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Consider the following algorithm called trisection search. Trisection search is an algorithm that, given a sorted list L of integers, determines whether or not a given integer x is an element of L. For convenience, let's assume that the length of Lis 3º for some integer p. Here's the algorithm: Algorithm Trisection Search(x, L): 1. If I has length 1, then return True if the single element of L is equal to x, and return False otherwise. 2. Divide L into 3 equal pieces, called L₁, L2, and L3. Let the final elements of each of these lists be l1, l2, and l3 respectively. ○ If x ≤ l₁, return TrisectionSearch(x, L₁). ○ Else, if l₁ < x ≤ l2, then return TrisectionSearch(x, L₂). o Else, if l2 < x, then return TrisectionSearch(x, L3). Part A Give a big-O estimate for the number of comparisons between integers used by trisection search on a list of length n 3º. To do so, use the following steps: = 1. Write down and justify a recurrence relation describing the number of comparisons required (Example 1 from the reading will be helpful). 2. Apply a theorem from the reading to obtain a big-O estimate. Part B For each Respond with a "true" or a "false" and a quick explanation to each of the following two statements: 1. Trisection search requires exactly as many comparisons between integers as binary search. 2. Trisection search requires no more than 10% more comparisons than binary search. 3. If n increased by a factor of 10, then the number of comparisons required by binary and trisection search would both increase by a similar (but not exactly the same) factor.

Consider the following algorithm called trisection search. Trisection search is an algorithm that, given a sorted list L of integers, determines whether or not a given integer x is an element of L. For convenience, let's assume that the length of Lis 3º for some integer p. Here's the algorithm: Algorithm Trisection Search(x, L): 1. If I has length 1, then return True if the single element of L is equal to x, and return False otherwise. 2. Divide L into 3 equal pieces, called L₁, L2, and L3. Let the final elements of each of these lists be l1, l2, and l3 respectively. ○ If x ≤ l₁, return TrisectionSearch(x, L₁). ○ Else, if l₁ < x ≤ l2, then return TrisectionSearch(x, L₂). o Else, if l2 < x, then return TrisectionSearch(x, L3). Part A Give a big-O estimate for the number of comparisons between integers used by trisection search on a list of length n 3º. To do so, use the following steps: = 1. Write down and justify a recurrence relation describing the number of comparisons required (Example 1 from the reading will be helpful). 2. Apply a theorem from the reading to obtain a big-O estimate. Part B For each Respond with a "true" or a "false" and a quick explanation to each of the following two statements: 1. Trisection search requires exactly as many comparisons between integers as binary search. 2. Trisection search requires no more than 10% more comparisons than binary search. 3. If n increased by a factor of 10, then the number of comparisons required by binary and trisection search would both increase by a similar (but not exactly the same) factor.

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
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Consider the following algorithm called trisection search. Trisection search is an algorithm that, given a sorted list L of integers, determines whether or not a given integer x is an element of L. For convenience, let's assume that the length of Lis 3º for some integer p. Here's the algorithm: Algorithm Trisection Search(x, L): 1. If I has length 1, then return True if the single element of L is equal to x, and return False otherwise. 2. Divide L into 3 equal pieces, called L₁, L2, and L3. Let the final elements of each of these lists be l1, l2, and l3 respectively. ○ If x ≤ l₁, return TrisectionSearch(x, L₁). ○ Else, if l₁ < x ≤ l2, then return TrisectionSearch(x, L₂). o Else, if l2 < x, then return TrisectionSearch(x, L3). Part A Give a big-O estimate for the number of comparisons between integers used by trisection search on a list of length n 3º. To do so, use the following steps: = 1. Write down and justify a recurrence relation describing the number of comparisons required (Example 1 from the reading will be helpful). 2. Apply a theorem from the reading to obtain a big-O estimate. Part B For each Respond with a "true" or a "false" and a quick explanation to each of the following two statements: 1. Trisection search requires exactly as many comparisons between integers as binary search. 2. Trisection search requires no more than 10% more comparisons than binary search. 3. If n increased by a factor of 10, then the number of comparisons required by binary and trisection search would both increase by a similar (but not exactly the same) factor.
Transcribed Image Text:Consider the following algorithm called trisection search. Trisection search is an algorithm that, given a sorted list L of integers, determines whether or not a given integer x is an element of L. For convenience, let's assume that the length of Lis 3º for some integer p. Here's the algorithm: Algorithm Trisection Search(x, L): 1. If I has length 1, then return True if the single element of L is equal to x, and return False otherwise. 2. Divide L into 3 equal pieces, called L₁, L2, and L3. Let the final elements of each of these lists be l1, l2, and l3 respectively. ○ If x ≤ l₁, return TrisectionSearch(x, L₁). ○ Else, if l₁ < x ≤ l2, then return TrisectionSearch(x, L₂). o Else, if l2 < x, then return TrisectionSearch(x, L3). Part A Give a big-O estimate for the number of comparisons between integers used by trisection search on a list of length n 3º. To do so, use the following steps: = 1. Write down and justify a recurrence relation describing the number of comparisons required (Example 1 from the reading will be helpful). 2. Apply a theorem from the reading to obtain a big-O estimate. Part B For each Respond with a "true" or a "false" and a quick explanation to each of the following two statements: 1. Trisection search requires exactly as many comparisons between integers as binary search. 2. Trisection search requires no more than 10% more comparisons than binary search. 3. If n increased by a factor of 10, then the number of comparisons required by binary and trisection search would both increase by a similar (but not exactly the same) factor.
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