/// <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(RandGraph(n, p));
avgColorUsed = Double.IsNaN(avgColorUsed) ? 0 : avgColorUsed;
avgColorUsed += aRandomGraph.ColorUsed();
}
avgColorUsed /= samples;
sb.AppendLine($"\"AvgColor\": {avgColorUsed}");
sb.AppendLine("},");
}
sb.AppendLine("]");
return(sb.ToString());
}
