public void DisjoinSetsPerformanceTest()
{
#region Arrange
var numElements = 1000000;
var djs = new DisjointSets(numElements);
#endregion
#region Act
var firstRoot = 0;
var secondRoot = numElements / 2;
djs.CreateSet(firstRoot);
djs.CreateSet(secondRoot);
for (int i = 0; i < numElements; i++)
{
if (i != firstRoot && i != secondRoot)
{
if (i < secondRoot)
{
djs.AddToSet(firstRoot, i);
}
else
{
djs.AddToSet(secondRoot, i);
}
}
}
djs.Union(firstRoot, secondRoot);
#endregion
#region Assert
Assert.AreEqual(1, djs.SetsCount);
for (int i = 0; i < numElements; i++)
{
Assert.AreEqual(0, djs.GetIncludingSetId(i));
}
#endregion
}
public void DisjoinSetsBaseScenarioTest()
{
var djs = new DisjointSets(4);
Assert.AreEqual(0, djs.SetsCount);
var setId = djs.CreateSet(0);
Assert.AreEqual(0, setId);
Assert.AreEqual(1, djs.SetsCount);
djs.AddToSet(setId, 1);
Assert.AreEqual(setId, djs.GetIncludingSetId(1));
var setId1 = djs.CreateSet(2);
Assert.AreEqual(2, djs.SetsCount);
djs.Union(setId, setId1);
Assert.AreEqual(1, djs.SetsCount);
Assert.AreEqual(setId, djs.GetIncludingSetId(2));
}
/// <summary>
/// Calculates minimal spanning tree using Kruskal algo.
/// Edges are required to be sorted by weigth.
/// </summary>
/// <param name="numNodes">Count of nodes</param>
/// <param name="edges">Edges data</param>
/// <returns>Array of indicies of edges in minimal spanning tree</returns>
public static int[] CalcKruskal(int numNodes,
GraphEdge[] edges)
{
int[] result = new int[numNodes - 1];
var ds = new DisjointSets(numNodes);
var connectedNodesCount = 0;
var currResultEdge = 0;
// for each edge try to include it in minimal spanning tree
for (int i = 0; i < edges.Length; i++)
{
var set1 = ds.GetIncludingSetId(edges[i].Node1);
var set2 = ds.GetIncludingSetId(edges[i].Node2);
if (set1 == set2 && set1 != -1)
{
// this edge will introduce cycle, skip it
// it already connects two nodes which are
// already in the same region
continue;
}
else
{
// edge connects two edges which are not in the same region
// so this edge can be included into MST
result[currResultEdge] = i;
currResultEdge++;
if (set1 != -1 && set2 != -1)
{
// edge connects two distinct regions - union them
ds.Union(set1, set2);
}
else if (set1 != -1 && set2 == -1)
{
// node 2 is single, add to gerion of node 1
ds.AddToSet(set1, edges[i].Node2);
connectedNodesCount += 1;
}
else if (set2 != -1 && set1 == -1)
{
// node 1 is single, add to gerion of node 2
ds.AddToSet(set2, edges[i].Node1);
connectedNodesCount += 1;
}
else
{
// both nodes are singe
// create region and add them into it
var newSet = ds.CreateSet(edges[i].Node1);
ds.AddToSet(newSet, edges[i].Node2);
connectedNodesCount += 2;
}
// if all nodes are connected and in the single region
// then MST is built
if (connectedNodesCount == numNodes && ds.SetsCount == 1)
{
return(result);
}
}
}
return(result);
}
