Problem 5: B-trees. (i) Suppose that we were to implement a search operation in a B-tree using binary search (bisection) rather than linear search within each node. Show that in this case searching for an element takes O(log n) comparisons, where n is the number of the elements in the structure. (ii) Let T and U be B-trees of order 4 and suppose that all elements in T are smaller then an element x, while all elements in U are larger then x. Suppose that there are n elements in T and m elements in U. Describe an algorithm with time complexity O(log n + log m), which merges T and U into a single B-tree T ∪ U of order 4 with m + n + 1 elements (T ∪ U consists of x and all elements in T and U).
Problem 5: B-trees. (i) Suppose that we were to implement a search operation in a B-tree using binary search (bisection) rather than linear search within each node. Show that in this case searching for an element takes O(log n) comparisons, where n is the number of the elements in the structure. (ii) Let T and U be B-trees of order 4 and suppose that all elements in T are smaller then an element x, while all elements in U are larger then x. Suppose that there are n elements in T and m elements in U. Describe an algorithm with time complexity O(log n + log m), which merges T and U into a single B-tree T ∪ U of order 4 with m + n + 1 elements (T ∪ U consists of x and all elements in T and U).
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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Problem 5: B-trees.
(i) Suppose that we were to implement a search operation in a B-tree using binary
search (bisection) rather than linear search within each node. Show that in this case
searching for an element takes O(log n) comparisons, where n is the number of the
elements in the structure.
(ii) Let T and U be B-trees of order 4 and suppose that all elements in T are smaller
then an element x, while all elements in U are larger then x. Suppose that there are
n elements in T and m elements in U. Describe an
O(log n + log m), which merges T and U into a single B-tree T ∪ U of order 4 with
m + n + 1 elements (T ∪ U consists of x and all elements in T and U).
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