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Consider an n x n matrix. We want to find an element in this matrix that is bigger or equal to each of its four adjacent elements (the elements on the corner only need to be bigger or equal than their 2 adjacent elements, and the elements on the sides only need to be bigger or equal than their 3 adjacent elements). For example, in the following matrix we are searching for one of the starred elements. 1 4 5* 6* 5 3 4* 11* 1 4 2 3 4 10* 7 7* 1 4 1 8* 4 5* 3 Assume we have an algorithm that works by selecting the middle column (of the remaining columns) in each step. In that column, it selects the maximum element. If this element is also bigger or equal than its left and right elements, we have found a solution. Otherwise, we select the side with the bigger element and repeat the algorithm with half the input (no longer considering the columns on the side with the smaller element). 1) The asymptotic complexity of this algorithm is O(nlogn). If we change the algorithm so that tin each phase: if the number of rows is more than the number of columns, choose the middle row instead of the middle column, find the max and remove half the rows as we did for columns. Then what is the asymptotiC complexity of the new algorithm? How does new algorithm work?(Prove) 2.

Consider an n x n matrix. We want to find an element in this matrix that is bigger or equal to each of its four adjacent elements (the elements on the corner only need to be bigger or equal than their 2 adjacent elements, and the elements on the sides only need to be bigger or equal than their 3 adjacent elements). For example, in the following matrix we are searching for one of the starred elements. 1 4 5* 6* 5 3 4* 11* 1 4 2 3 4 10* 7 7* 1 4 1 8* 4 5* 3 Assume we have an algorithm that works by selecting the middle column (of the remaining columns) in each step. In that column, it selects the maximum element. If this element is also bigger or equal than its left and right elements, we have found a solution. Otherwise, we select the side with the bigger element and repeat the algorithm with half the input (no longer considering the columns on the side with the smaller element). 1) The asymptotic complexity of this algorithm is O(nlogn). If we change the algorithm so that tin each phase: if the number of rows is more than the number of columns, choose the middle row instead of the middle column, find the max and remove half the rows as we did for columns. Then what is the asymptotiC complexity of the new algorithm? How does new algorithm work?(Prove) 2.

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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The asymptotic complexity of this algorithm is O(nlogn). If we change the algorithm so that tin each phase: if the number of rows is more than the number of columns, choose the middle row instead of the middle column, find the max and remove half the rows as we did for columns. Then what is the asymptotic complexity of the new algorithm? How does new algorithm work?(Prove)

Consider an n × n matrix. We want to find an element in this matrix that is bigger or equal to each of its four adjacent elements (the elements on the corner only need to be bigger or equal than their 2 adjacent elements, and the elements on the sides only need to be bigger or equal than their 3 adjacent elements). For example, in the following matrix we are searching for one of the starred elements. 14 5* 6* 5 2 4* 3 11* 1 4 3 4 10* 7 7* 1 4 1 8* 4 5* 3. Assume we have an algorithm that works by selecting the middle column (of the remaining columns) in each step. In that column, it selects the maximum element. If this element is also bigger or equal than its left and right elements, we have found a solution. Otherwise, we select the side with the bigger element and repeat the algorithm with half the input (no longer considering the columns on the side with the smaller element). 1) The asymptotic complexity of this algorithm is O(nlogn). If we change the algorithm so that tin each phase: if the number of rows is more than the number of columns, choose the middle row instead of the middle column, find the max and remove half the rows as we did for columns. Then what is the asymptotic complexity of the new algorithm? How does new algorithm work?(Prove) 2. 2.
Transcribed Image Text:Consider an n × n matrix. We want to find an element in this matrix that is bigger or equal to each of its four adjacent elements (the elements on the corner only need to be bigger or equal than their 2 adjacent elements, and the elements on the sides only need to be bigger or equal than their 3 adjacent elements). For example, in the following matrix we are searching for one of the starred elements. 14 5* 6* 5 2 4* 3 11* 1 4 3 4 10* 7 7* 1 4 1 8* 4 5* 3. Assume we have an algorithm that works by selecting the middle column (of the remaining columns) in each step. In that column, it selects the maximum element. If this element is also bigger or equal than its left and right elements, we have found a solution. Otherwise, we select the side with the bigger element and repeat the algorithm with half the input (no longer considering the columns on the side with the smaller element). 1) The asymptotic complexity of this algorithm is O(nlogn). If we change the algorithm so that tin each phase: if the number of rows is more than the number of columns, choose the middle row instead of the middle column, find the max and remove half the rows as we did for columns. Then what is the asymptotic complexity of the new algorithm? How does new algorithm work?(Prove) 2. 2.
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