UVa 10034 - Freckles

10034 - Freckles

 * http://acm.uva.es/p/v100/10034.html

Summary
Given N (less than 100) points in the plane, find the weight of the minimum spanning tree.

Explanation
Use any minimum spanning tree algorithm, and compute the weight. Since there are $$o(n^2)$$ edges, this can be done in $$O(n^2)$$, which is fast enough for this problem.

Note that the minimum spanning tree of a set of points in the plane can be found in $$O( n \log n )$$ by a more complex algorithm. The Delaunay Triangulation of a set of points in the plane can be calculated in $$O( n \log n )$$, with $$O( n )$$ edges in the resultant graph. Since the minimum spanning tree is a subset of the Delaunay triangulation, we can apply any of the MST algorithms on the resultant Delaunay triangulation and thus achieving the $$O( n \log n )$$ bound. This is not necessary for this problem.

Input
1

3 1.0 1.0 2.0 2.0 2.0 4.0

Output
3.41