sort list of points by distance in .NET

Question

I need to sort a list of points by distance.

So for e.g.

input : [[1,2],[5,10],[2,4]...]
output : [[1,2],[2,4],[5,10]...]

(assuming that geometrically [1,2] and [2,4] are nearest & [2,4] & [5,10] are nearest.

I need them to sort it so they are ordered by distance i.e. on the geometrical graph, point a is nearest to point b , point b is nearest to c and so on.

Any idea?

Edit: Code example

public class Point
{
   public double X {get;set;}
   public double Y {get;set;}
}


List<Point> points = new List<Point>();

let say my points list is getting populated in random order (not by geometrical distance). So points would look something like...

point ~ [[1,2],[5,10],[2,4]...]

Now my charting control just take the first & second point and draw a line between them. Which means it does not care which geometrical order is it in. If I simply supply the "points" list as above its going to draw lines between each points and from charting point of view it would not look correct as they would be "zig-zag".

To make sure the charting control draws a straight line (& and not zig-zag) I have to pass the points in the right order which would look something like ...

destination points ~ [[1,2],[2,4],[5,10]...]

So my question is how to achieve this.

Note: Changing chart control is not an option here.

Thanks

could you please post an explicit example with an input and an output? thank you in advance. — Christos, May 09 '14 at 08:46
for the voting down, could you please let me know what research effort that I have missed here. so that I can correct them! — activebiz, May 09 '14 at 08:49
Create a method that returns the distance([here](http://stackoverflow.com/questions/3819396/how-can-i-measure-diagonal-distance-points)), then use that method for `List.Sort` or `Array.Sort`. — Tim Schmelter, May 09 '14 at 08:50
So you start from one point and look for the nearest one, then you "move" to that one and look for the nearest to that second ponit and so on... is that correct? Also, which criteria do you use to select the starting point? — Marcello Romani, May 09 '14 at 08:56
@Christos ok. so in that example. if c is equally near to a and b then it can in any order. The idea is to create a line from sequential points. My line chart plot lines as per the order of the points in the array. if they are not order by "points nearest to each other" then random points are joined to plot a line which makes it all zig-zag. — activebiz, May 09 '14 at 08:56
@user25018 It's not sorting. It's a travelling salesman problem. — Tarec, May 09 '14 at 08:56
So, how should a list like `[1,1], [3,2], [2,3], [4,4], [2,5], [5,2]` be ordered? — sloth, May 09 '14 at 08:59
I think the downvotes are most likely because "it is unclear" - what data types is your input. String, Tuple, Class with x,y properties, etc. You need to show some code to help use help you — Matt Wilko, May 09 '14 at 09:00
[Sorting a two-dimensional array in C#](http://www.codeproject.com/Tips/164526/Sorting-a-two-dimensional-array-in-C)?? — huMpty duMpty, May 09 '14 at 09:01
http://stackoverflow.com/questions/20290046/algorithm-to-find-the-shortest-path-in-a-matrix — Jodrell, May 09 '14 at 09:10
@AlyEl-Haddad Thanks for the reply. That one looks like more useful unlike others who were more keen on down voting the question. I'll let you know if whether it worked or not. — activebiz, May 11 '14 at 09:37

Aly Elhaddad · Accepted Answer · 2014-05-09T14:12:08.640

The code first takes the nearest point to (0, 0) at the '0' index then start sorting the points by distance from the last spotted point..

C#:

    List<Point> SortByDistance(List<Point> lst)
    {
        List<Point> output = new List<Point>();
        output.Add(lst[NearestPoint(new Point(0, 0), lst)]);
        lst.Remove(output[0]);
        int x = 0;
        for (int i = 0; i < lst.Count + x; i++)
        {
            output.Add(lst[NearestPoint(output[output.Count - 1], lst)]);
            lst.Remove(output[output.Count - 1]);
            x++;
        }
        return output;
    }

    int NearestPoint(Point srcPt, List<Point> lookIn)
    {
        KeyValuePair<double, int> smallestDistance = new KeyValuePair<double, int>();
        for (int i = 0; i < lookIn.Count; i++)
        {
            double distance = Math.Sqrt(Math.Pow(srcPt.X - lookIn[i].X, 2) + Math.Pow(srcPt.Y - lookIn[i].Y, 2));
            if (i == 0)
            {
                smallestDistance = new KeyValuePair<double, int>(distance, i);
            }
            else
            {
                if (distance < smallestDistance.Key)
                {
                    smallestDistance = new KeyValuePair<double, int>(distance, i);
                }
            }
        }
        return smallestDistance.Value;
    }

VB.Net:

Function SortByDistance(ByVal lst As List(Of Point)) As List(Of Point)
    Dim out As New List(Of Point)
    out.Add(lst(NearestPoint(New Point(0, 0), lst)))
    lst.Remove(out(0))
    Dim x As Integer = 0
    For i As Integer = 0 To lst.Count - 1 + x
        out.Add(lst(NearestPoint(out(out.Count - 1), lst)))
        lst.Remove(out(out.Count - 1))
        x += 1
    Next
    Return out
End Function

Function NearestPoint(ByVal srcPt As Point, ByVal lookIn As List(Of Point)) As Integer
    Dim smallestDistance As KeyValuePair(Of Double, Integer)
    For i As Integer = 0 To lookIn.Count - 1
        Dim distance As Double = Math.Sqrt(Math.Pow(srcPt.X - lookIn(i).X, 2) + Math.Pow(srcPt.Y - lookIn(i).Y, 2))
        If i = 0 Then
            smallestDistance = New KeyValuePair(Of Double, Integer)(distance, i)
        Else
            If distance < smallestDistance.Key Then
                smallestDistance = New KeyValuePair(Of Double, Integer)(distance, i)
            End If
        End If
    Next
    Return smallestDistance.Value
End Function

@Tarec yes I know, the asker used the 'vb.net' tag, now he edited the post and removed the tag... — Aly Elhaddad, May 09 '14 at 12:17

score 1 · Answer 2 · answered May 09 '14 at 09:22

I think you want this, Dijkstra's algorithm. There is a c# project here.

What follows is unmodified code from that link

class Dijkstra
    {        
        private int rank = 0;
        private int[,] L;
        private int[] C; 
        public int[] D;
        private int trank = 0;
        public Dijkstra(int paramRank,int [,]paramArray)
        {
            L = new int[paramRank, paramRank];
            C = new int[paramRank];
            D = new int[paramRank];
            rank = paramRank;
            for (int i = 0; i < rank; i++)
            {
                for (int j = 0; j < rank; j++) {
                    L[i, j] = paramArray[i, j];
                }
            }

            for (int i = 0; i < rank; i++)
            {
                C[i] = i;
            }
            C[0] = -1;          
            for (int i = 1; i < rank; i++)
                D[i] = L[0, i];
        }
        public void DijkstraSolving()
        {            
            int minValue = Int32.MaxValue;
            int minNode = 0;
            for (int i = 0; i < rank; i++)
            {
                if (C[i] == -1)
                    continue;
                if (D[i] > 0 && D[i] < minValue)
                {
                    minValue = D[i];
                    minNode = i;
                }
            }
            C[minNode] = -1;
            for (int i = 0; i < rank; i++)
            { 
                if (L[minNode, i] < 0)
                    continue;
                if (D[i] < 0) {
                    D[i] = minValue + L[minNode, i];
                    continue;
                }
                if ((D[minNode] + L[minNode, i]) < D[i])
                    D[i] = minValue+ L[minNode, i];
            }
        }
        public void Run()
        {
            for (trank = 1; trank >rank; trank++)
            {
                DijkstraSolving();
                Console.WriteLine("iteration" + trank);
                for (int i = 0; i < rank; i++)
                    Console.Write(D[i] + " ");
                Console.WriteLine("");
                for (int i = 0; i < rank; i++)
                    Console.Write(C[i] + " ");
                Console.WriteLine("");                
            }
        }
 }

Victor Mukherjee · Answer 3 · 2014-05-09T10:46:23.990

0

In a graph, a set of points (x1,y1), (x2,y2), (x3,y3)...(xn,yn) should be ordered on the value of any one co ordinate because it is not the nearest point that should come next in order, but the one with nearest x or y (whichever axis is taken as reference) co-ordinate value. So, the array to pass for charting should be:

var orderedPoints=points.OrderBy(p=>p.X);

enter image description here

In the above image, the length of the line L1 is greater than L2. But the point P2 and not P3 should be come after P1 since P2.X<P3.X

edited May 09 '14 at 10:46

answered May 09 '14 at 10:01

Victor Mukherjee

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can the downvoter please suggest what is wrong with this answer? – Victor Mukherjee May 09 '14 at 12:12
Here I come with my rescue vote! It's kinda hard to solve a problem, that hasn't been actually established properly. – Tarec May 09 '14 at 12:17

sort list of points by distance in .NET

3 Answers3