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(a) If a hash table uses a hash function that does not satisfy the simple uniform hashing assumption, then look-up operations may fail to return the correct result. (b) Suppose we have a list that is already sorted. We run the merge sort algorithm on the list, obtaining a new sorted list The ordering of the items in and is guaranteed to be identical. (c) Suppose we use the merge() subroutine of merge sort to merge two lists and, whose lengths are and respectively. The subroutine will run in time. (d) The running time of an algorithm can be expressed recursively as. This algorithm runs in time. (e) A post-order traversal of a binary tree is guaranteed to visit a leaf node first. (f) Consider a doubly-linked list with elements, where. The time to access the element at location is in . (g) Suppose the best-case running time of an algorithm is in and. Then the best-case running time is also in . (h) Suppose the best-case running time of an algorithm is in and. Then the worst-case running time is in. (i) Consider a connected graph containing the three vertices ,, . Suppose the shortest path from to has length 5, the shortest path from to has length 7, and the shortest path from to has length 8. We perform a breadth-first traversal of the graph beginning at. Then we are guaranteed to visit before. (j) In a complete binary tree of nodes, the number of internal nodes is in .

(a) If a hash table uses a hash function that does not satisfy the simple uniform hashing assumption, then look-up operations may fail to return the correct result. (b) Suppose we have a list that is already sorted. We run the merge sort algorithm on the list, obtaining a new sorted list The ordering of the items in and is guaranteed to be identical. (c) Suppose we use the merge() subroutine of merge sort to merge two lists and, whose lengths are and respectively. The subroutine will run in time. (d) The running time of an algorithm can be expressed recursively as. This algorithm runs in time. (e) A post-order traversal of a binary tree is guaranteed to visit a leaf node first. (f) Consider a doubly-linked list with elements, where. The time to access the element at location is in . (g) Suppose the best-case running time of an algorithm is in and. Then the best-case running time is also in . (h) Suppose the best-case running time of an algorithm is in and. Then the worst-case running time is in. (i) Consider a connected graph containing the three vertices ,, . Suppose the shortest path from to has length 5, the shortest path from to has length 7, and the shortest path from to has length 8. We perform a breadth-first traversal of the graph beginning at. Then we are guaranteed to visit before. (j) In a complete binary tree of nodes, the number of internal nodes is in .

Database System Concepts
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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determine if each following statement is True or False

(a) If a hash table uses a hash function that does not satisfy the simple uniform hashing assumption, then look-up operations may fail to return the correct result. (b) Suppose we have a list that is already sorted. We run the merge sort algorithm on the list, obtaining a new sorted list . The ordering of the items in and is guaranteed to be identical. (c) Suppose we use the merge() subroutine of merge sort to merge two lists and, whose lengths are and respectively. The subroutine will run in time. (d) The running time of an algorithm can be expressed recursively as. This algorithm runs in time. (e) A post-order traversal of a binary tree is guaranteed to visit a leaf node first. (f) Consider a doubly-linked list with elements, where. The time to access the element at location is in . (g) Suppose the best-case running time of an algorithm is in and. Then the best-case running time is also in . (h) Suppose the best-case running time of an algorithm is in and. Then the worst-case running time is in . (i) Consider a connected graph containing the three vertices Suppose the shortest path from to has length 5, the shortest path from to has length 7, and the shortest path from to has length 8. We perform a breadth-first traversal of the graph beginning at . Then we are guaranteed to visit before. (j) In a complete binary tree of nodes, the number of internal nodes is in.
Transcribed Image Text:(a) If a hash table uses a hash function that does not satisfy the simple uniform hashing assumption, then look-up operations may fail to return the correct result. (b) Suppose we have a list that is already sorted. We run the merge sort algorithm on the list, obtaining a new sorted list . The ordering of the items in and is guaranteed to be identical. (c) Suppose we use the merge() subroutine of merge sort to merge two lists and, whose lengths are and respectively. The subroutine will run in time. (d) The running time of an algorithm can be expressed recursively as. This algorithm runs in time. (e) A post-order traversal of a binary tree is guaranteed to visit a leaf node first. (f) Consider a doubly-linked list with elements, where. The time to access the element at location is in . (g) Suppose the best-case running time of an algorithm is in and. Then the best-case running time is also in . (h) Suppose the best-case running time of an algorithm is in and. Then the worst-case running time is in . (i) Consider a connected graph containing the three vertices Suppose the shortest path from to has length 5, the shortest path from to has length 7, and the shortest path from to has length 8. We perform a breadth-first traversal of the graph beginning at . Then we are guaranteed to visit before. (j) In a complete binary tree of nodes, the number of internal nodes is in.
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