Class: Salgo::Btree

Inherits:
Object
  • Object
show all
Defined in:
lib/salgo/btree.rb

Defined Under Namespace

Classes: Key, Node

Instance Attribute Summary collapse

Instance Method Summary collapse

Constructor Details

#initialize(minnodes = 2) ⇒ Btree

Returns a new instance of Btree.



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# File 'lib/salgo/btree.rb', line 188

def initialize(minnodes=2)
    @minnodes = ( minnodes < 2 )? 2 : minnodes
    @maxnodes = 2 * minnodes
    @root     = Node.new()
    @size     = 0
end

Instance Attribute Details

#size ⇒ Object (readonly)

Returns the value of attribute size.



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# File 'lib/salgo/btree.rb', line 186

def size
  @size
end

Instance Method Details

#[]=(key, val) ⇒ Object Also known as: store

Set the key in this tree to the given value. If there is already a value at the given key, it is replaced and the old value is returned. Nil is returned otherwise.



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# File 'lib/salgo/btree.rb', line 485

def []=(key, val)

    k = find_key(Key.new(key))
    
    if ( k.nil? )
        insert(key, val)
        nil
    else
        v = k.val
        k.val = val
        v
    end
end

#delete(key) ⇒ Object 



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# File 'lib/salgo/btree.rb', line 473

def delete(key)
    
    key = delete_key(Key.new(key))
    
    (key.nil?)? nil : key.val
end

#delete_key(key, node = @root) ⇒ Object 



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# File 'lib/salgo/btree.rb', line 410

def delete_key(key, node=@root)
    
    candidate, candidate_idx = node.find_node_or_key_containing_key(key)
    
    return nil if candidate.nil?
    
    # Delete from this node.
    if ( candidate.is_a?(Key) )
        
        # If it's a simple delete...
        if node.leaf? 
            node.keys.delete_at(candidate_idx)
            @size -= 1
            return candidate
        elsif has_extra_keys?(node.nodes[candidate_idx])
            node.keys[candidate_idx] = delete_max_key(node.nodes[candidate_idx])
            return candidate
        elsif has_extra_keys?(node.nodes[candidate_idx+1])
            node.keys[candidate_idx] = delete_min_key(node.nodes[candidate_idx+1])
            return candidate
        else
            node = merge_with_right(node, candidate_idx)
            
            # The merge_with_right call left the root with no keys and 1 child node. 
            # Replace the root and delete from the root.
            @root = @root.nodes[0] if ( @root.nodes.size == 1 )

            return delete_key(key, node)
        end
        
    elsif candidate.is_a?(Node)
        
        # Ensure that the node can sustain a delete BEFORE entering it...
        unless has_extra_keys?(candidate) 
            
            if ( node.first_node?(candidate) )
                if ( has_extra_keys?(node.nodes[1]))
                    another_key, another_node = node.nodes[1].take_min
                    candidate.put_max(node.keys[0], another_node)
                    node.keys[0] = another_key
                else
                    merge_with_right(node, candidate_idx)
                end
            #elsif ( node.last_node?(candidate) )
            else
                if ( has_extra_keys?(node.nodes[candidate_idx-1]) )
                    another_key, another_node = node.nodes[candidate_idx-1].take_max
                    candidate.put_min(node.keys[candidate_idx-1], another_node)
                    node.keys[candidate_idx-1] = another_key
                else
                    merge_with_left(node, candidate_idx)
                end
            end
        end
        
        # If one of the above merges removed all keys from the root, then there is only 1 node.
        # Promote that node as the root.
        candidate = @root = @root.nodes[0] if ( @root.nodes.size == 1 )                    

        delete_key(key, candidate)                
    end
end

#delete_max_key(node = @root) ⇒ Object

Delete from a subtree. We assume the node can withstand delete when called. They key object is returned.



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# File 'lib/salgo/btree.rb', line 330

def delete_max_key(node=@root)
    
    return nil if @size == 0

    if root?(node) and @root.keys.size == 0 and @root.nodes.size == 1
        @root = node = @root.nodes[0]
    end
    
    while(true) do
        if ( node.leaf? )
            @size -= 1
            return node.take_max()[0]
        else
            
            # Fix up the node before deleting from it.
            if has_minimum_keys?(node.nodes[-1])
                if has_minimum_keys?(node.nodes[-2])

                    node = merge_with_left(node, node.nodes.size-1)
                    
                else

                    # Pull the max key and node from our "left" sibling.
                    # Make the left key be our parent and put the node
                    # in the minimum of the right tree node.
                    another_key, another_node = node.nodes[-2].take_max
                    
                    node.nodes[-1].put_min(node.keys[-1], another_node)
                    node.keys[-1] = another_key

                    node = node.nodes[-1]

                end
            else
                node = node.nodes[-1]
            end
        end
    end
end

#delete_min_key(node = @root) ⇒ Object

Delete from a subtree. We assume the node can withstand delete when called. The key object is returned.



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# File 'lib/salgo/btree.rb', line 372

def delete_min_key(node=@root)
    
    return nil if @size == 0
    
    if root?(node) and @root.keys.size == 0 and @root.nodes.size == 1
        @root = node = @root.nodes[0]
    end
    
    while(true) do
        if ( node.leaf? )
            @size -= 1
            return node.take_min()[0]
        else
            # Fix up the node before deleting from it.
            if has_minimum_keys?(node.nodes[0])
                if has_minimum_keys?(node.nodes[1]) 
                    node = merge_with_right(node, 0)
                    
                else

                    # Pull the min key and node from our "right" sibling.
                    # Make the right key be our parent and put the node
                    # in the minimum of the right tree node.
                    another_key, another_node = node.nodes[1].take_min
                    
                    node.nodes[0].put_max(node.keys[0], another_node)
                    node.keys[0] = another_key

                    node = node.nodes[0]
                end
            else
                node = node.nodes[0]
            end
                
        end
    end
end

#each(node = @root, &call) ⇒ Object 



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# File 'lib/salgo/btree.rb', line 499

def each(node=@root, &call)
    
    proc_child = ( node.leaf?() )? lambda { |x| } : lambda { |child_node| each(child_node, &call) }
    
    index = 0 


    node.keys.each do |key|
        proc_child.call(node.nodes[index])
        
        call.call(key.key, key.val)
        
        index+=1
        
    end
    
    proc_child.call(node.nodes[index])
end

#find(key) ⇒ Object Also known as: [] 



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# File 'lib/salgo/btree.rb', line 286

def find(key)
    k = find_key(Key.new(key, nil))
    
    (k.nil?) ? nil : k.val
end

#find_key(key) ⇒ Object 



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# File 'lib/salgo/btree.rb', line 267

def find_key(key)

    node = @root

    candidate, candidate_idx = node.find_node_or_key_containing_key(key)

    while( ! candidate.nil?)
        if ( candidate.is_a?(Key) )
        
            return candidate
        end
        
        node = candidate
        candidate, candidate_idx = node.find_node_or_key_containing_key(key)
    end
    
    return nil
end

#full?(node) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/salgo/btree.rb', line 199

def full?(node)
    node.keys.size == @maxnodes-1
end

#has_extra_keys?(node) ⇒ Boolean

Is there an extra key to take, should we need it.

Returns:

  • (Boolean) 


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# File 'lib/salgo/btree.rb', line 213

def has_extra_keys?(node)
    node.keys.size >= @minnodes
end

#has_key?(key) ⇒ Boolean Also known as: member?, include?, key?

Returns:

  • (Boolean) 


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# File 'lib/salgo/btree.rb', line 518

def has_key?(key)
    ! find_key(Key.new(key)).nil?
end

#has_minimum_keys?(node) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/salgo/btree.rb', line 208

def has_minimum_keys?(node)
    node.keys.size < @minnodes
end

#insert(key, val) ⇒ Object

Insert a new value at the given key. Duplicate values are allowed in this data structure and insert does not prevent them. The []= method will replace values.



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# File 'lib/salgo/btree.rb', line 227

def insert(key, val)
    key = Key.new(key, val)
    
    # Always make sure our special friend "root" is OK and has room for an insert.
    split_root if full?(@root)

    parent_node = nil
    node = @root

    not_inserted = true
    
    while(not_inserted)
        if ( full? node )
                
            median_key, lnode, rnode = node.split()
            
            # NOTE: Because we always split full root nodes, we will never enter here with parent_node=nil
            # Oh good, we can do a normal split and insert the result in the parent.
            parent_node.insert(median_key, lnode, rnode)
            
            if ( key < median_key )
                node = lnode
            else
                node = rnode
            end
        end
        
        # Can we insert?
        if ( node.leaf? )
            node.insert(key)
            @size += 1
            not_inserted = false
        else
            # which node to examine?
            parent_node = node
            node = node.find_node_containing_key(key)
        end
    end
end

#mergable?(node) ⇒ Boolean

Does the given node have enough keys (and perhaps nodes) to merge with another node?

Returns:

  • (Boolean) 


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# File 'lib/salgo/btree.rb', line 204

def mergable?(node)
    node.keys.size < @minnodes
end

#merge_with_left(parent, child_index) ⇒ Object

Given the parent node and the child_index of a child node, this method will merge with the sibling to the left of the child. The resulting “unknown” tree will be placed on the left and the known-filled node will be placed in the child node’s current spot. The new target node is returned.



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# File 'lib/salgo/btree.rb', line 298

def merge_with_left(parent, child_index)
    
    child      = parent.nodes[child_index]
    sibling    = parent.nodes[child_index-1]
    node       = Node.new()
    
    node.nodes = sibling.nodes + child.nodes
    
    node.keys  = sibling.keys  + [ parent.keys[child_index-1] ] + child.keys
    parent.take(child_index-1)
    parent.nodes[child_index-1] = node
    node
end

#merge_with_right(parent, child_index) ⇒ Object

Same as merge_with_right, but the roles are reversed as are the locations of the resulting subtrees. The new target node is returned.



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# File 'lib/salgo/btree.rb', line 315

def merge_with_right(parent, child_index)
    child      = parent.nodes[child_index]
    sibling    = parent.nodes[child_index+1]
    node       = Node.new()
    
    node.nodes =  child.nodes + sibling.nodes
    
    node.keys  = child.keys  + [ parent.keys[child_index] ] + sibling.keys
    parent.take(child_index)
    parent.nodes[child_index] = node
    node
end

#root?(node) ⇒ Boolean

Returns:

  • (Boolean) 


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# File 'lib/salgo/btree.rb', line 195

def root?(node) 
    @root.equal? node 
end

#split_root ⇒ Object 



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# File 'lib/salgo/btree.rb', line 217

def split_root
    node = Node.new()
    
    node.insert(*@root.split())
    
    @root = node
end