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
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
Related questions
Question
The asymptotic complexity of this
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.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 3 images
Recommended textbooks for you
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
Database System Concepts
Computer Science
ISBN:
9780078022159
Author:
Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:
McGraw-Hill Education
Starting Out with Python (4th Edition)
Computer Science
ISBN:
9780134444321
Author:
Tony Gaddis
Publisher:
PEARSON
Digital Fundamentals (11th Edition)
Computer Science
ISBN:
9780132737968
Author:
Thomas L. Floyd
Publisher:
PEARSON
C How to Program (8th Edition)
Computer Science
ISBN:
9780133976892
Author:
Paul J. Deitel, Harvey Deitel
Publisher:
PEARSON
Database Systems: Design, Implementation, & Manag…
Computer Science
ISBN:
9781337627900
Author:
Carlos Coronel, Steven Morris
Publisher:
Cengage Learning
Programmable Logic Controllers
Computer Science
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education