> For the complete documentation index, see [llms.txt](https://gitbook.testingwaters.in/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://gitbook.testingwaters.in/geometry-1/travelling-salesman-problem.md).

# Travelling Salesman Problem

![](/files/-MkbvHdrBbAD1zAjBipP)

```d
// Check for Self Intersection
def pgnInt (pts:var[]..[],pnt:var)
{
	//Edges with existing points
	pg01 = Polygon.ByPoints(pts).Explode();
	in01 = 1..List.Count(pg01);
	//Distance to New point
	ds01 = pnt.DistanceTo(pg01);
	//Index of closest edge to new point
	in02 = List.SortByKey(in01,ds01)["sortedList"];
	//Shift indices of points list
	pt01 = List.ShiftIndices(pts,List.FirstItem(-in02));


	return [Imperative]
	{
		bl01 = true;
		n = 0;
		pt11 = [];

		while (bl01)
		{
			// Shift insertion index
			pt10 = List.ShiftIndices(pt01,n);
			//Add new point to top of list
			pt11 = List.AddItemToFront(pnt,pt10);
			pg11 = Polygon.ByPoints(pt11);
			//Check Self Intersection
			it11 = pg11.SelfIntersections();
			n = n + 1;
			bl01 = List.Count(it11) != 0;
		}
		return pt11;
	}
};

// Add Closest Neighbour
def clsNgh (pnt:var[]..[])
{
	occ = pnt[0];
	avl = pnt[1];
	pg01 = Polygon.ByPoints(occ);
	ds01 = pg01.DistanceTo(avl);
	pt01 = List.SortByKey(avl,ds01)["sortedList"];
	pt02 = List.FirstItem(pt01);
	pt03 = List.RestOfItems(pt01);
	pt04 = pgnInt (occ,pt02);
	return [pt04,pt03];
};

// Repeat until all points are included
def tsp (pt01:var[]..[])
{
	ds01 = List.FirstItem(pt01).DistanceTo(pt01);
	pt02 = List.SortByKey(pt01,ds01)["sortedList"];
	pt11 = [List.TakeItems(pt02,3),List.DropItems(pt02,3)];
	return [Imperative]
	{
		a = [];
		c = List.Count(pt11[1]);
		while (c > 0)
		{
			a = clsNgh (pt11);
			pt11 = a;
			c = c - 1;
		}
		return a[0];
};
};


// Implementation on lists of Random points
n = [25,50,75,100];

pt01 = Point.ByCoordinates
(Math.RandomList(n)*8000,Math.RandomList(n)*6000);

pt02 =tsp(pt01<1>);
[pt02[0],GeometryColor.ByGeometryColor
(Polygon.ByPoints(pt02[0]),Color.ByARGB(255,255,0,0))];
[pt02[1],GeometryColor.ByGeometryColor
(Polygon.ByPoints(pt02[1]),Color.ByARGB(255,0,255,0))];
[pt02[2],GeometryColor.ByGeometryColor
(Polygon.ByPoints(pt02[2]),Color.ByARGB(255,0,0,255))];
[pt02[3],GeometryColor.ByGeometryColor
(Polygon.ByPoints(pt02[3]),Color.ByARGB(255,255,0,250))];
```


---

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