/// <summary>
/// Return the compositions list containing only the first `k` elements
/// of the input. In the worst case, performs `O(k log k)` element compositions,
/// in order to maintain the right-associative bias. If you wish to run `composed`
/// on the result of `take`, use `takeComposed` for better performance.
/// </summary>
public static Compositions <A> take <MonoidA, A>(int amount, Compositions <A> compositions) where MonoidA : struct, Monoid <A>
{
Seq <Compositions <A> .Node> go(int n, Seq <Compositions <A> .Node> nodes)
{
if (nodes.IsEmpty)
{
return(nodes);
}
if (n <= 0)
{
return(Seq <Compositions <A> .Node>());
}
var x = nodes.Head;
var s = x.Size;
var c = x.Children;
var ri = nodes.Tail;
var ord = n.CompareTo(s);
if (ord < 0)
{
var(l, r) = c.IfNone((default(Compositions <A> .Node), default(Compositions <A> .Node)));
return(go(n, l.Cons(r.Cons(ri))));
}
else
{
return(default(MCompositions <MonoidA, A>)
.Append(new Compositions <A>(Seq1(x)), new Compositions <A>(go(n - s, ri)))
.Tree);
}
}
return(new Compositions <A>(go(amount, compositions.Tree)));
}
/// <summary>
/// Return the compositions list with the first `k` elements removed, in `O(log k)` time.
/// </summary>
public static Compositions <A> skip <A>(int amount, Compositions <A> compositions)
{
Seq <Compositions <A> .Node> go(int n, Seq <Compositions <A> .Node> nodes)
{
if (nodes.IsEmpty)
{
return(nodes);
}
if (n <= 0)
{
return(nodes);
}
var s = nodes.Head.Size;
var c = nodes.Head.Children;
var ri = nodes.Tail;
var ord = n.CompareTo(s);
if (ord < 0)
{
var(l, r) = c.IfNone((default(Compositions <A> .Node), default(Compositions <A> .Node)));
return(go(n, l.Cons(r.Cons(ri))));
}
else
{
return(go(n - s, ri));
}
}
return(new Compositions <A>(go(amount, compositions.Tree)));
}
/// <summary>
/// Returns the composition of the first `k` elements of the compositions list, doing only `O(log k)` compositions.
/// Faster than simply using `take` and then `composed` separately.
/// </summary>
public static A takeComposed <MonoidA, A>(int amount, Compositions <A> compositions) where MonoidA : struct, Monoid <A>
{
A go(int n, Seq <Compositions <A> .Node> nodes)
{
if (nodes.IsEmpty)
{
return(default(MonoidA).Empty());
}
if (n <= 0)
{
return(default(MonoidA).Empty());
}
var x = nodes.Head;
var s = x.Size;
var c = x.Children;
var v = x.Value;
var ri = nodes.Tail;
var ord = n.CompareTo(s);
if (ord < 0)
{
var(l, r) = c.IfNone((default(Compositions <A> .Node), default(Compositions <A> .Node)));
return(go(n, l.Cons(r.Cons(ri))));
}
else
{
return(default(MonoidA).Append(v, go(n - s, ri)));
}
}
return(go(amount, compositions.Tree));
}
/// <summary>
/// Returns true if the given tree is appropriately right-biased.
/// </summary>
public static bool wellFormed <MonoidEqA, A>(Compositions <A> ca) where MonoidEqA : struct, Monoid <A>, Eq <A>
{
bool wellFormedNode(int n, Compositions <A> .Node node)
{
var ni = node.Size;
if (n == 1 && ni == 1 && node.Children.IsNone)
{
return(true);
}
else if (node.Children.IsSome && n == ni)
{
var v = node.Value;
var(l, r) = node.Children.IfNone((default(Compositions <A> .Node), default(Compositions <A> .Node)));
return(wellFormedNode(n / 2, l) &&
default(MonoidEqA).Equals(v, default(MonoidEqA).Append(l.Value, r.Value)) &&
wellFormedNode(n / 2, r));
}
else
{
return(false);
}
}
bool go(int m, Seq <Compositions <A> .Node> ma)
{
if (ma.IsEmpty)
{
return(true);
}
var x = ma.Head;
var xs = ma.Tail;
var s = x.Size;
return(s >= m && wellFormedNode(s, x) && go(s * 2, xs));
}
return(go(1, ca.Tree));
}
/// <summary> /// Returns the composition of the first `k` elements of the compositions list, doing only `O(log k)` compositions. /// Faster than simply using `take` and then `composed` separately. /// </summary> public A TakeComposed <MonoidA>(int amount) where MonoidA : struct, Monoid <A> => Compositions.takeComposed <MonoidA, A>(amount, this);
/// <summary> /// Return the compositions list with the first `k` elements removed, in `O(log k)` time. /// </summary> public Compositions <A> Skip(int amount) => Compositions.skip(amount, this);
/// <summary> /// Returns true if the given tree is appropriately right-biased. /// </summary> public bool WellFormed <MonoidEqA>() where MonoidEqA : struct, Monoid <A>, Eq <A> => Compositions.wellFormed <MonoidEqA, A>(this);