### Red-Black Tree

"Introduction to Algorithms" (Cormen et al, 3rd ed.), Chapter 13

1. Every node is either red or black.
2. The root is black.
3. Every leaf (NIL) is black.
4. If a node is red, then both its children are black.
5. For each node, all simple paths from the node to descendant leaves contain the same number of black nodes.

For example,

``````import (
"fmt"

)

func main() {
ivt.Insert(NewInt64Interval(510, 511), 0)
ivt.Insert(NewInt64Interval(82, 83), 0)
ivt.Insert(NewInt64Interval(830, 831), 0)
...
``````

After inserting the values `510`, `82`, `830`, `11`, `383`, `647`, `899`, `261`, `410`, `514`, `815`, `888`, `972`, `238`, `292`, `953`.

Deleting the node `514` should not trigger any rebalancing:

Deleting the node `11` triggers multiple rotates for rebalancing:

Try yourself at https://www.cs.usfca.edu/~galles/visualization/RedBlack.html.

## Documentation ¶

### Overview ¶

Package adt implements useful abstract data types.

Example
```Output:

Overlapping range: &{Ivl:{Begin:7 End:20} Val:789}
Overlapping range: &{Ivl:{Begin:9 End:13} Val:456}
```

### Constants ¶

This section is empty.

### Variables ¶

This section is empty.

### Functions ¶

This section is empty.

### Types ¶

#### type BytesAffineComparable ¶

`type BytesAffineComparable []byte`

BytesAffineComparable treats empty byte arrays as > all other byte arrays

#### func (BytesAffineComparable) Compare ¶

`func (b BytesAffineComparable) Compare(c Comparable) int`

#### type Comparable ¶

```type Comparable interface {
// Compare gives the result of a 3-way comparison
// a.Compare(b) = 1 => a > b
// a.Compare(b) = 0 => a == b
// a.Compare(b) = -1 => a < b
Compare(c Comparable) int
}```

Comparable is an interface for trichotomic comparisons.

#### type Int64Comparable ¶

`type Int64Comparable int64`

#### func (Int64Comparable) Compare ¶

`func (v Int64Comparable) Compare(c Comparable) int`

#### type Interval ¶

```type Interval struct {
Begin Comparable
End   Comparable
}```

Interval implements a Comparable interval [begin, end) TODO: support different sorts of intervals: (a,b), [a,b], (a, b]

#### func NewBytesAffineInterval ¶

`func NewBytesAffineInterval(begin, end []byte) Interval`

#### func NewBytesAffinePoint ¶

`func NewBytesAffinePoint(b []byte) Interval`

#### func NewInt64Interval ¶

`func NewInt64Interval(a int64, b int64) Interval`

#### func NewInt64Point ¶

`func NewInt64Point(a int64) Interval`

#### func NewStringAffineInterval ¶

`func NewStringAffineInterval(begin, end string) Interval`

#### func NewStringAffinePoint ¶

`func NewStringAffinePoint(s string) Interval`

#### func NewStringInterval ¶

`func NewStringInterval(begin, end string) Interval`

#### func NewStringPoint ¶

`func NewStringPoint(s string) Interval`

#### func (*Interval) Compare ¶

`func (ivl *Interval) Compare(c Comparable) int`

Compare on an interval gives == if the interval overlaps.

#### type IntervalTree ¶

```type IntervalTree interface {
// Insert adds a node with the given interval into the tree.
Insert(ivl Interval, val interface{})
// Delete removes the node with the given interval from the tree, returning
// true if a node is in fact removed.
Delete(ivl Interval) bool
// Len gives the number of elements in the tree.
Len() int
// Height is the number of levels in the tree; one node has height 1.
Height() int
// MaxHeight is the expected maximum tree height given the number of nodes.
MaxHeight() int
// Visit calls a visitor function on every tree node intersecting the given interval.
// It will visit each interval [x, y) in ascending order sorted on x.
Visit(ivl Interval, ivv IntervalVisitor)
// Find gets the IntervalValue for the node matching the given interval
Find(ivl Interval) *IntervalValue
// Intersects returns true if there is some tree node intersecting the given interval.
Intersects(iv Interval) bool
// Contains returns true if the interval tree's keys cover the entire given interval.
Contains(ivl Interval) bool
// Stab returns a slice with all elements in the tree intersecting the interval.
Stab(iv Interval) []*IntervalValue
// Union merges a given interval tree into the receiver.
Union(inIvt IntervalTree, ivl Interval)
}```

IntervalTree represents a (mostly) textbook implementation of the "Introduction to Algorithms" (Cormen et al, 3rd ed.) chapter 13 red-black tree and chapter 14.3 interval tree with search supporting "stabbing queries".

#### func NewIntervalTree ¶

`func NewIntervalTree() IntervalTree`

NewIntervalTree returns a new interval tree.

#### type IntervalValue ¶

```type IntervalValue struct {
Ivl Interval
Val interface{}
}```

IntervalValue represents a range tree node that contains a range and a value.

#### type IntervalVisitor ¶

`type IntervalVisitor func(n *IntervalValue) bool`

IntervalVisitor is used on tree searches; return false to stop searching.

#### type StringAffineComparable ¶

`type StringAffineComparable string`

StringAffineComparable treats "" as > all other strings

#### func (StringAffineComparable) Compare ¶

`func (s StringAffineComparable) Compare(c Comparable) int`

#### type StringComparable ¶

`type StringComparable string`

#### func (StringComparable) Compare ¶

`func (s StringComparable) Compare(c Comparable) int`