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4. Consider using a simple linked list as a dictionary. Assume the client will never provide duplicate elements, so we can just insert elements at the beginning of the list. Now assume the peculiar situation that the client may perform any number of insert operations but will only ever perform at most one lookup operation. (a) What is the worst-case running-time of the operations performed on this data structure under the assumptions above? Briefly justify your answer. (b) What is the worst-case amortized running-time of the operations performed on this data structure under the assumptions above? Briefly justify your answer. Solution: (a) inserts are O(1) (push on the front of a linked list), but the lookup is O(n) where n is the number of inserted items since the lookup may be last and be for one of the earliest inserted items

4. Consider using a simple linked list as a dictionary. Assume the client will never provide duplicate elements, so we can just insert elements at the beginning of the list. Now assume the peculiar situation that the client may perform any number of insert operations but will only ever perform at most one lookup operation. (a) What is the worst-case running-time of the operations performed on this data structure under the assumptions above? Briefly justify your answer. (b) What is the worst-case amortized running-time of the operations performed on this data structure under the assumptions above? Briefly justify your answer. Solution: (a) inserts are O(1) (push on the front of a linked list), but the lookup is O(n) where n is the number of inserted items since the lookup may be last and be for one of the earliest inserted items

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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8:20 ← more_examples_midterm2_solved.pdf 54% 4. Consider using a simple linked list as a dictionary. Assume the client will never provide duplicate elements, so we can just insert elements at the beginning of the list. Now assume the peculiar situation that the client may perform any number of insert operations but will only ever perform at most one lookup operation. (a) What is the worst-case running-time of the operations performed on this data structure under the assumptions above? Briefly justify your answer. (b) What is the worst-case amortized running-time of the operations performed on this data structure under the assumptions above? Briefly justify your answer. Solution: (a) inserts are O(1) (push on the front of a linked list), but the lookup is O(n) where n is the number of inserted items since the lookup may be last and be for one of the earliest inserted items (b) amortized all operations are now 0(1). Inserts are still O(1). And the lookup can take at most
Transcribed Image Text:8:20 ← more_examples_midterm2_solved.pdf 54% 4. Consider using a simple linked list as a dictionary. Assume the client will never provide duplicate elements, so we can just insert elements at the beginning of the list. Now assume the peculiar situation that the client may perform any number of insert operations but will only ever perform at most one lookup operation. (a) What is the worst-case running-time of the operations performed on this data structure under the assumptions above? Briefly justify your answer. (b) What is the worst-case amortized running-time of the operations performed on this data structure under the assumptions above? Briefly justify your answer. Solution: (a) inserts are O(1) (push on the front of a linked list), but the lookup is O(n) where n is the number of inserted items since the lookup may be last and be for one of the earliest inserted items (b) amortized all operations are now 0(1). Inserts are still O(1). And the lookup can take at most
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