B-tree of order n is an order-n multiway tree in which each non-root node contains
Question
B-tree of order n
A B-tree of order n is an order-n multiway tree in which each non-root node contains:
Solution
between n-1 and 2n-1 elements.
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A B-tree of order n is a balanced search tree where each node has a specific number of elements and children, depending on the order of the tree.
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The root node of a B-tree can have between 1 and 2n-1 elements.
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Any other non-root node in the B-tree must have between n-1 and 2n-1 elements.
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Each non-root node in the B-tree also has one more child than it has elements. So, if a non-root node has k elements, it must have k+1 children.
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The elements in each node of the B-tree are ordered, and they separate the values in its children. If a node has k elements a1, a2, ..., ak, and k+1 children b1, b2, ..., bk+1, then all elements in bi are less than ai for i=1,2,...,k, and all elements in bk+1 are greater than ak.
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All leaves in the B-tree are at the same level, which means the tree is balanced. This property ensures that the time complexity for search, insert, and delete operations in the B-tree is logarithmic.
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