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  <h1>Package btree</h1>


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			<dd><code>import "github.com/google/btree"</code></dd>
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				<p>
Package btree implements in-memory B-Trees of arbitrary degree.
</p>
<p>
btree implements an in-memory B-Tree for use as an ordered data structure.
It is not meant for persistent storage solutions.
</p>
<p>
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:
</p>
<pre><a href="http://google-opensource.blogspot.com/2013/01/c-containers-that-save-memory-and-time.html">http://google-opensource.blogspot.com/2013/01/c-containers-that-save-memory-and-time.html</a>
</pre>
<p>
Note, though, that this project is in no way related to the C++ B-Tree
implementation written about there.
</p>
<p>
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:
</p>
<pre>* 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.
</pre>
<p>
These issues don&#39;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.
</p>
<p>
This implementation is designed to be a drop-in replacement to gollrb.LLRB
trees, (<a href="http://github.com/petar/gollrb">http://github.com/petar/gollrb</a>), 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&#39;t
support storing multiple equivalent values.
</p>

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			<dl>
			
				<dd><a href="index.html#pkg-constants">Constants</a></dd>
			
			
				<dd><a href="index.html#BTree">type BTree</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#New">func New(degree int) *BTree</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#NewWithFreeList">func NewWithFreeList(degree int, f *FreeList) *BTree</a></dd>
				
				
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.Ascend">func (t *BTree) Ascend(iterator ItemIterator)</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.AscendGreaterOrEqual">func (t *BTree) AscendGreaterOrEqual(pivot Item, iterator ItemIterator)</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.AscendLessThan">func (t *BTree) AscendLessThan(pivot Item, iterator ItemIterator)</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.AscendRange">func (t *BTree) AscendRange(greaterOrEqual, lessThan Item, iterator ItemIterator)</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.Delete">func (t *BTree) Delete(item Item) Item</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.DeleteMax">func (t *BTree) DeleteMax() Item</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.DeleteMin">func (t *BTree) DeleteMin() Item</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.Descend">func (t *BTree) Descend(iterator ItemIterator)</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.DescendGreaterThan">func (t *BTree) DescendGreaterThan(pivot Item, iterator ItemIterator)</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.DescendLessOrEqual">func (t *BTree) DescendLessOrEqual(pivot Item, iterator ItemIterator)</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.DescendRange">func (t *BTree) DescendRange(lessOrEqual, greaterThan Item, iterator ItemIterator)</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.Get">func (t *BTree) Get(key Item) Item</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.Has">func (t *BTree) Has(key Item) bool</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.Len">func (t *BTree) Len() int</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.Max">func (t *BTree) Max() Item</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.Min">func (t *BTree) Min() Item</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#BTree.ReplaceOrInsert">func (t *BTree) ReplaceOrInsert(item Item) Item</a></dd>
				
			
				<dd><a href="index.html#FreeList">type FreeList</a></dd>
				
					
					<dd>&nbsp; &nbsp; <a href="index.html#NewFreeList">func NewFreeList(size int) *FreeList</a></dd>
				
				
				<dd><a href="index.html#Int">type Int</a></dd>
				
				
					<dd>&nbsp; &nbsp; <a href="index.html#Int.Less">func (a Int) Less(b Item) bool</a></dd>
				
			
				<dd><a href="index.html#Item">type Item</a></dd>
				
				
				<dd><a href="index.html#ItemIterator">type ItemIterator</a></dd>
				
				
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			<h4>Examples</h4>
			<dl>
			
			<dd><a class="exampleLink" href="index.html#example_BTree">BTree</a></dd>
			
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			<h4>Package files</h4>
			<p>
			<span style="font-size:90%">
			
				<a href="http://localhost:6060/src/github.com/google/btree/btree.go">btree.go</a>
			
			</span>
			</p>
		
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			<h2 class="toggleButton" title="Click to hide Internal Call Graph section">Internal call graph ▾</h2>
			<p>
			  In the call graph viewer below, each node
			  is a function belonging to this package
			  and its children are the functions it
			  calls&mdash;perhaps dynamically.
			</p>
			<p>
			  The root nodes are the entry points of the
			  package: functions that may be called from
			  outside the package.
			  There may be non-exported or anonymous
			  functions among them if they are called
			  dynamically from another package.
			</p>
			<p>
			  Click a node to visit that function's source code.
			  From there you can visit its callers by
			  clicking its declaring <code>func</code>
			  token.
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			  Functions may be omitted if they were
			  determined to be unreachable in the
			  particular programs or tests that were
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			<h2 id="pkg-constants">Constants</h2>
			
				<pre>const (
    <span id="DefaultFreeListSize">DefaultFreeListSize</span> = 32
)</pre>
				
			
			<h2 id="BTree">type <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=15979:16064#L527">BTree</a></h2>
			<pre>type BTree struct {
    <span class="comment">// contains filtered or unexported fields</span>
}</pre>
			<p>
BTree is an implementation of a B-Tree.
</p>
<p>
BTree stores Item instances in an ordered structure, allowing easy insertion,
removal, and iteration.
</p>
<p>
Write operations are not safe for concurrent mutation by multiple
goroutines, but Read operations are.
</p>


			<div id="example_BTree" class="toggle">
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		<p class="exampleHeading toggleButton">▹ <span class="text">Example</span></p>
	</div>
	<div class="expanded">
		<p class="exampleHeading toggleButton">▾ <span class="text">Example</span></p>
		
		
			<p>Code:</p>
			<pre class="code">tr := New(*btreeDegree)
for i := Int(0); i &lt; 10; i++ {
    tr.ReplaceOrInsert(i)
}
fmt.Println(&#34;len:       &#34;, tr.Len())
fmt.Println(&#34;get3:      &#34;, tr.Get(Int(3)))
fmt.Println(&#34;get100:    &#34;, tr.Get(Int(100)))
fmt.Println(&#34;del4:      &#34;, tr.Delete(Int(4)))
fmt.Println(&#34;del100:    &#34;, tr.Delete(Int(100)))
fmt.Println(&#34;replace5:  &#34;, tr.ReplaceOrInsert(Int(5)))
fmt.Println(&#34;replace100:&#34;, tr.ReplaceOrInsert(Int(100)))
fmt.Println(&#34;min:       &#34;, tr.Min())
fmt.Println(&#34;delmin:    &#34;, tr.DeleteMin())
fmt.Println(&#34;max:       &#34;, tr.Max())
fmt.Println(&#34;delmax:    &#34;, tr.DeleteMax())
fmt.Println(&#34;len:       &#34;, tr.Len())
<span class="comment"></pre>
			
			<p>Output:</p>
			<pre class="output">len:        10
get3:       3
get100:     &lt;nil&gt;
del4:       4
del100:     &lt;nil&gt;
replace5:   5
replace100: &lt;nil&gt;
min:        0
delmin:     0
max:        100
delmax:     100
len:        8
</pre>
			
		
	</div>
</div>

			
				<h3 id="New">func <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=4217:4244#L106">New</a></h3>
				<pre>func New(degree <a href="../../../builtin/index.html#int">int</a>) *<a href="index.html#BTree">BTree</a></pre>
				<p>
New creates a new B-Tree with the given degree.
</p>
<p>
New(2), for example, will create a 2-3-4 tree (each node contains 1-3 items
and 2-4 children).
</p>

				
				<h3 id="NewWithFreeList">func <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=4392:4444#L111">NewWithFreeList</a></h3>
				<pre>func NewWithFreeList(degree <a href="../../../builtin/index.html#int">int</a>, f *<a href="index.html#FreeList">FreeList</a>) *<a href="index.html#BTree">BTree</a></pre>
				<p>
NewWithFreeList creates a new B-Tree that uses the given node free list.
</p>

				
				<h3 id="BTree.Ascend">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=19353:19398#L650">Ascend</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) Ascend(iterator <a href="index.html#ItemIterator">ItemIterator</a>)</pre>
				<p>
Ascend calls the iterator for every value in the tree within the range
[first, last], until iterator returns false.
</p>

				
				<h3 id="BTree.AscendGreaterOrEqual">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=19063:19134#L641">AscendGreaterOrEqual</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) AscendGreaterOrEqual(pivot <a href="index.html#Item">Item</a>, iterator <a href="index.html#ItemIterator">ItemIterator</a>)</pre>
				<p>
AscendGreaterOrEqual calls the iterator for every value in the tree within
the range [pivot, last], until iterator returns false.
</p>

				
				<h3 id="BTree.AscendLessThan">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=18764:18829#L632">AscendLessThan</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) AscendLessThan(pivot <a href="index.html#Item">Item</a>, iterator <a href="index.html#ItemIterator">ItemIterator</a>)</pre>
				<p>
AscendLessThan calls the iterator for every value in the tree within the range
[first, pivot), until iterator returns false.
</p>

				
				<h3 id="BTree.AscendRange">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=18441:18522#L623">AscendRange</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) AscendRange(greaterOrEqual, lessThan <a href="index.html#Item">Item</a>, iterator <a href="index.html#ItemIterator">ItemIterator</a>)</pre>
				<p>
AscendRange calls the iterator for every value in the tree within the range
[greaterOrEqual, lessThan), until iterator returns false.
</p>

				
				<h3 id="BTree.Delete">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=17507:17545#L589">Delete</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) Delete(item <a href="index.html#Item">Item</a>) <a href="index.html#Item">Item</a></pre>
				<p>
Delete removes an item equal to the passed in item from the tree, returning
it.  If no such item exists, returns nil.
</p>

				
				<h3 id="BTree.DeleteMax">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=17878:17910#L601">DeleteMax</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) DeleteMax() <a href="index.html#Item">Item</a></pre>
				<p>
DeleteMax removes the largest item in the tree and returns it.
If no such item exists, returns nil.
</p>

				
				<h3 id="BTree.DeleteMin">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=17697:17729#L595">DeleteMin</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) DeleteMin() <a href="index.html#Item">Item</a></pre>
				<p>
DeleteMin removes the smallest item in the tree and returns it.
If no such item exists, returns nil.
</p>

				
				<h3 id="BTree.Descend">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=20556:20602#L686">Descend</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) Descend(iterator <a href="index.html#ItemIterator">ItemIterator</a>)</pre>
				<p>
Descend calls the iterator for every value in the tree within the range
[last, first], until iterator returns false.
</p>

				
				<h3 id="BTree.DescendGreaterThan">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=20265:20334#L677">DescendGreaterThan</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) DescendGreaterThan(pivot <a href="index.html#Item">Item</a>, iterator <a href="index.html#ItemIterator">ItemIterator</a>)</pre>
				<p>
DescendGreaterThan calls the iterator for every value in the tree within
the range (pivot, last], until iterator returns false.
</p>

				
				<h3 id="BTree.DescendLessOrEqual">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=19964:20033#L668">DescendLessOrEqual</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) DescendLessOrEqual(pivot <a href="index.html#Item">Item</a>, iterator <a href="index.html#ItemIterator">ItemIterator</a>)</pre>
				<p>
DescendLessOrEqual calls the iterator for every value in the tree within the range
[pivot, first], until iterator returns false.
</p>

				
				<h3 id="BTree.DescendRange">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=19635:19717#L659">DescendRange</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) DescendRange(lessOrEqual, greaterThan <a href="index.html#Item">Item</a>, iterator <a href="index.html#ItemIterator">ItemIterator</a>)</pre>
				<p>
DescendRange calls the iterator for every value in the tree within the range
[lessOrEqual, greaterThan), until iterator returns false.
</p>

				
				<h3 id="BTree.Get">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=20804:20838#L695">Get</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) Get(key <a href="index.html#Item">Item</a>) <a href="index.html#Item">Item</a></pre>
				<p>
Get looks for the key item in the tree, returning it.  It returns nil if
unable to find that item.
</p>

				
				<h3 id="BTree.Has">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=21210:21244#L713">Has</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) Has(key <a href="index.html#Item">Item</a>) <a href="../../../builtin/index.html#bool">bool</a></pre>
				<p>
Has returns true if the given key is in the tree.
</p>

				
				<h3 id="BTree.Len">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=21334:21359#L718">Len</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) Len() <a href="../../../builtin/index.html#int">int</a></pre>
				<p>
Len returns the number of items currently in the tree.
</p>

				
				<h3 id="BTree.Max">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=21105:21131#L708">Max</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) Max() <a href="index.html#Item">Item</a></pre>
				<p>
Max returns the largest item in the tree, or nil if the tree is empty.
</p>

				
				<h3 id="BTree.Min">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=20979:21005#L703">Min</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) Min() <a href="index.html#Item">Item</a></pre>
				<p>
Min returns the smallest item in the tree, or nil if the tree is empty.
</p>

				
				<h3 id="BTree.ReplaceOrInsert">func (*BTree) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=16819:16866#L564">ReplaceOrInsert</a></h3>
				<pre>func (t *<a href="index.html#BTree">BTree</a>) ReplaceOrInsert(item <a href="index.html#Item">Item</a>) <a href="index.html#Item">Item</a></pre>
				<p>
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.
</p>
<p>
nil cannot be added to the tree (will panic).
</p>

				
			<h2 id="FreeList">type <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=3258:3300#L70">FreeList</a></h2>
			<pre>type FreeList struct {
    <span class="comment">// contains filtered or unexported fields</span>
}</pre>
			<p>
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 not safe for concurrent write access.
</p>


				<h3 id="NewFreeList">func <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=3397:3433#L76">NewFreeList</a></h3>
				<pre>func NewFreeList(size <a href="../../../builtin/index.html#int">int</a>) *<a href="index.html#FreeList">FreeList</a></pre>
				<p>
NewFreeList creates a new free list.
size is the maximum size of the returned free list.
</p>

				
			<h2 id="Int">type <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=21433:21445#L723">Int</a></h2>
			<pre>type Int <a href="../../../builtin/index.html#int">int</a></pre>
			<p>
Int implements the Item interface for integers.
</p>


				<h3 id="Int.Less">func (Int) <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=21488:21518#L726">Less</a></h3>
				<pre>func (a <a href="index.html#Int">Int</a>) Less(b <a href="index.html#Item">Item</a>) <a href="../../../builtin/index.html#bool">bool</a></pre>
				<p>
Less returns true if int(a) &lt; int(b).
</p>

				
			<h2 id="Item">type <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=2623:2915#L48">Item</a></h2>
			<pre>type Item interface {
    <span class="comment">// Less tests whether the current item is less than the given argument.</span>
    <span class="comment">//</span>
    <span class="comment">// This must provide a strict weak ordering.</span>
    <span class="comment">// If !a.Less(b) &amp;&amp; !b.Less(a), we treat this to mean a == b (i.e. we can only</span>
    <span class="comment">// hold one of either a or b in the tree).</span>
    Less(than <a href="index.html#Item">Item</a>) <a href="../../../builtin/index.html#bool">bool</a>
}</pre>
			<p>
Item represents a single object in the tree.
</p>


			<h2 id="ItemIterator">type <a href="http://localhost:6060/src/github.com/google/btree/btree.go?s=4025:4060#L100">ItemIterator</a></h2>
			<pre>type ItemIterator func(i <a href="index.html#Item">Item</a>) <a href="../../../builtin/index.html#bool">bool</a></pre>
			<p>
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.
</p>


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