A **B-tree of order $m$** is a tree that satisfies the following properties:
* Every node has at most $m$ children.
* Every node, except for the root, has at least $m / 2$ children.
* All leaves appear on the same level.
* A node with $k$ children contains $k - 1$ keys sorted in monotonically increasing order.
The above is a modification of Knuth's definition in his "Art of Computer Programming" that defines leaves of the tree more consistently with how I use the term elsewhere. It also pulls in concepts from CLRS (such as keys needing to be sorted within nodes).
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Basic
What hyperparameter is used to define a B-tree?
Back: It's order, i.e. the maximum number of a children a node can have.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
In what direction do B-trees grow?
Back: From bottom to top.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
Consider B-tree of order $m$. What does $m$ refer to?
Back: The maximum number of children a node can have.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
What is the maximum number of children a node in a B-tree have?
Back: N/A. It depends on the tree's order.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
What is the maximum number of children a node in a B-tree of order $m$ can have?
Back: $m$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
What is the minimum number of children a non-root node in a B-tree of order $m$ can have?
Back: $\lceil m / 2 \rceil$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
What is the maximum number of keys a node in a B-tree of order $m$ can have?
Back: $m - 1$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
What is the minimum number of keys a non-root node in a B-tree can have?
Back: N/A. It depends on the tree's order.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
What is the minimum number of keys a non-root node in a B-tree of order $m$ can have?
Back: $\lceil m / 2 \rceil - 1$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
A node in a B-tree of order $m$ has $k$ keys. How many children does it have?
Back: $k + 1$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
A node in a B-tree of order $m$ has $k$ children. How many keys does it have?
Back: $k - 1$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
*When* does a B-tree gain height?
Back: When the root node is split.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
Consider a B-tree of order $7$. How many children $c$ can each non-root node have?
Back: $4 \leq c \leq 7$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
Consider a B-tree of order $7$. How many children $c$ can the root have?
Back: $0 \leq c \leq 7$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
Consider a B-tree of order $7$. How many keys $k$ can each non-root node have?
Back: $3 \leq k <7$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
Consider a B-tree of order $7$. How many keys $k$ can the root have?
Back: $0 \leq k <7$
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
What instances exist of a B-tree of order $1$?
Back: Just the empty tree.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
*Why* can't we define a nonempty B-tree of order $1$?
Back: Each node can have at most $1$ child, meaning each node contains $0$ keys.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
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Basic
How are keys arranged within a B-tree's nodes?
Back: In monotonically increasing order.
Reference: Donald Ervin Knuth, _Art of Computer Programming, 3: Sorting and Searching_, 2. ed., 34. (Reading, Mass: Addison-Wesley, 1995).
