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Questions and Answers
What is the primary use of M-ary search trees in Secondary (External) Memory (SM)?
What is the primary use of M-ary search trees in Secondary (External) Memory (SM)?
Representing M-ary search trees in Secondary (External) Memory (SM)
In an M-ary search tree of order N, what is the maximum number of ordered values that a node can contain?
In an M-ary search tree of order N, what is the maximum number of ordered values that a node can contain?
N-1
What does the degree of a node represent in an M-ary search tree?
What does the degree of a node represent in an M-ary search tree?
The current number of children
What is the relationship between the degree of a node and the number of values it contains?
What is the relationship between the degree of a node and the number of values it contains?
What is the minimum degree of a node in an M-ary search tree?
What is the minimum degree of a node in an M-ary search tree?
All values in the subtree of Child1 in an M-ary search tree are greater than val1.
All values in the subtree of Child1 in an M-ary search tree are greater than val1.
All values in the subtree of Childj in an M-ary search tree are greater than valj-1 and less than valj, where j is between 2 and degree-1.
All values in the subtree of Childj in an M-ary search tree are greater than valj-1 and less than valj, where j is between 2 and degree-1.
All values in the subtree of Childdegree in an M-ary search tree are less than valdegree-1.
All values in the subtree of Childdegree in an M-ary search tree are less than valdegree-1.
What is the tree depth or height of an M-ary search tree?
What is the tree depth or height of an M-ary search tree?
What is the 'Top-Down Property' of an M-ary search tree?
What is the 'Top-Down Property' of an M-ary search tree?
How are blocks linked in a file organized as an M-ary search tree?
How are blocks linked in a file organized as an M-ary search tree?
Where is the root block number stored in a file organized as an M-ary search tree?
Where is the root block number stored in a file organized as an M-ary search tree?
What is the type of the Tval variable used as an index in SM towards a data file in M-ary search trees?
What is the type of the Tval variable used as an index in SM towards a data file in M-ary search trees?
What is the type of the Tval variable used as a data file organized using a tree in SM in M-ary search trees?
What is the type of the Tval variable used as a data file organized using a tree in SM in M-ary search trees?
How does searching for a value C in an M-ary search tree begin?
How does searching for a value C in an M-ary search tree begin?
In searching for a value C in an M-ary search tree, when does the search stop successfully?
In searching for a value C in an M-ary search tree, when does the search stop successfully?
If the searched value C is not found in node P during a search in an M-ary search tree, what is the next step?
If the searched value C is not found in node P during a search in an M-ary search tree, what is the next step?
If Childk in an M-ary search tree is not null, what is the next step?
If Childk in an M-ary search tree is not null, what is the next step?
If Childk is null in an M-ary search tree, what is the result?
If Childk is null in an M-ary search tree, what is the result?
What is the variable type used for storing data related to blocks in the Search Algorithm?
What is the variable type used for storing data related to blocks in the Search Algorithm?
In the Search Algorithm, what is the purpose of the variable numB?
In the Search Algorithm, what is the purpose of the variable numB?
In the Search Algorithm, what is the initial value assigned to the variable found?
In the Search Algorithm, what is the initial value assigned to the variable found?
In the Search Algorithm, how is the block data read?
In the Search Algorithm, how is the block data read?
In the Search Algorithm, where is the value c searched for?
In the Search Algorithm, where is the value c searched for?
In the Search Algorithm, what action is taken if the desired value 'c' is not found within the current block?
In the Search Algorithm, what action is taken if the desired value 'c' is not found within the current block?
What is the purpose of the 'P' variable in the Search Algorithm?
What is the purpose of the 'P' variable in the Search Algorithm?
In the Search Algorithm, what does the function 'CreateStack(P)' do?
In the Search Algorithm, what does the function 'CreateStack(P)' do?
What is the value of 'found' at the beginning of the Search Algorithm?
What is the value of 'found' at the beginning of the Search Algorithm?
What value is assigned to the variable 'i' at the start of the Search Algorithm?
What value is assigned to the variable 'i' at the start of the Search Algorithm?
How is the block associated with 'i' in the Search Algorithm accessed and stored in 'buf'?
How is the block associated with 'i' in the Search Algorithm accessed and stored in 'buf'?
How is the target value 'c' searched for within the 'buf' variable in the Search Algorithm?
How is the target value 'c' searched for within the 'buf' variable in the Search Algorithm?
What happens in the Search Algorithm if the target value 'c' is not found within the current block 'buf'?
What happens in the Search Algorithm if the target value 'c' is not found within the current block 'buf'?
What does 'inorder traversal' refer to in the context of M-ary search trees?
What does 'inorder traversal' refer to in the context of M-ary search trees?
Where is the smallest value in the tree typically located?
Where is the smallest value in the tree typically located?
How do you locate the inorder successor of a value in an M-ary search tree?
How do you locate the inorder successor of a value in an M-ary search tree?
What is the rule for determining the next inorder value when the right child of a value is null and the value's position is less than degree - 1?
What is the rule for determining the next inorder value when the right child of a value is null and the value's position is less than degree - 1?
What is the rule for determining the next inorder value when the right child of a value is null and the value's position is equal to degree - 1?
What is the rule for determining the next inorder value when the right child of a value is null and the value's position is equal to degree - 1?
What is the rule for determining the next inorder value when the right child of a value is not null?
What is the rule for determining the next inorder value when the right child of a value is not null?
What is an interval query in the context of M-ary search trees?
What is an interval query in the context of M-ary search trees?
What are the hints provided for implementing the algorithm for an interval query in M-ary search trees?
What are the hints provided for implementing the algorithm for an interval query in M-ary search trees?
Under what condition is a new value inserted into a node during the insertion process in M-ary search trees?
Under what condition is a new value inserted into a node during the insertion process in M-ary search trees?
What action is taken to insert a new value when the last accessed node is full during the insertion process in M-ary search trees?
What action is taken to insert a new value when the last accessed node is full during the insertion process in M-ary search trees?
What is the primary objective of the insertion mechanism in M-ary search trees?
What is the primary objective of the insertion mechanism in M-ary search trees?
What is one potential drawback of the insertion mechanism in M-ary search trees?
What is one potential drawback of the insertion mechanism in M-ary search trees?
What is a possible solution or mitigation strategy for addressing imbalances in M-ary search trees caused by insertion processes?
What is a possible solution or mitigation strategy for addressing imbalances in M-ary search trees caused by insertion processes?
What are the two main approaches to value deletion in an M-ary search tree?
What are the two main approaches to value deletion in an M-ary search tree?
How is logical deletion implemented in an M-ary search tree?
How is logical deletion implemented in an M-ary search tree?
What does physical deletion involve in an M-ary search tree?
What does physical deletion involve in an M-ary search tree?
When deleting a value in an M-ary search tree with physical deletion, what is the first step?
When deleting a value in an M-ary search tree with physical deletion, what is the first step?
When deleting a value in an M-ary search tree, what is the action taken if the value is found in a leaf node?
When deleting a value in an M-ary search tree, what is the action taken if the value is found in a leaf node?
When deleting a value from an M-ary search tree with physical deletion, what is the first step if the value is found in an internal node?
When deleting a value from an M-ary search tree with physical deletion, what is the first step if the value is found in an internal node?
After finding the next or previous inorder value in an M-ary search tree during the physical deletion process, what is the next step?
After finding the next or previous inorder value in an M-ary search tree during the physical deletion process, what is the next step?
After replacing the original value with the successor/predecessor value in an M-ary search tree during the physical deletion process, what is the final step?
After replacing the original value with the successor/predecessor value in an M-ary search tree during the physical deletion process, what is the final step?
Flashcards
M-ary Search Tree
M-ary Search Tree
A tree structure where each node can hold a limited number of ordered values and children, used in external memory.
Order (N)
Order (N)
A parameter in an M-ary search tree defining the maximum number of values and children a node can hold.
Degree
Degree
The current number of children a node has in an M-ary search tree.
Value Ordering
Value Ordering
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Subtree relationship
Subtree relationship
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Tree Depth
Tree Depth
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Internal Node
Internal Node
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Leaf Node
Leaf Node
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Top-Down Property
Top-Down Property
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Study Notes
Chapter 4: Trees in External Memory
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Organizing Files Using M-ary Search Trees:
- File blocks can be organized as a tree of blocks.
- Useful for secondary (external) memory.
- An M-ary search tree of order N has nodes containing at most N-1 ordered values and N children.
- Node degree represents the current number of children.
- Degree is at least 2 and at most N.
- Properties of M-ary search tree nodes :
- All values in subtree of child 1 are less than val1.
- All values in subtree of child j (j in [2, degree-1]) are greater than val(j-1) and less than val(j).
- All values in subtree of child (degree) are greater than val(degree-1).
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Organizing Files Using B-Trees:
- Definitions and Properties
- Algorithms: Insertion, Deletion, Optimized Loading
- Variants: B+-Trees, Prefix B+-Trees, B*-Trees.
Example of an M-ary Search Tree (Order = 5)
- Root Node: i (32, 33, 40, 99)
- Internal Nodes: Nodes containing more than one value (e.g., a, h, k, d, f).
- Leaf Nodes: Nodes with no children (e.g., b, c, g, j).
Uses of M-ary Search Trees
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Index:
- Used as an index in secondary memory for data files.
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Data File:
- Data file can be organized as a tree in secondary memory.
Search Algorithm
- Starts from the root node.
- If the value is found, the search stops successfully.
- If not, follows the appropriate child branch based on value order.
- Search stops with failure if relevant child is not available.
Search Algorithm (Detailed)
- Algorithm uses a stack to keep track of visited nodes.
- Opens a file and gets the header.
- Loops until the value is found or all node paths are explored.
- Reads the block and searches for the value.
- If not found, pushes the current block, index, and position onto the stack.
- Continues until the value is found or the stack is empty.
Inorder Traversal
- Process: Visits nodes in ascending order.
- Result: Values are visited in ascending order.
Next Inorder
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Process: Finds the next value in an inorder traversal from a given value.
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Conditions: If the current child position plus one is less than the degree number and the child is not -1, the next value will be in the next child.
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Algorithm: Details on finding the successor.
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If a value is an internal node, finds the successor value in the branch.
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If a value is a leaf node and the right child is -1, and it's the last value in the node,the next value depends on its position in the tree
- If a value is not an internal node the next value is in next node depending on its position.
Insertion Mechanism
- Full Node: If the last accessed node is full, a new block is allocated and added to the tree.
- It adds the value into the previously allocated block.
Deletion Mechanism
-
Logical Deletion: Adds a logical deletion indicator to the node containing the value to be deleted.
-
Physical Deletion:
- Searches for the node containing the value to be deleted.
- If node is a leaf, deletes using shifts. If it's empty free it and go to the parent.
- If node is not a leaf, find the next/previous value using an inorder traversal, replace the value to be deleted with the next/previous value, and repeat the process for the next Node recursively.
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