/// <summary>
/// Finds the weight that the program that unbalances the structure should be to balance it, if found.
/// </summary>
/// <param name="root">The root node of the structure.</param>
/// <returns>
/// The weight the program that unbalances the tower described by <paramref name="root"/> should be, if any; otherwise zero.
/// </returns>
private static int FindDesiredWeightOfUnbalancedDisc(ProgramDisc root)
{
if (root.ProgramsHeld.Length == 0)
{
// Leaf node, no children to inspect
return(0);
}
var unbalancedSubtree = root.Children
.GroupBy((p) => FindDesiredWeightOfUnbalancedDisc(p))
.Where((p) => p.Key is not 0)
.SingleOrDefault();
if (unbalancedSubtree != null)
{
// The unbalanced program was found in the subtree
return(unbalancedSubtree.Key);
}
var childWeights = root.Children.GroupBy((p) => p.TotalWeight);
ProgramDisc?unbalanced = childWeights.FirstOrDefault((p) => p.ExactCount(1))?.FirstOrDefault();
if (unbalanced is null)
{
// All children's trees weigh the same
return(0);
}
int currentWeight = unbalanced.TotalWeight;
int targetWeight = childWeights.First((p) => !p.ExactCount(1)).Key;
int delta = currentWeight - targetWeight;
return(unbalanced.Weight - delta);
}
/// <summary>
/// Finds the weight that the program that unbalances the structure should be to balance it.
/// </summary>
/// <param name="structure">A collection of strings representing the structure of the tower.</param>
/// <returns>
/// The weight the program that unbalances the tower described by <paramref name="structure"/> should be.
/// </returns>
public static int FindDesiredWeightOfUnbalancedDisc(IEnumerable <string> structure)
{
var tower = BuildStructure(structure);
string bottomName = FindBottomProgramName(tower.Values);
ProgramDisc bottom = tower[bottomName];
return(FindDesiredWeightOfUnbalancedDisc(bottom));
}
/// <summary>
/// Builds the structure of discs.
/// </summary>
/// <param name="structure">A collection of strings representing the structure of the tower.</param>
/// <returns>
/// An <see cref="IDictionary{TKey, TValue}"/> containing the programs with references to their parent and children, keyed by their names.
/// </returns>
private static Dictionary <string, ProgramDisc> BuildStructure(IEnumerable <string> structure)
{
var programs = structure
.Select((p) => new ProgramDisc(p))
.ToDictionary((p) => p.Name, (p) => p);
foreach (ProgramDisc program in programs.Values)
{
foreach (string name in program.ProgramsHeld)
{
ProgramDisc child = programs[name];
child.Parent = program;
program.Children.Add(child);
}
}
return(programs);
}
