/// <summary>
/// Implements search algorithm;
/// </summary>
/// <remarks>
/// From the given input we collect only numbers that can form a valid path;
/// each such number is stored together with calculated subtotal and
/// is linked to a valid (parent) number from previous line;
/// so when the last number of the input is traversed (i.e. no more input data),
/// we will just need to choose such number selected in the last line number,
/// that has a maximum subtotal and follow links to reach the top element,
/// to restore all the path.
/// </remarks>
private Result Solve()
{
var root = LineNumber.AsRoot(_numbers.Current);
var parity = root.Value.GetParity();
var lineNumber = 1;
var pathEndings = new List <LineNumber>(1)
{
root
};
while (_numbers.MoveNext())
{
parity = parity.InvertParity();
pathEndings = FindNumbersInLine(++lineNumber, parity, pathEndings);
if (pathEndings.Count == 0)
{
throw new ArgumentException("The given sequence of numbers doesn't contain any valid path!");
}
}
return(GetResult(pathEndings, lineNumber));
}
public LineNumber(int index, int value, LineNumber parent = null)
{
Index = index;
Value = value;
SubTotal = value + (parent?.SubTotal ?? 0);
Parent = parent;
}
public bool MoveNext()
{
if (++index >= items.Count)
{
return(false);
}
Current = items[index];
return(true);
}
/// <summary>
/// Searches for related number in previous line by given index of a number in current line
/// </summary>
/// <remarks>
/// Line j-1: N(i-1) N(i)
/// Line j : N(i)
///
/// here N(k) denotes some number with index k,
///
/// a number N(i) from line j IS in relation only with a number N(i-1) or N(i) from line j-1,
/// (a number N(0) as well as N(j) has only one relation, all other have two relations)
/// </remarks>
/// <returns>True, if was able to locate such number</returns>
private bool TryFindRelatedNumber(int itemIndex, ref LineIterator iterator, out LineNumber related)
{
related = null;
if (!iterator.CanIterate)
{
return(false);
}
do
{
// take a number from previous line, that is not yet linked
var current = iterator.Current;
var currentIndex = current.Index;
if (itemIndex < currentIndex)
{
return(false);
}
if (itemIndex - 1 == currentIndex)
{
// case when for a number N(i) in line j (i == itemIndex)
// found number N(i-1) in line j-1
related = iterator.Next;
// before return we need to check, if N(i) in line j-1 is also selected as valid;
// if both exists, then we choose for relation one, having bigger subtotal
var isNextRelated =
related != null &&
related.Index == itemIndex &&
related.SubTotal >= current.SubTotal;
if (!isNextRelated)
{
related = current;
}
return(true);
}
if (itemIndex == currentIndex)
{
// case when for a number N(i) in line j (i == itemIndex)
// found number N(i) in line j-1,
// and if we are here, than N(i-1) is not selected as valid
related = current;
return(true);
}
} while (iterator.MoveNext());
return(false);
}
public LineIterator(IReadOnlyList <LineNumber> source)
{
items = source;
index = 0;
Current = items[0];
}