/// <summary>Determines the efficiency of a packer with a packing area of 70x70</summary>
/// <param name="packer">Packer with a packing area of 70x70 units</param>
/// <returns>The efficiency factor of the packer</returns>
/// <remarks>
/// A perfect packer would achieve an efficiency rating of 1.0. This is
/// impossible however since the 24 squares cannot all be packed into
/// the 70x70 square with no overlap (Bitner & Reingold 1975). The closer
/// the efficiency rating is to 1.0, the better, with 0.99 being the
/// mathematically best rating achievable.
/// </remarks>
protected float CalculateEfficiency(RectanglePacker packer) {
// If we take a 1x1 square, a 2x2 square, etc. up to a 24x24 square,
// the sum of the areas of these squares is 4900, which is 70². This
// is the only nontrivial sum of consecutive squares starting with
// one which is a perfect square (Watson 1918).
int areaCovered = 0;
for(int size = 24; size >= 1; --size) {
Point placement;
if(packer.TryPack(size, size, out placement))
areaCovered += size * size;
}
return (float)areaCovered / 4900.0f;
}
/// <summary>Determines the efficiency of a packer with a packing area of 70x70</summary>
/// <param name="packer">Packer with a packing area of 70x70 units</param>
/// <returns>The efficiency factor of the packer</returns>
/// <remarks>
/// A perfect packer would achieve an efficiency rating of 1.0. This is
/// impossible however since the 24 squares cannot all be packed into
/// the 70x70 square with no overlap (Bitner & Reingold 1975). The closer
/// the efficiency rating is to 1.0, the better, with 0.99 being the
/// mathematically best rating achievable.
/// </remarks>
protected float CalculateEfficiency(RectanglePacker packer)
{
// If we take a 1x1 square, a 2x2 square, etc. up to a 24x24 square,
// the sum of the areas of these squares is 4900, which is 70². This
// is the only nontrivial sum of consecutive squares starting with
// one which is a perfect square (Watson 1918).
int areaCovered = 0;
for (int size = 24; size >= 1; --size)
{
Point placement;
if (packer.TryPack(size, size, out placement))
{
areaCovered += size * size;
}
}
return((float)areaCovered / 4900.0f);
}
/// <summary>Benchmarks the provided rectangle packer using random data</summary>
/// <param name="buildPacker">
/// Rectangle packer build method returning new rectangle packers
/// with an area of 1024 x 1024
/// </param>
/// <returns>The achieved benchmark score</returns>
protected float Benchmark(RectanglePackerBuilder buildPacker)
{
// How many runs to perform for getting a stable average
const int averagingRuns = 1;
// Generates the random number seeds. This is used so that each run produces
// the same number sequences and makes the comparison of different algorithms
// a little bit more stable.
Random seedGenerator = new Random(12345);
int rectanglesPacked = 0;
// Perform a number of runs to get a semi-stable average score
for (int averagingRun = 0; averagingRun < averagingRuns; ++averagingRun)
{
Random dimensionGenerator = new Random(seedGenerator.Next());
RectanglePacker packer = buildPacker();
// Try to cramp as many rectangles into the packing area as possible
for (; ; ++rectanglesPacked)
{
Point placement;
int width = dimensionGenerator.Next(16, 64);
int height = dimensionGenerator.Next(16, 64);
// As soon as the packer rejects the first rectangle, the run is over
if (!packer.TryPack(width, height, out placement))
{
break;
}
}
}
// Return the average score achieved by the packer
return((float)rectanglesPacked / (float)averagingRuns);
}
