/// <summary>
/// Generate a random graph and then use it to color it.
///
/// This method investigate: How much color is needed on average for a graph with 1000
/// vertex, where p varies from 0.002 to 0.02
/// </summary>
public static string RandomGraphColoringReport(
int n = 1000,
double p_start = 0.002,
double p_end = 0.02,
int N = 10, // Increment for edge density
int samples = 100
)
{
StringBuilder sb = new StringBuilder();
sb.AppendLine("[");
for (double p = p_start, delta = (p_end - p_start) / N; p <= p_end; p += delta)
{
sb.AppendLine("{");
sb.AppendLine($"\"n\":{n},");
sb.AppendLine($"\"p\":{p},");
double avgColorUsed = Double.NaN;
for (int I = 0; I < samples; I++)
{
var aRandomGraph = new ColoringGraph(KissMe.RandGraph(n, p));
avgColorUsed = Double.IsNaN(avgColorUsed) ? 0 : avgColorUsed;
avgColorUsed += aRandomGraph.ColorUsed();
}
avgColorUsed /= samples;
sb.AppendLine($"\"AvgColor\": {avgColorUsed}");
sb.AppendLine($"}} {(p == p_end ? ' ' : ',')}");
}
sb.AppendLine("]");
return(sb.ToString());
}
/// <summary>
/// Function will print result for this experiment to the console.
/// </summary>
private static void PrintHW3ConnectedComponents()
{
int n = (int)1e4;
double range = 1.5e-3;
int N = 30;
double delta = range / N;
double[] p = new double[N];
for (int I = 0; I < N; I++)
{
p[I] = Math.Log(n) / n - range + (I + N / 2) * delta;
}
WriteLine("The graph has 10^4 vertex and it's randomly generated with different " +
"edge density, here is the statistics regarding it's connected components: ");
WriteLine("Vertex, Edge_Density, TotalComponents, Max_Component_Size" +
", Min_Component_size, Size_SD");
for (int I = 0; I < p.Length; I++)
{
//0, 2, 3, 4
var G = KissMe.RandGraph(n, p[I]);
var g = new SimpleGraph(G);
var res = g.ProduceStats();
WriteLine($"{n}, {p[I]}, {res[0]}, {res[2]}, {res[3]}, {res[4]}");
}
}
/// <summary>
/// The result will get printed out to the console and you should copy then and get the
/// image elsewhere.
///
/// The printed result will be formatted as json file for convenience.
/// </summary>
public static void HW4P4PrintVertexDegreeDistribution(
int n = 1000,
double p_start = 0.002,
double p_end = 0.02,
int N = 10)
{
double[] EdgeDensity = new double[N];
StringBuilder sb = new StringBuilder();
sb.AppendLine("[");
for (double P = p_start, delta = (p_end - p_start) / N;
P <= p_end;
P += delta)
{
var G = new ColoringGraph(KissMe.RandGraph(n, P));
//output.WriteLine($"Ded Distribution with p = {P}; n = {n};");
sb.AppendLine("{");
sb.AppendLine($"\t\"p\":{P},");
sb.AppendLine($"\t\"n\":{n},");
foreach (KeyValuePair <int, int> kvp in G.GetDegStats())
{
sb.AppendLine($"\t\"{kvp.Key}\": {kvp.Value},");
}
sb.Remove(sb.Length - 3, 2);
sb.AppendLine("},");
}
sb.Remove(sb.Length - 3, 2);
sb.AppendLine("]");
WriteLine(sb.ToString());
}