
{
Node node = new Node(u);
heapQueue.Add(node, dist2[u]);
}
while (heapQueue.count > 0)
{
Node min = heapQueue.ExtractMin();
foreach (int adj in adjacencyList[min.pointsIndex])
{
double newDistance = dist2[min.pointsIndex] + edi.getMagnitude(min, adj, points);
if (dist2[adj] > newDistance)
{
dist2[adj] = newDistance;
prev2[adj] = min.pointsIndex;
heapQueue.DecreasePriority(adj, newDistance);
}
}
}
//Draw the shortest path with the costs backwards
//Time: O(|v|) Because you may have to draw each point at worst.
//Space: O(1) Beacuse you only change one point.
int currIndexToDraw = stopNodeIndex;
while (currIndexToDraw != startNodeIndex)
{
int prevIndex = prev2[currIndexToDraw];
//Console.WriteLine("Here");
//Console.WriteLine("Prev " + points[currIndexToDraw]);
//make sure that we can actually reach this thing
if (prevIndex > points.Count - 1 || prevIndex < 0)
{
this.pathCostBox.Text = "unreachable";
return;
}
graphics.DrawLine(p, points[currIndexToDraw], points[prevIndex]);
double currDistance = edi.calculate(points[prevIndex], points[currIndexToDraw]);
totalDistance += currDistance;
String text = Convert.ToString((int)currDistance);
RectangleF drawingBox = new RectangleF(Math.Abs(points[prevIndex].X + points[currIndexToDraw].X) / 2,
Math.Abs(points[prevIndex].Y + points[currIndexToDraw].Y) / 2, 80, 80);
graphics.DrawString(text, new Font("Arial", 11), Brushes.Black, drawingBox);
currIndexToDraw = prev2[currIndexToDraw];
}
this.pathCostBox.Text = Convert.ToString(totalDistance);
//Now set the time it takes for all this to happen
elapsedMillisecondsTime = (DateTime.Now - startTime).TotalMilliseconds;
heapTime = elapsedMillisecondsTime / 10000;
this.heapTimeBox.Text = Convert.ToString(heapTime);
if (arrayCheckBox.Checked == true)
{
this.differenceBox.Text = Convert.ToString(arrayTime / heapTime);
}
}