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package btree

import "github.com/google/btree"

Package btree implements in-memory B-Trees of arbitrary degree.

btree implements an in-memory B-Tree for use as an ordered data structure. It is not meant for persistent storage solutions.

It has a flatter structure than an equivalent red-black or other binary tree, which in some cases yields better memory usage and/or performance. See some discussion on the matter here:

Note, though, that this project is in no way related to the C++ B-Tree implementation written about there.

Within this tree, each node contains a slice of items and a (possibly nil) slice of children. For basic numeric values or raw structs, this can cause efficiency differences when compared to equivalent C++ template code that stores values in arrays within the node:

* Due to the overhead of storing values as interfaces (each value needs to be stored as the value itself, then 2 words for the interface pointing to that value and its type), resulting in higher memory use. * Since interfaces can point to values anywhere in memory, values are most likely not stored in contiguous blocks, resulting in a higher number of cache misses.

These issues don't tend to matter, though, when working with strings or other heap-allocated structures, since C++-equivalent structures also must store pointers and also distribute their values across the heap.

This implementation is designed to be a drop-in replacement to gollrb.LLRB trees, (http://github.com/petar/gollrb), an excellent and probably the most widely used ordered tree implementation in the Go ecosystem currently. Its functions, therefore, exactly mirror those of llrb.LLRB where possible. Unlike gollrb, though, we currently don't support storing multiple equivalent values.

btree.go

❖ const ( DefaultFreeListSize = 32 )

❖ type BTree struct { // contains filtered or unexported fields }

BTree is an implementation of a B-Tree.

BTree stores Item instances in an ordered structure, allowing easy insertion, removal, and iteration.

Write operations are not safe for concurrent mutation by multiple goroutines, but Read operations are.

Example Code: tr := New(*btreeDegree) for i := Int(0); i < 10; i++ { tr.ReplaceOrInsert(i) } fmt.Println("len: ", tr.Len()) fmt.Println("get3: ", tr.Get(Int(3))) fmt.Println("get100: ", tr.Get(Int(100))) fmt.Println("del4: ", tr.Delete(Int(4))) fmt.Println("del100: ", tr.Delete(Int(100))) fmt.Println("replace5: ", tr.ReplaceOrInsert(Int(5))) fmt.Println("replace100:", tr.ReplaceOrInsert(Int(100))) fmt.Println("min: ", tr.Min()) fmt.Println("delmin: ", tr.DeleteMin()) fmt.Println("max: ", tr.Max()) fmt.Println("delmax: ", tr.DeleteMax()) fmt.Println("len: ", tr.Len()) Output: len: 10 get3: 3 get100: <nil> del4: 4 del100: <nil> replace5: 5 replace100: <nil> min: 0 delmin: 0 max: 100 delmax: 100 len: 8

New creates a new B-Tree with the given degree.

New(2), for example, will create a 2-3-4 tree (each node contains 1-3 items and 2-4 children).

❖ func NewWithFreeList(degree int, f *FreeList) *BTree

NewWithFreeList creates a new B-Tree that uses the given node free list.

Ascend calls the iterator for every value in the tree within the range [first, last], until iterator returns false.

❖ func (t *BTree) AscendGreaterOrEqual(pivot Item, iterator ItemIterator)

AscendGreaterOrEqual calls the iterator for every value in the tree within the range [pivot, last], until iterator returns false.

❖ func (t *BTree) AscendLessThan(pivot Item, iterator ItemIterator)

AscendLessThan calls the iterator for every value in the tree within the range [first, pivot), until iterator returns false.

❖ func (t *BTree) AscendRange(greaterOrEqual, lessThan Item, iterator ItemIterator)

AscendRange calls the iterator for every value in the tree within the range [greaterOrEqual, lessThan), until iterator returns false.

Clear removes all items from the btree. If addNodesToFreelist is true, t's nodes are added to its freelist as part of this call, until the freelist is full. Otherwise, the root node is simply dereferenced and the subtree left to Go's normal GC processes.

This can be much faster than calling Delete on all elements, because that requires finding/removing each element in the tree and updating the tree accordingly. It also is somewhat faster than creating a new tree to replace the old one, because nodes from the old tree are reclaimed into the freelist for use by the new one, instead of being lost to the garbage collector.

This call takes:

O(1): when addNodesToFreelist is false, this is a single operation. O(1): when the freelist is already full, it breaks out immediately O(freelist size): when the freelist is empty and the nodes are all owned by this tree, nodes are added to the freelist until full. O(tree size): when all nodes are owned by another tree, all nodes are iterated over looking for nodes to add to the freelist, and due to ownership, none are.

Clone clones the btree, lazily. Clone should not be called concurrently, but the original tree (t) and the new tree (t2) can be used concurrently once the Clone call completes.

The internal tree structure of b is marked read-only and shared between t and t2. Writes to both t and t2 use copy-on-write logic, creating new nodes whenever one of b's original nodes would have been modified. Read operations should have no performance degredation. Write operations for both t and t2 will initially experience minor slow-downs caused by additional allocs and copies due to the aforementioned copy-on-write logic, but should converge to the original performance characteristics of the original tree.

Delete removes an item equal to the passed in item from the tree, returning it. If no such item exists, returns nil.

DeleteMax removes the largest item in the tree and returns it. If no such item exists, returns nil.

DeleteMin removes the smallest item in the tree and returns it. If no such item exists, returns nil.

Descend calls the iterator for every value in the tree within the range [last, first], until iterator returns false.

❖ func (t *BTree) DescendGreaterThan(pivot Item, iterator ItemIterator)

DescendGreaterThan calls the iterator for every value in the tree within the range [last, pivot), until iterator returns false.

❖ func (t *BTree) DescendLessOrEqual(pivot Item, iterator ItemIterator)

DescendLessOrEqual calls the iterator for every value in the tree within the range [pivot, first], until iterator returns false.

❖ func (t *BTree) DescendRange(lessOrEqual, greaterThan Item, iterator ItemIterator)

DescendRange calls the iterator for every value in the tree within the range [lessOrEqual, greaterThan), until iterator returns false.

Get looks for the key item in the tree, returning it. It returns nil if unable to find that item.

Has returns true if the given key is in the tree.

Len returns the number of items currently in the tree.

Max returns the largest item in the tree, or nil if the tree is empty.

Min returns the smallest item in the tree, or nil if the tree is empty.

ReplaceOrInsert adds the given item to the tree. If an item in the tree already equals the given one, it is removed from the tree and returned. Otherwise, nil is returned.

nil cannot be added to the tree (will panic).

❖ type FreeList struct { // contains filtered or unexported fields }

FreeList represents a free list of btree nodes. By default each BTree has its own FreeList, but multiple BTrees can share the same FreeList. Two Btrees using the same freelist are safe for concurrent write access.

NewFreeList creates a new free list. size is the maximum size of the returned free list.

❖ type Int int

Int implements the Item interface for integers.

Less returns true if int(a) < int(b).

❖ type Item interface { // Less tests whether the current item is less than the given argument. // // This must provide a strict weak ordering. // If !a.Less(b) && !b.Less(a), we treat this to mean a == b (i.e. we can only // hold one of either a or b in the tree). Less (than Item) bool }

Item represents a single object in the tree.

❖ type ItemIterator func(i Item) bool

ItemIterator allows callers of Ascend* to iterate in-order over portions of the tree. When this function returns false, iteration will stop and the associated Ascend* function will immediately return.