/// <summary>
/// Randomized insertion.
/// make new node the root with uniform probability
/// </summary>
/// <param name="x"></param>
/// <param name="key"></param>
/// <param name="val"></param>
/// <returns></returns>
internal override BaseNode <TKey, TValue> PutKey(BaseNode <TKey, TValue> x, TKey key, TValue val)
{
if (x == null)
{
return(new BaseNode <TKey, TValue>(key, val, 1));
}
int cmp = key.CompareTo(x.key);
if (cmp == 0)
{
x.val = val;
return(x);
}
if (StdRandom.bernoulli(1.0 / (x.Size + 1.0)))
{
return(PutRoot(x, key, val));
}
if (cmp < 0)
{
x.left = PutKey(x.left, key, val);
}
else
{
x.right = PutKey(x.right, key, val);
}
x.UpdateSize();
return(x);
}
/// <summary>
/// Randomized deletion.
/// </summary>
/// <param name="a"></param>
/// <param name="b"></param>
/// <returns></returns>
private BaseNode <TKey, TValue> joinLR(BaseNode <TKey, TValue> a, BaseNode <TKey, TValue> b)
{
if (a == null)
{
return(b);
}
if (b == null)
{
return(a);
}
if (StdRandom.bernoulli((double)a.Size / (a.Size + b.Size)))
{
a.right = joinLR(a.right, b);
a.UpdateSize();
return(a);
}
else
{
b.left = joinLR(a, b.left);
b.UpdateSize();
return(b);
}
}
