def __init__(self, degree):
# This method is complete.
self.degree = degree
self.rootNode = BTreeNode(degree)
# If time, file creation code, etc.
self.nodes = {}
self.stackOfNodes = MyStack()
self.rootNode.setIndex(1)
self.writeAt(1, self.rootNode)
self.rootIndex = 1
self.freeIndex = 2
def __init__(self, degree):
# This method is complete.
self.degree = degree
self.rootNode = BTreeNode(degree)
# If time, file creation code, etc.
self.nodes = {}
self.stackOfNodes = MyStack()
self.rootNode.setIndex(1)
self.writeAt(1, self.rootNode)
self.rootIndex = 1
self.freeIndex = 2
def insert(self, anItem):
''' Answer None if the BTree already contains a matching
item. If not, insert a deep copy of anItem and answer
anItem.
'''
searchResult = self.searchTree(anItem) #search for anItem
if searchResult['found']: #if anItem already exists in the tree, return None
return None
else: #if anItem doesn't exist in the tree
insertNode = self.readFrom(searchResult['fileIndex']) #get the node anItem should belong in
if insertNode.isFull(): #if the node is full, need to split the node
toParent = deepcopy(anItem) #make a deepcopy of the item we want to insert
leftChild = None #since inserting into a leaf node, left and right children are None
rightChild = None
while insertNode.isFull():
splitNode = insertNode.addItemAndSplit(toParent, leftChild, rightChild) #split the full node
splitNode.setIndex(self.freeIndex) #set the index of the new node to be the next available index
self.freeIndex += 1 #increment the free index number
toParent = deepcopy(insertNode.getItems()[insertNode.getNumberOfKeys()-1]) #get the item that will go to the parent node
insertNode.getItems()[insertNode.getNumberOfKeys()-1] = None #get rid of the record of the parent item
insertNode.getChild()[insertNode.getNumberOfKeys()] = None #get rid of the right child of the parent in the insertNode
insertNode.setNumberOfKeys(insertNode.getNumberOfKeys()-1)
leftChild = insertNode.getIndex() #get the left and right indices of the parent
rightChild = splitNode.getIndex()
self.writeAt(leftChild, insertNode) #write both nodes to the file
self.writeAt(rightChild, splitNode)
insertNode = self.stackOfNodes.pop() #get the parent node
if insertNode == None: #if there is no parent, create a new root node
insertNode = BTreeNode(self.degree) #create a new node
insertNode.setIndex(self.freeIndex) #set the index of the new root node
self.rootNode = insertNode
self.rootIndex = self.freeIndex #set the root index
self.freeIndex += 1 #increment the free index number
insertNode.insertItem(toParent, leftChild, rightChild)#if the parent node isn't full, just insert the item
self.writeAt(insertNode.getIndex(), insertNode) #write the final node to the file
else: #there is room for anItem, so just perform an insert
insertNode.insertItem(deepcopy(anItem))
self.writeAt(searchResult['fileIndex'], insertNode) #write the node to the file
return anItem #return the item
def __init__(self, table_dir, column, p) :
self.table_dir = table_dir
self.column = column
infile = open('{}/header'.format(table_dir),'r')
header = infile.read().strip().split(',')
if column in header:
self.colnum = header.index(column) # set this from dir/header and check it exists!
else:
print('Column named {} does not exist!'.format(column))
infile.close()
self.p = p
self.root = BTreeNode(p)
def delete(self, anItem):
''' Answer None if a matching item is not found. If found,
answer the entire item.
'''
searchResult = self.searchTree(anItem)
n = self.degree
if searchResult['found']: #the item is in the tree; delete it
aNode = self.readFrom(
searchResult['fileIndex']) #get the node that contains anItem
nodeIndex = searchResult['nodeIndex']
done = False
if not aNode.isLeaf(
): #if anItem is in a leaf node, find the inorder successor
(ioSuc, iosNode) = self.inorderSuccessor(aNode, nodeIndex)
searchResult = self.searchTree(
ioSuc
) #search the tree in order to get the stack of nodes on the search path
aNode.getItems(
)[nodeIndex] = ioSuc #replace anItem with the inorder successor
iosNode.removeItem(
0) #remove the inorder successor from its original node
self.writeAt(aNode.getIndex(),
aNode) #write the revised aNode to the file
aNode = iosNode #reset what aNode refers to
anItem = ioSuc
else: #if anItem was already in a leaf node
aNode.removeItem(nodeIndex) #remove anItem from the leaf node
while not done and aNode.getNumberOfKeys() < n and aNode.getIndex(
) != self.rootIndex: #while aNode has less than n keys and is not the root
parentNode = self.stackOfNodes.pop() #get the parent node
(parentIndex,
siblingNode, sibSide) = self.findParentAndSibling(
anItem, parentNode) #get the parent index and the sibling
totNumKeys = siblingNode.getNumberOfKeys(
) + aNode.getNumberOfKeys(
) + 1 #find the total number of keys, including the parent item
tempNode = BTreeNode(2 * n) #create a temporary BTreeNode
if sibSide == "right": #if using the right sibling, copy aNode, then parent, then sibling
tempNode.copyItemsAndChildren(aNode, 0,
aNode.getNumberOfKeys() - 1,
0)
tempNode.getItems()[aNode.getNumberOfKeys(
)] = parentNode.getItems()[parentIndex]
tempNode.copyItemsAndChildren(
siblingNode, 0,
siblingNode.getNumberOfKeys() - 1,
aNode.getNumberOfKeys() + 1)
else: #if using the left sibling, copy the sibling, then parent, then aNode
tempNode.copyItemsAndChildren(
siblingNode, 0,
siblingNode.getNumberOfKeys() - 1, 0)
tempNode.getItems()[siblingNode.getNumberOfKeys(
)] = parentNode.getItems()[parentIndex]
tempNode.copyItemsAndChildren(
aNode, 0,
aNode.getNumberOfKeys() - 1,
siblingNode.getNumberOfKeys() + 1)
aNode.clear() #clear the items and children from the two nodes
siblingNode.clear()
if totNumKeys > 2 * n: #case 2a: redistribute
sepKey = (totNumKeys +
1) // 2 #find the new separating key
aNode.copyItemsAndChildren(
tempNode, 0, sepKey - 2, 0
) #put the items of the temp node back to where they belong, redistributed
parentNode.getItems()[parentIndex] = tempNode.getItems()[
sepKey - 1]
siblingNode.copyItemsAndChildren(tempNode, sepKey,
totNumKeys - 1, 0)
aNode.setNumberOfKeys(sepKey - 1)
siblingNode.setNumberOfKeys(totNumKeys - sepKey)
else: #case 2b: merge
parentNode.removeItem(
parentIndex
) #remove the parent item from the parent node
if sibSide == "right": #remove the child representing the right sibling
parentNode.removeChild(parentIndex + 1)
if parentNode.getNumberOfKeys(
) == 0: #if the parent is now empty after the merge, make aNode the root of the tree
done = True
self.rootNode = aNode
self.rootIndex = aNode.getIndex()
aNode.copyItemsAndChildren(
tempNode, 0, totNumKeys - 1,
0) #merge all the items into aNode
aNode.setNumberOfKeys(totNumKeys)
else: #remove the child representing the right sibling (aNode)
parentNode.removeChild(parentIndex + 1)
if parentNode.getNumberOfKeys(
) == 0: #if the parent is now empty after the merge, make sibNode the root of the tree
done = True
self.rootNode = siblingNode
self.rootIndex = siblingNode.getIndex()
siblingNode.copyItemsAndChildren(
tempNode, 0, totNumKeys - 1,
0) #merge all the items into the sibling node
siblingNode.setNumberOfKeys(totNumKeys)
self.writeAt(aNode.getIndex(),
aNode) #write the updates to the file
self.writeAt(siblingNode.getIndex(), siblingNode)
self.writeAt(parentNode.getIndex(), parentNode)
aNode = parentNode #move up the tree and check if it's ok
else: #the item is not in the tree; return None
return None
def insert(self, anItem):
''' Answer None if the BTree already contains a matching
item. If not, insert a deep copy of anItem and answer
anItem.
'''
searchResult = self.searchTree(anItem) #search for anItem
if searchResult[
'found']: #if anItem already exists in the tree, return None
return None
else: #if anItem doesn't exist in the tree
insertNode = self.readFrom(searchResult['fileIndex']
) #get the node anItem should belong in
if insertNode.isFull(
): #if the node is full, need to split the node
toParent = deepcopy(
anItem) #make a deepcopy of the item we want to insert
leftChild = None #since inserting into a leaf node, left and right children are None
rightChild = None
while insertNode.isFull():
splitNode = insertNode.addItemAndSplit(
toParent, leftChild, rightChild) #split the full node
splitNode.setIndex(
self.freeIndex
) #set the index of the new node to be the next available index
self.freeIndex += 1 #increment the free index number
toParent = deepcopy(insertNode.getItems()[
insertNode.getNumberOfKeys() -
1]) #get the item that will go to the parent node
insertNode.getItems()[
insertNode.getNumberOfKeys() -
1] = None #get rid of the record of the parent item
insertNode.getChild()[insertNode.getNumberOfKeys(
)] = None #get rid of the right child of the parent in the insertNode
insertNode.setNumberOfKeys(insertNode.getNumberOfKeys() -
1)
leftChild = insertNode.getIndex(
) #get the left and right indices of the parent
rightChild = splitNode.getIndex()
self.writeAt(leftChild,
insertNode) #write both nodes to the file
self.writeAt(rightChild, splitNode)
insertNode = self.stackOfNodes.pop() #get the parent node
if insertNode == None: #if there is no parent, create a new root node
insertNode = BTreeNode(self.degree) #create a new node
insertNode.setIndex(
self.freeIndex
) #set the index of the new root node
self.rootNode = insertNode
self.rootIndex = self.freeIndex #set the root index
self.freeIndex += 1 #increment the free index number
insertNode.insertItem(
toParent, leftChild, rightChild
) #if the parent node isn't full, just insert the item
self.writeAt(insertNode.getIndex(),
insertNode) #write the final node to the file
else: #there is room for anItem, so just perform an insert
insertNode.insertItem(deepcopy(anItem))
self.writeAt(searchResult['fileIndex'],
insertNode) #write the node to the file
return anItem #return the item
class BTree:
''' This module implements the BTree class -- a tree of BTreeNodes. Items can
be inserted and deleted from the tree. Each node must have at least
degree items in it (except for the root node)
'''
def __init__(self, degree):
# This method is complete.
self.degree = degree
self.rootNode = BTreeNode(degree)
# If time, file creation code, etc.
self.nodes = {}
self.stackOfNodes = MyStack()
self.rootNode.setIndex(1)
self.writeAt(1, self.rootNode)
self.rootIndex = 1
self.freeIndex = 2
def __str__(self):
# This method is complete.
st = ' The degree of the BTree is ' + str(self.degree)+\
'.\n'
st += ' The index of the root node is ' + \
str(self.rootIndex) + '.\n'
for x in range(1, self.freeIndex):
node = self.readFrom(x)
if node.getNumberOfKeys() > 0:
st += str(node)
return st
def delete(self, anItem):
''' Answer None if a matching item is not found. If found,
answer the entire item.
'''
searchResult = self.searchTree(anItem)
n = self.degree
if searchResult['found']: #the item is in the tree; delete it
aNode = self.readFrom(
searchResult['fileIndex']) #get the node that contains anItem
nodeIndex = searchResult['nodeIndex']
done = False
if not aNode.isLeaf(
): #if anItem is in a leaf node, find the inorder successor
(ioSuc, iosNode) = self.inorderSuccessor(aNode, nodeIndex)
searchResult = self.searchTree(
ioSuc
) #search the tree in order to get the stack of nodes on the search path
aNode.getItems(
)[nodeIndex] = ioSuc #replace anItem with the inorder successor
iosNode.removeItem(
0) #remove the inorder successor from its original node
self.writeAt(aNode.getIndex(),
aNode) #write the revised aNode to the file
aNode = iosNode #reset what aNode refers to
anItem = ioSuc
else: #if anItem was already in a leaf node
aNode.removeItem(nodeIndex) #remove anItem from the leaf node
while not done and aNode.getNumberOfKeys() < n and aNode.getIndex(
) != self.rootIndex: #while aNode has less than n keys and is not the root
parentNode = self.stackOfNodes.pop() #get the parent node
(parentIndex,
siblingNode, sibSide) = self.findParentAndSibling(
anItem, parentNode) #get the parent index and the sibling
totNumKeys = siblingNode.getNumberOfKeys(
) + aNode.getNumberOfKeys(
) + 1 #find the total number of keys, including the parent item
tempNode = BTreeNode(2 * n) #create a temporary BTreeNode
if sibSide == "right": #if using the right sibling, copy aNode, then parent, then sibling
tempNode.copyItemsAndChildren(aNode, 0,
aNode.getNumberOfKeys() - 1,
0)
tempNode.getItems()[aNode.getNumberOfKeys(
)] = parentNode.getItems()[parentIndex]
tempNode.copyItemsAndChildren(
siblingNode, 0,
siblingNode.getNumberOfKeys() - 1,
aNode.getNumberOfKeys() + 1)
else: #if using the left sibling, copy the sibling, then parent, then aNode
tempNode.copyItemsAndChildren(
siblingNode, 0,
siblingNode.getNumberOfKeys() - 1, 0)
tempNode.getItems()[siblingNode.getNumberOfKeys(
)] = parentNode.getItems()[parentIndex]
tempNode.copyItemsAndChildren(
aNode, 0,
aNode.getNumberOfKeys() - 1,
siblingNode.getNumberOfKeys() + 1)
aNode.clear() #clear the items and children from the two nodes
siblingNode.clear()
if totNumKeys > 2 * n: #case 2a: redistribute
sepKey = (totNumKeys +
1) // 2 #find the new separating key
aNode.copyItemsAndChildren(
tempNode, 0, sepKey - 2, 0
) #put the items of the temp node back to where they belong, redistributed
parentNode.getItems()[parentIndex] = tempNode.getItems()[
sepKey - 1]
siblingNode.copyItemsAndChildren(tempNode, sepKey,
totNumKeys - 1, 0)
aNode.setNumberOfKeys(sepKey - 1)
siblingNode.setNumberOfKeys(totNumKeys - sepKey)
else: #case 2b: merge
parentNode.removeItem(
parentIndex
) #remove the parent item from the parent node
if sibSide == "right": #remove the child representing the right sibling
parentNode.removeChild(parentIndex + 1)
if parentNode.getNumberOfKeys(
) == 0: #if the parent is now empty after the merge, make aNode the root of the tree
done = True
self.rootNode = aNode
self.rootIndex = aNode.getIndex()
aNode.copyItemsAndChildren(
tempNode, 0, totNumKeys - 1,
0) #merge all the items into aNode
aNode.setNumberOfKeys(totNumKeys)
else: #remove the child representing the right sibling (aNode)
parentNode.removeChild(parentIndex + 1)
if parentNode.getNumberOfKeys(
) == 0: #if the parent is now empty after the merge, make sibNode the root of the tree
done = True
self.rootNode = siblingNode
self.rootIndex = siblingNode.getIndex()
siblingNode.copyItemsAndChildren(
tempNode, 0, totNumKeys - 1,
0) #merge all the items into the sibling node
siblingNode.setNumberOfKeys(totNumKeys)
self.writeAt(aNode.getIndex(),
aNode) #write the updates to the file
self.writeAt(siblingNode.getIndex(), siblingNode)
self.writeAt(parentNode.getIndex(), parentNode)
aNode = parentNode #move up the tree and check if it's ok
else: #the item is not in the tree; return None
return None
def inorderSuccessor(self, node, nodeIndex):
'''This method finds the inorder successor given the node containing
the original item and the node index of the original item. It
returns a tuple containing the inorder successor along with the
node containing the inorder successor
'''
fIndex = node.getChild()[nodeIndex +
1] #get the right child of the item
aNode = self.readFrom(fIndex) #get the corresponding node
while not aNode.isLeaf(): #while it's not a leaf node
fIndex = aNode.getChild()[0] #get the index of the left-most child
aNode = self.readFrom(fIndex) #get the corresponding node
inorderSuccessor = aNode.getItems()[0] #get the inorder successor
return (inorderSuccessor, aNode)
def findParentAndSibling(self, anItem, parentNode):
'''This method finds the parent index and the sibling node given the item and
the parent node.
It returns the right child (if it exists), otherwise the left child.
'''
currentIndex = 0
found = False
parentItems = parentNode.getItems()
parentChild = parentNode.getChild()
while not found: #find the index of the parent and the sibling
if currentIndex == parentNode.getNumberOfKeys(
): #we found the parent and we have a left sibling
parentIndex = currentIndex - 1
siblingIndex = parentChild[currentIndex - 1]
sibSide = "left"
found = True
elif parentItems[
currentIndex] > anItem: #we found the parent and we have a right sibling
parentIndex = currentIndex
siblingIndex = parentChild[currentIndex + 1]
sibSide = "right"
found = True
else: #if haven't found parent yet, increment the currentIndex
currentIndex += 1
sibling = self.readFrom(siblingIndex) #get the sibling node
return (parentIndex, sibling, sibSide)
def inorderOn(self, aFile):
'''
Print the items of the BTree in inorder on the file
aFile. aFile is open for writing.
This method is complete at this time.
'''
aFile.write("An inorder traversal of the BTree:\n")
self.inorderOnFrom(aFile, self.rootIndex)
def inorderOnFrom(self, aFile, index):
''' Print the items of the subtree of the BTree, which is
rooted at index, in inorder on aFile.
'''
node = self.readFrom(index) #get the node corresponding to the index
for i in range(node.getNumberOfKeys()): #for each item in the node
left = node.getChild()[i] #get the index of the left child
if left != None: #visit the left
self.inorderOnFrom(aFile, left)
aFile.write(str(node.getItems()[i]) + "\n") #visit the middle
right = node.getChild()[
node.getNumberOfKeys()] #get the index of the right child
if right != None: #visit the rightmost child
self.inorderOnFrom(aFile, right)
def insert(self, anItem):
''' Answer None if the BTree already contains a matching
item. If not, insert a deep copy of anItem and answer
anItem.
'''
searchResult = self.searchTree(anItem) #search for anItem
if searchResult[
'found']: #if anItem already exists in the tree, return None
return None
else: #if anItem doesn't exist in the tree
insertNode = self.readFrom(searchResult['fileIndex']
) #get the node anItem should belong in
if insertNode.isFull(
): #if the node is full, need to split the node
toParent = deepcopy(
anItem) #make a deepcopy of the item we want to insert
leftChild = None #since inserting into a leaf node, left and right children are None
rightChild = None
while insertNode.isFull():
splitNode = insertNode.addItemAndSplit(
toParent, leftChild, rightChild) #split the full node
splitNode.setIndex(
self.freeIndex
) #set the index of the new node to be the next available index
self.freeIndex += 1 #increment the free index number
toParent = deepcopy(insertNode.getItems()[
insertNode.getNumberOfKeys() -
1]) #get the item that will go to the parent node
insertNode.getItems()[
insertNode.getNumberOfKeys() -
1] = None #get rid of the record of the parent item
insertNode.getChild()[insertNode.getNumberOfKeys(
)] = None #get rid of the right child of the parent in the insertNode
insertNode.setNumberOfKeys(insertNode.getNumberOfKeys() -
1)
leftChild = insertNode.getIndex(
) #get the left and right indices of the parent
rightChild = splitNode.getIndex()
self.writeAt(leftChild,
insertNode) #write both nodes to the file
self.writeAt(rightChild, splitNode)
insertNode = self.stackOfNodes.pop() #get the parent node
if insertNode == None: #if there is no parent, create a new root node
insertNode = BTreeNode(self.degree) #create a new node
insertNode.setIndex(
self.freeIndex
) #set the index of the new root node
self.rootNode = insertNode
self.rootIndex = self.freeIndex #set the root index
self.freeIndex += 1 #increment the free index number
insertNode.insertItem(
toParent, leftChild, rightChild
) #if the parent node isn't full, just insert the item
self.writeAt(insertNode.getIndex(),
insertNode) #write the final node to the file
else: #there is room for anItem, so just perform an insert
insertNode.insertItem(deepcopy(anItem))
self.writeAt(searchResult['fileIndex'],
insertNode) #write the node to the file
return anItem #return the item
def levelByLevel(self, aFile):
''' Print the nodes of the BTree level-by-level on aFile.
'''
aFile.write("A level-by-level listing of the nodes:\n")
aQueue = Queue() #create an empty queue
aQueue.enqueue(self.rootNode) #enqueue the root node
while not aQueue.isEmpty():
aNode = aQueue.dequeue() #get the next node in the queue
aFile.write(str(aNode)) #write the node to the file
for i in range(aNode.getNumberOfKeys() +
1): #for each of the items in the node
child = self.readFrom(aNode.getChild()[i]) #get the child node
if child != None: #if there is a child node, enqueue it
aQueue.enqueue(child)
def readFrom(self, index):
''' Answer the node at entry index of the btree structure.
Later adapt to files. This method is complete at this time.
'''
if self.nodes.__contains__(index):
return self.nodes[index]
else:
return None
def recycle(self, aNode):
# For now, do nothing
# This method is complete at this time.
aNode.clear()
def retrieve(self, anItem):
''' If found, answer a deep copy of the matching item.
If not found, answer None
'''
searchResult = self.searchTree(anItem)
if searchResult['found']: #if anItem is in the tree
node = self.readFrom(
searchResult['fileIndex']) #get the node that anItem is in
return deepcopy(node.getItems()[
searchResult['nodeIndex']]) #return a deepcopy of anItem
else:
return None
def searchTree(self, anItem):
''' Answer a dictionary. If there is a matching item, at
'found' is True, at 'fileIndex' is the index of the node
in the BTree with the matching item, and at 'nodeIndex'
is the index into the node of the matching item. If not,
at 'found' is False, but the entry for 'fileIndex' is the
leaf node where the search terminated. An important
function of this method is that it pushes all of the
nodes of the search path from the rootnode, down to,
but not including the corresponding leaf node of a search
(or the node containing a match). Again, the rootnode
is pushed if it is not a leaf node and has no match.
'''
self.stackOfNodes.clear() #clear the existing stack
currentNode = self.readFrom(self.rootIndex) #get the root node
searchResult = currentNode.searchNode(
anItem) #search the root node for anItem
while not searchResult['found'] and not currentNode.isLeaf(
): #while we haven't found anItem and the current node we're looking at isn't a leaf node
self.stackOfNodes.push(
currentNode) #push the current node onto the stack
nextNodeIndex = currentNode.getChild()[searchResult[
'nodeIndex']] #get the next index on the search path
currentNode = self.readFrom(
nextNodeIndex) #get the node associated with the next index
searchResult = currentNode.searchNode(
anItem) #search that node for anItem
searchResult['fileIndex'] = currentNode.getIndex(
) #set the file index to be the index of the last node searched
return searchResult
def update(self, anItem):
''' If found, update the item with a matching key to be a
deep copy of anItem and answer anItem. If not, answer None.
'''
searchResult = self.searchTree(anItem) #search for anItem
if searchResult['found']: #if anItem is in the tree
fileIndex = searchResult['fileIndex']
nodeIndex = searchResult['nodeIndex']
uNode = self.readFrom(fileIndex) #get the node that anItem is in
if uNode != None:
uNode.getItems()[nodeIndex] = deepcopy(
anItem) #update the node with anItem
return anItem
else:
return None
else:
return None
def writeAt(self, index, aNode):
''' Set the element in the btree with the given index
to aNode. This method must be invoked to make any
permanent changes to the btree. We may later change
this method to work with files.
This method is complete at this time.
'''
self.nodes[index] = aNode
def delete(self, anItem):
''' Answer None if a matching item is not found. If found,
answer the entire item.
'''
searchResult = self.searchTree(anItem)
n = self.degree
if searchResult['found']: #the item is in the tree; delete it
aNode = self.readFrom(searchResult['fileIndex']) #get the node that contains anItem
nodeIndex = searchResult['nodeIndex']
done = False
if not aNode.isLeaf(): #if anItem is in a leaf node, find the inorder successor
(ioSuc, iosNode) = self.inorderSuccessor(aNode, nodeIndex)
searchResult = self.searchTree(ioSuc) #search the tree in order to get the stack of nodes on the search path
aNode.getItems()[nodeIndex] = ioSuc #replace anItem with the inorder successor
iosNode.removeItem(0) #remove the inorder successor from its original node
self.writeAt(aNode.getIndex(), aNode) #write the revised aNode to the file
aNode = iosNode #reset what aNode refers to
anItem = ioSuc
else: #if anItem was already in a leaf node
aNode.removeItem(nodeIndex) #remove anItem from the leaf node
while not done and aNode.getNumberOfKeys() < n and aNode.getIndex() != self.rootIndex: #while aNode has less than n keys and is not the root
parentNode = self.stackOfNodes.pop() #get the parent node
(parentIndex, siblingNode, sibSide) = self.findParentAndSibling(anItem, parentNode) #get the parent index and the sibling
totNumKeys = siblingNode.getNumberOfKeys() + aNode.getNumberOfKeys() + 1 #find the total number of keys, including the parent item
tempNode = BTreeNode(2*n) #create a temporary BTreeNode
if sibSide == "right": #if using the right sibling, copy aNode, then parent, then sibling
tempNode.copyItemsAndChildren(aNode, 0, aNode.getNumberOfKeys()-1, 0)
tempNode.getItems()[aNode.getNumberOfKeys()] = parentNode.getItems()[parentIndex]
tempNode.copyItemsAndChildren(siblingNode, 0, siblingNode.getNumberOfKeys()-1, aNode.getNumberOfKeys()+1)
else: #if using the left sibling, copy the sibling, then parent, then aNode
tempNode.copyItemsAndChildren(siblingNode, 0, siblingNode.getNumberOfKeys()-1, 0)
tempNode.getItems()[siblingNode.getNumberOfKeys()] = parentNode.getItems()[parentIndex]
tempNode.copyItemsAndChildren(aNode, 0, aNode.getNumberOfKeys()-1, siblingNode.getNumberOfKeys()+1)
aNode.clear() #clear the items and children from the two nodes
siblingNode.clear()
if totNumKeys > 2*n: #case 2a: redistribute
sepKey = (totNumKeys + 1)//2 #find the new separating key
aNode.copyItemsAndChildren(tempNode, 0, sepKey-2, 0) #put the items of the temp node back to where they belong, redistributed
parentNode.getItems()[parentIndex] = tempNode.getItems()[sepKey-1]
siblingNode.copyItemsAndChildren(tempNode, sepKey, totNumKeys-1, 0)
aNode.setNumberOfKeys(sepKey-1)
siblingNode.setNumberOfKeys(totNumKeys-sepKey)
else: #case 2b: merge
parentNode.removeItem(parentIndex) #remove the parent item from the parent node
if sibSide == "right": #remove the child representing the right sibling
parentNode.removeChild(parentIndex+1)
if parentNode.getNumberOfKeys() == 0: #if the parent is now empty after the merge, make aNode the root of the tree
done = True
self.rootNode = aNode
self.rootIndex = aNode.getIndex()
aNode.copyItemsAndChildren(tempNode, 0, totNumKeys-1, 0) #merge all the items into aNode
aNode.setNumberOfKeys(totNumKeys)
else: #remove the child representing the right sibling (aNode)
parentNode.removeChild(parentIndex+1)
if parentNode.getNumberOfKeys() == 0: #if the parent is now empty after the merge, make sibNode the root of the tree
done = True
self.rootNode = siblingNode
self.rootIndex = siblingNode.getIndex()
siblingNode.copyItemsAndChildren(tempNode, 0, totNumKeys-1, 0) #merge all the items into the sibling node
siblingNode.setNumberOfKeys(totNumKeys)
self.writeAt(aNode.getIndex(), aNode) #write the updates to the file
self.writeAt(siblingNode.getIndex(), siblingNode)
self.writeAt(parentNode.getIndex(), parentNode)
aNode = parentNode #move up the tree and check if it's ok
else: #the item is not in the tree; return None
return None
class BTree:
''' This module implements the BTree class -- a tree of BTreeNodes. Items can
be inserted and deleted from the tree. Each node must have at least
degree items in it (except for the root node)
'''
def __init__(self, degree):
# This method is complete.
self.degree = degree
self.rootNode = BTreeNode(degree)
# If time, file creation code, etc.
self.nodes = {}
self.stackOfNodes = MyStack()
self.rootNode.setIndex(1)
self.writeAt(1, self.rootNode)
self.rootIndex = 1
self.freeIndex = 2
def __str__(self):
# This method is complete.
st = ' The degree of the BTree is ' + str(self.degree)+\
'.\n'
st += ' The index of the root node is ' + \
str(self.rootIndex) + '.\n'
for x in range(1, self.freeIndex):
node = self.readFrom(x)
if node.getNumberOfKeys() > 0:
st += str(node)
return st
def delete(self, anItem):
''' Answer None if a matching item is not found. If found,
answer the entire item.
'''
searchResult = self.searchTree(anItem)
n = self.degree
if searchResult['found']: #the item is in the tree; delete it
aNode = self.readFrom(searchResult['fileIndex']) #get the node that contains anItem
nodeIndex = searchResult['nodeIndex']
done = False
if not aNode.isLeaf(): #if anItem is in a leaf node, find the inorder successor
(ioSuc, iosNode) = self.inorderSuccessor(aNode, nodeIndex)
searchResult = self.searchTree(ioSuc) #search the tree in order to get the stack of nodes on the search path
aNode.getItems()[nodeIndex] = ioSuc #replace anItem with the inorder successor
iosNode.removeItem(0) #remove the inorder successor from its original node
self.writeAt(aNode.getIndex(), aNode) #write the revised aNode to the file
aNode = iosNode #reset what aNode refers to
anItem = ioSuc
else: #if anItem was already in a leaf node
aNode.removeItem(nodeIndex) #remove anItem from the leaf node
while not done and aNode.getNumberOfKeys() < n and aNode.getIndex() != self.rootIndex: #while aNode has less than n keys and is not the root
parentNode = self.stackOfNodes.pop() #get the parent node
(parentIndex, siblingNode, sibSide) = self.findParentAndSibling(anItem, parentNode) #get the parent index and the sibling
totNumKeys = siblingNode.getNumberOfKeys() + aNode.getNumberOfKeys() + 1 #find the total number of keys, including the parent item
tempNode = BTreeNode(2*n) #create a temporary BTreeNode
if sibSide == "right": #if using the right sibling, copy aNode, then parent, then sibling
tempNode.copyItemsAndChildren(aNode, 0, aNode.getNumberOfKeys()-1, 0)
tempNode.getItems()[aNode.getNumberOfKeys()] = parentNode.getItems()[parentIndex]
tempNode.copyItemsAndChildren(siblingNode, 0, siblingNode.getNumberOfKeys()-1, aNode.getNumberOfKeys()+1)
else: #if using the left sibling, copy the sibling, then parent, then aNode
tempNode.copyItemsAndChildren(siblingNode, 0, siblingNode.getNumberOfKeys()-1, 0)
tempNode.getItems()[siblingNode.getNumberOfKeys()] = parentNode.getItems()[parentIndex]
tempNode.copyItemsAndChildren(aNode, 0, aNode.getNumberOfKeys()-1, siblingNode.getNumberOfKeys()+1)
aNode.clear() #clear the items and children from the two nodes
siblingNode.clear()
if totNumKeys > 2*n: #case 2a: redistribute
sepKey = (totNumKeys + 1)//2 #find the new separating key
aNode.copyItemsAndChildren(tempNode, 0, sepKey-2, 0) #put the items of the temp node back to where they belong, redistributed
parentNode.getItems()[parentIndex] = tempNode.getItems()[sepKey-1]
siblingNode.copyItemsAndChildren(tempNode, sepKey, totNumKeys-1, 0)
aNode.setNumberOfKeys(sepKey-1)
siblingNode.setNumberOfKeys(totNumKeys-sepKey)
else: #case 2b: merge
parentNode.removeItem(parentIndex) #remove the parent item from the parent node
if sibSide == "right": #remove the child representing the right sibling
parentNode.removeChild(parentIndex+1)
if parentNode.getNumberOfKeys() == 0: #if the parent is now empty after the merge, make aNode the root of the tree
done = True
self.rootNode = aNode
self.rootIndex = aNode.getIndex()
aNode.copyItemsAndChildren(tempNode, 0, totNumKeys-1, 0) #merge all the items into aNode
aNode.setNumberOfKeys(totNumKeys)
else: #remove the child representing the right sibling (aNode)
parentNode.removeChild(parentIndex+1)
if parentNode.getNumberOfKeys() == 0: #if the parent is now empty after the merge, make sibNode the root of the tree
done = True
self.rootNode = siblingNode
self.rootIndex = siblingNode.getIndex()
siblingNode.copyItemsAndChildren(tempNode, 0, totNumKeys-1, 0) #merge all the items into the sibling node
siblingNode.setNumberOfKeys(totNumKeys)
self.writeAt(aNode.getIndex(), aNode) #write the updates to the file
self.writeAt(siblingNode.getIndex(), siblingNode)
self.writeAt(parentNode.getIndex(), parentNode)
aNode = parentNode #move up the tree and check if it's ok
else: #the item is not in the tree; return None
return None
def inorderSuccessor(self, node, nodeIndex):
'''This method finds the inorder successor given the node containing
the original item and the node index of the original item. It
returns a tuple containing the inorder successor along with the
node containing the inorder successor
'''
fIndex = node.getChild()[nodeIndex+1] #get the right child of the item
aNode = self.readFrom(fIndex) #get the corresponding node
while not aNode.isLeaf(): #while it's not a leaf node
fIndex = aNode.getChild()[0] #get the index of the left-most child
aNode = self.readFrom(fIndex) #get the corresponding node
inorderSuccessor = aNode.getItems()[0] #get the inorder successor
return (inorderSuccessor, aNode)
def findParentAndSibling(self, anItem, parentNode):
'''This method finds the parent index and the sibling node given the item and
the parent node.
It returns the right child (if it exists), otherwise the left child.
'''
currentIndex = 0
found = False
parentItems = parentNode.getItems()
parentChild = parentNode.getChild()
while not found: #find the index of the parent and the sibling
if currentIndex == parentNode.getNumberOfKeys(): #we found the parent and we have a left sibling
parentIndex = currentIndex - 1
siblingIndex = parentChild[currentIndex-1]
sibSide = "left"
found = True
elif parentItems[currentIndex] > anItem: #we found the parent and we have a right sibling
parentIndex = currentIndex
siblingIndex = parentChild[currentIndex+1]
sibSide = "right"
found = True
else: #if haven't found parent yet, increment the currentIndex
currentIndex += 1
sibling = self.readFrom(siblingIndex) #get the sibling node
return (parentIndex, sibling, sibSide)
def inorderOn(self, aFile):
'''
Print the items of the BTree in inorder on the file
aFile. aFile is open for writing.
This method is complete at this time.
'''
aFile.write("An inorder traversal of the BTree:\n")
self.inorderOnFrom( aFile, self.rootIndex)
def inorderOnFrom(self, aFile, index):
''' Print the items of the subtree of the BTree, which is
rooted at index, in inorder on aFile.
'''
node = self.readFrom(index) #get the node corresponding to the index
for i in range(node.getNumberOfKeys()): #for each item in the node
left = node.getChild()[i] #get the index of the left child
if left != None: #visit the left
self.inorderOnFrom(aFile, left)
aFile.write(str(node.getItems()[i])+"\n") #visit the middle
right = node.getChild()[node.getNumberOfKeys()]#get the index of the right child
if right != None: #visit the rightmost child
self.inorderOnFrom(aFile, right)
def insert(self, anItem):
''' Answer None if the BTree already contains a matching
item. If not, insert a deep copy of anItem and answer
anItem.
'''
searchResult = self.searchTree(anItem) #search for anItem
if searchResult['found']: #if anItem already exists in the tree, return None
return None
else: #if anItem doesn't exist in the tree
insertNode = self.readFrom(searchResult['fileIndex']) #get the node anItem should belong in
if insertNode.isFull(): #if the node is full, need to split the node
toParent = deepcopy(anItem) #make a deepcopy of the item we want to insert
leftChild = None #since inserting into a leaf node, left and right children are None
rightChild = None
while insertNode.isFull():
splitNode = insertNode.addItemAndSplit(toParent, leftChild, rightChild) #split the full node
splitNode.setIndex(self.freeIndex) #set the index of the new node to be the next available index
self.freeIndex += 1 #increment the free index number
toParent = deepcopy(insertNode.getItems()[insertNode.getNumberOfKeys()-1]) #get the item that will go to the parent node
insertNode.getItems()[insertNode.getNumberOfKeys()-1] = None #get rid of the record of the parent item
insertNode.getChild()[insertNode.getNumberOfKeys()] = None #get rid of the right child of the parent in the insertNode
insertNode.setNumberOfKeys(insertNode.getNumberOfKeys()-1)
leftChild = insertNode.getIndex() #get the left and right indices of the parent
rightChild = splitNode.getIndex()
self.writeAt(leftChild, insertNode) #write both nodes to the file
self.writeAt(rightChild, splitNode)
insertNode = self.stackOfNodes.pop() #get the parent node
if insertNode == None: #if there is no parent, create a new root node
insertNode = BTreeNode(self.degree) #create a new node
insertNode.setIndex(self.freeIndex) #set the index of the new root node
self.rootNode = insertNode
self.rootIndex = self.freeIndex #set the root index
self.freeIndex += 1 #increment the free index number
insertNode.insertItem(toParent, leftChild, rightChild)#if the parent node isn't full, just insert the item
self.writeAt(insertNode.getIndex(), insertNode) #write the final node to the file
else: #there is room for anItem, so just perform an insert
insertNode.insertItem(deepcopy(anItem))
self.writeAt(searchResult['fileIndex'], insertNode) #write the node to the file
return anItem #return the item
def levelByLevel(self, aFile):
''' Print the nodes of the BTree level-by-level on aFile.
'''
aFile.write("A level-by-level listing of the nodes:\n")
aQueue = Queue() #create an empty queue
aQueue.enqueue(self.rootNode) #enqueue the root node
while not aQueue.isEmpty():
aNode = aQueue.dequeue() #get the next node in the queue
aFile.write(str(aNode)) #write the node to the file
for i in range(aNode.getNumberOfKeys()+1): #for each of the items in the node
child = self.readFrom(aNode.getChild()[i]) #get the child node
if child != None: #if there is a child node, enqueue it
aQueue.enqueue(child)
def readFrom(self, index):
''' Answer the node at entry index of the btree structure.
Later adapt to files. This method is complete at this time.
'''
if self.nodes.__contains__(index):
return self.nodes[index]
else:
return None
def recycle(self, aNode):
# For now, do nothing
# This method is complete at this time.
aNode.clear()
def retrieve(self, anItem):
''' If found, answer a deep copy of the matching item.
If not found, answer None
'''
searchResult = self.searchTree(anItem)
if searchResult['found']: #if anItem is in the tree
node = self.readFrom(searchResult['fileIndex']) #get the node that anItem is in
return deepcopy(node.getItems()[searchResult['nodeIndex']]) #return a deepcopy of anItem
else:
return None
def searchTree(self, anItem):
''' Answer a dictionary. If there is a matching item, at
'found' is True, at 'fileIndex' is the index of the node
in the BTree with the matching item, and at 'nodeIndex'
is the index into the node of the matching item. If not,
at 'found' is False, but the entry for 'fileIndex' is the
leaf node where the search terminated. An important
function of this method is that it pushes all of the
nodes of the search path from the rootnode, down to,
but not including the corresponding leaf node of a search
(or the node containing a match). Again, the rootnode
is pushed if it is not a leaf node and has no match.
'''
self.stackOfNodes.clear() #clear the existing stack
currentNode = self.readFrom(self.rootIndex) #get the root node
searchResult = currentNode.searchNode(anItem) #search the root node for anItem
while not searchResult['found'] and not currentNode.isLeaf(): #while we haven't found anItem and the current node we're looking at isn't a leaf node
self.stackOfNodes.push(currentNode) #push the current node onto the stack
nextNodeIndex = currentNode.getChild()[searchResult['nodeIndex']] #get the next index on the search path
currentNode = self.readFrom(nextNodeIndex) #get the node associated with the next index
searchResult = currentNode.searchNode(anItem) #search that node for anItem
searchResult['fileIndex'] = currentNode.getIndex() #set the file index to be the index of the last node searched
return searchResult
def update(self, anItem):
''' If found, update the item with a matching key to be a
deep copy of anItem and answer anItem. If not, answer None.
'''
searchResult = self.searchTree(anItem) #search for anItem
if searchResult['found']: #if anItem is in the tree
fileIndex = searchResult['fileIndex']
nodeIndex = searchResult['nodeIndex']
uNode = self.readFrom(fileIndex) #get the node that anItem is in
if uNode != None:
uNode.getItems()[nodeIndex] = deepcopy(anItem) #update the node with anItem
return anItem
else:
return None
else:
return None
def writeAt(self, index, aNode):
''' Set the element in the btree with the given index
to aNode. This method must be invoked to make any
permanent changes to the btree. We may later change
this method to work with files.
This method is complete at this time.
'''
self.nodes[index] = aNode
