private static IntervalCollection <T> LowUnionOf <T>(Interval <T> a, Interval <T> b)
{
if (Interval.IsNullOrEmpty(a))
{
return(new IntervalCollection <T>(b));
}
if (Interval.IsNullOrEmpty(b))
{
return(new IntervalCollection <T>(a));
}
var result = new List <Interval <T> >(3);
result.AddRange(a.DifferenceWith(b));
result.AddRange(b.DifferenceWith(a));
var intersection = default(Interval <T>);
if (TryIntersectionOf(a, b, out intersection))
{
result.Add(intersection);
}
result.Sort();
return(new IntervalCollection <T>(result));
}
/// <summary>
/// Determines the complement of an <see cref="Interval<T>"/>.
/// </summary>
/// <typeparam name="T">The value type of the interval.</typeparam>
/// <param name="value">An <see cref="Interval<T>"/> reference.</param>
/// <returns>An <see cref="IntervalCollection<T>"/> that contains elements not in the specified interval.</returns>
/// <seealso href="http://en.wikipedia.org/wiki/Complement_(set_theory)">Complement (set theory)</seealso>
public static IntervalCollection <T> ComplementOf <T>(Interval <T> value)
{
if (Interval.IsNullOrEmpty(value))
{
return(new IntervalCollection <T>
(
new Interval <T>(Bound <T> .LowestBound, Bound <T> .UpmostBound)
));
}
var lowerBound = value.LowerBound;
var upperBound = value.UpperBound;
var result = new List <Interval <T> >(2);
if (object.Equals(lowerBound, Bound <T> .LowestBound) && object.Equals(upperBound, Bound <T> .UpmostBound))
{
}
else if (object.Equals(lowerBound, Bound <T> .LowestBound))
{
result.Add(new Interval <T>
(new Bound <T>(BoundType.Lower, Bound.Reverse(upperBound.Direction), upperBound.Value)
, Bound <T> .UpmostBound));
}
else if (object.Equals(upperBound, Bound <T> .UpmostBound))
{
result.Add(new Interval <T>
(Bound <T> .LowestBound
, new Bound <T>(BoundType.Upper, Bound.Reverse(lowerBound.Direction), lowerBound.Value)));
}
else
{
var iLower = Bound <T> .LowestBound;
var iUpper = new Bound <T>(BoundType.Upper, Bound.Reverse(lowerBound.Direction), lowerBound.Value);
var jLower = new Bound <T>(BoundType.Lower, Bound.Reverse(upperBound.Direction), upperBound.Value);
var jUpper = Bound <T> .UpmostBound;
Interval <T> i;
if (Interval.TryParse(iLower, iUpper, out i))
{
result.Add(i);
}
Interval <T> j;
if (Interval.TryParse(jLower, jUpper, out j))
{
result.Add(j);
}
}
return(new IntervalCollection <T>(result));
}
/// <summary>
/// Determines the difference of two intervals.
/// </summary>
/// <typeparam name="T">The value type of the interval.</typeparam>
/// <param name="a">The first interval.</param>
/// <param name="b">The second interval.</param>
/// <returns>An <see cref="IntervalCollection<T>"/> that contains elements in <paramref name="a"/> but not in <paramref name="b"/>.</returns>
/// <seealso href="http://en.wikipedia.org/wiki/Complement_(set_theory)">Relative complement (set theory)</seealso>
public static IntervalCollection <T> DifferenceOf <T>(Interval <T> a, Interval <T> b)
{
if (Interval.IsNullOrEmpty(a))
{
return(new IntervalCollection <T>(a));
}
if (Interval.IsNullOrEmpty(b))
{
return(new IntervalCollection <T>(a));
}
// A - B = A ∩ Bc
if (object.Equals(a, b))
{
return(new IntervalCollection <T>());
}
var c = b.Complement;
var args = new Interval <T> [c.Count + 1];
args[0] = a;
c.CopyTo(args, 1);
var result = new List <Interval <T> >(2);
foreach (var i in c)
{
var value = a.IntersectionWith(i);
if (!Interval.IsNullOrEmpty(value))
{
result.Add(value);
}
}
return(new IntervalCollection <T>(result));
}
private static IntervalCollection <T> HighUnionOf <T>(Interval <T> a, Interval <T> b)
{
if (Interval.IsNullOrEmpty(a))
{
return(new IntervalCollection <T>(b));
}
if (Interval.IsNullOrEmpty(b))
{
return(new IntervalCollection <T>(a));
}
var lowestBound = Bound.Min(a.LowerBound, b.LowerBound);
var upmostValue = Bound.Max(a.UpperBound, b.UpperBound);
var lowerBound = default(Bound <T>);
var upperBound = default(Bound <T>);
// a
//-------------
// b
// ---------
if (object.Equals(lowestBound, a.LowerBound) &&
object.Equals(upmostValue, a.UpperBound))
{
lowerBound = new Bound <T>(BoundType.Lower
, object.Equals(a.LowerBound.Value, b.LowerBound.Value)
? Bound.Max(a.LowerBound.Direction, b.LowerBound.Direction)
: a.LowerBound.Direction
, a.LowerBound.Value);
upperBound = new Bound <T>(BoundType.Upper
, object.Equals(a.UpperBound.Value, b.UpperBound.Value)
? Bound.Max(a.UpperBound.Direction, b.UpperBound.Direction)
: a.UpperBound.Direction
, a.UpperBound.Value);
}
// a
// ---------
// b
//-------------
else if (object.Equals(lowestBound, b.LowerBound) &&
object.Equals(upmostValue, b.UpperBound))
{
lowerBound = new Bound <T>(BoundType.Lower
, object.Equals(a.LowerBound.Value, b.LowerBound.Value)
? Bound.Max(a.LowerBound.Direction, b.LowerBound.Direction)
: b.LowerBound.Direction
, b.LowerBound.Value);
upperBound = new Bound <T>(BoundType.Upper
, object.Equals(a.UpperBound.Value, b.UpperBound.Value)
? Bound.Max(a.UpperBound.Direction, b.UpperBound.Direction)
: b.UpperBound.Direction
, b.UpperBound.Value);
}
// a
//---------
// b
// -------------
else if (object.Equals(lowestBound, a.LowerBound) &&
object.Equals(upmostValue, b.UpperBound) &&
a.UpperBound.UnionCompareTo(b.LowerBound) >= 0)
{
lowerBound = new Bound <T>(BoundType.Lower
, object.Equals(a.LowerBound.Value, b.LowerBound.Value)
? Bound.Max(a.LowerBound.Direction, b.LowerBound.Direction)
: a.LowerBound.Direction
, a.LowerBound.Value);
upperBound = new Bound <T>(BoundType.Upper
, object.Equals(a.UpperBound.Value, b.UpperBound.Value)
? Bound.Max(a.UpperBound.Direction, b.UpperBound.Direction)
: b.UpperBound.Direction
, b.UpperBound.Value);
}
// a
// -------------
// b
//---------
else if (object.Equals(lowestBound, b.LowerBound) &&
object.Equals(upmostValue, a.UpperBound) &&
b.UpperBound.UnionCompareTo(a.LowerBound) >= 0)
{
lowerBound = new Bound <T>(BoundType.Lower
, object.Equals(a.LowerBound.Value, b.LowerBound.Value)
? Bound.Max(a.LowerBound.Direction, b.LowerBound.Direction)
: b.LowerBound.Direction
, b.LowerBound.Value);
upperBound = new Bound <T>(BoundType.Upper
, object.Equals(a.UpperBound.Value, b.UpperBound.Value)
? Bound.Max(a.UpperBound.Direction, b.UpperBound.Direction)
: a.UpperBound.Direction
, a.UpperBound.Value);
}
else
{
return(new IntervalCollection <T>(a, b));
}
Interval <T> result;
return(TryParse(lowerBound, upperBound, out result)
? new IntervalCollection <T>(result)
: new IntervalCollection <T>(a, b));
}
/// <summary>
/// Determines the intersection of two intervals.
/// </summary>
/// <typeparam name="T">The value type of the intervals.</typeparam>
/// <param name="a">The first interval.</param>
/// <param name="b">The second interval.</param>
/// <returns>An <see cref="Interval<T>"/> that contains all elements of <paramref name="a"/>
/// that also belong to <paramref name="b"/> (or equivalently, all elements of <paramref name="b"/>
/// that also belong to <paramref name="a"/>), but no other elements.</returns>
/// <seealso href="http://en.wikipedia.org/wiki/Intersection_(set_theory)">Intersection (set theory)</seealso>
private static Interval <T> IntersectionOf <T>(Interval <T> a, Interval <T> b)
{
if (Interval.IsNullOrEmpty(a))
{
return(a);
}
if (Interval.IsNullOrEmpty(b))
{
return(b);
}
var lowestBound = Bound.Min(a.LowerBound, b.LowerBound);
var upmostValue = Bound.Max(a.UpperBound, b.UpperBound);
var lowerBound = default(Bound <T>);
var upperBound = default(Bound <T>);
// a
//-------------
// b
// ---------
if (object.Equals(lowestBound, a.LowerBound) &&
object.Equals(upmostValue, a.UpperBound))
{
lowerBound = new Bound <T>(BoundType.Lower
, object.Equals(a.LowerBound.Value, b.LowerBound.Value)
? Bound.Min(a.LowerBound.Direction, b.LowerBound.Direction)
: b.LowerBound.Direction
, b.LowerBound.Value);
upperBound = new Bound <T>(BoundType.Upper
, object.Equals(a.UpperBound.Value, b.UpperBound.Value)
? Bound.Min(a.UpperBound.Direction, b.UpperBound.Direction)
: b.UpperBound.Direction
, b.UpperBound.Value);
}
// a
// ---------
// b
//-------------
else if (object.Equals(lowestBound, b.LowerBound) &&
object.Equals(upmostValue, b.UpperBound))
{
lowerBound = new Bound <T>(BoundType.Lower
, object.Equals(a.LowerBound.Value, b.LowerBound.Value)
? Bound.Min(a.LowerBound.Direction, b.LowerBound.Direction)
: a.LowerBound.Direction
, a.LowerBound.Value);
upperBound = new Bound <T>(BoundType.Upper
, object.Equals(a.UpperBound.Value, b.UpperBound.Value)
? Bound.Min(a.UpperBound.Direction, b.UpperBound.Direction)
: a.UpperBound.Direction
, a.UpperBound.Value);
}
// a
//---------
// b
// -------------
else if (object.Equals(lowestBound, a.LowerBound) &&
object.Equals(upmostValue, b.UpperBound))
{
lowerBound = new Bound <T>(BoundType.Lower
, object.Equals(a.LowerBound.Value, b.LowerBound.Value)
? Bound.Min(a.LowerBound.Direction, b.LowerBound.Direction)
: b.LowerBound.Direction
, b.LowerBound.Value);
upperBound = new Bound <T>(BoundType.Upper
, object.Equals(a.UpperBound.Value, b.UpperBound.Value)
? Bound.Min(a.UpperBound.Direction, b.UpperBound.Direction)
: a.UpperBound.Direction
, a.UpperBound.Value);
}
// a
// -------------
// b
//---------
else if (object.Equals(lowestBound, b.LowerBound) &&
object.Equals(upmostValue, a.UpperBound))
{
lowerBound = new Bound <T>(BoundType.Lower
, object.Equals(a.LowerBound.Value, b.LowerBound.Value)
? Bound.Min(a.LowerBound.Direction, b.LowerBound.Direction)
: a.LowerBound.Direction
, a.LowerBound.Value);
upperBound = new Bound <T>(BoundType.Upper
, object.Equals(a.UpperBound.Value, b.UpperBound.Value)
? Bound.Min(a.UpperBound.Direction, b.UpperBound.Direction)
: b.UpperBound.Direction
, b.UpperBound.Value);
}
else
{
return(Interval.Empty <T>());
}
Interval <T> result;
return(TryParse(lowerBound, upperBound, out result)
? result
: Interval.Empty <T>());
}
