Assume the existence of an N x M matrix of characters, you are requested to find the character that is most commonly used in the whole matrix. For example: Input: C E F A [F [F [E [C [D [D G F A A F В C G A Output: The most common characters are: F and A a) Design an efficient algorithm with the lowest possible complexity to solve this problem, and explain why your algorithm is efficient. b) Analyze the complexity of your algorithm. (10 marks) (5 marks) Question 4: (15 Marks) Find the complexity of the following blocks of code or algorithm's description. [Note: your answer must show the steps that lead to your final answer] (5 marks each) The algorithm solves the problem of 2) 1) size n by recursively solving sub- problems of size n – 1, and then combining the solutions in constant time. The algorithm solves the problem by breaking it into 16 sub- problems of 1/4 the scale, recursively solving each sub- maze, and then combining the solutions in linear time 3) The algorithm solves the problem of size n by dividing it into 32 sub- problems of size n/2, recursively solving each sub-problem, and then combining the solutions in O(n5) time Page 4 of 5 따E미어미시미이 CAACE☺ED ACAFE wAE O BFEW ODD

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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Question
Question 3: (15 Marks)
Assume the existence of an N x M matrix of characters, you are requested to find the
character that is most commonly used in the whole matrix.
For example:
Input:
C
E
C
F
A
B
A
A
[F
[F
[E
[C
[D
[D
G
F
F
A
A
B
G
D
A
Output:
The most common characters are: F and A
a) Design an efficient algorithm with the lowest possible complexity to solve this
problem, and explain why your algorithm is efficient.
b) Analyze the complexity of your algorithm.
(10 marks)
(5 marks)
Question 4: (15 Marks)
Find the complexity of the following blocks of code or algorithm's description.
[Note: your answer must show the steps that lead to your final answer] (5 marks each)
The algorithm solves the problem of 2)
size n by recursively solving sub-
problems of size n – 1, and then
combining the solutions in constant
time.
1)
The algorithm solves the problem
by breaking it into 16 sub-
problems of 1/4 the scale,
recursively solving each sub-
maze, and then combining the
solutions in linear time
3)
The algorithm solves the problem of
size n by dividing it
problems of size n/2, recursively
solving each sub-problem, and then
combining the solutions in O(n5)
time
32 sub
Page 4 of 5
고ㄷ미어미식미어
ACAFE wAE
O ME uw UDD
---- --- L
Transcribed Image Text:Question 3: (15 Marks) Assume the existence of an N x M matrix of characters, you are requested to find the character that is most commonly used in the whole matrix. For example: Input: C E C F A B A A [F [F [E [C [D [D G F F A A B G D A Output: The most common characters are: F and A a) Design an efficient algorithm with the lowest possible complexity to solve this problem, and explain why your algorithm is efficient. b) Analyze the complexity of your algorithm. (10 marks) (5 marks) Question 4: (15 Marks) Find the complexity of the following blocks of code or algorithm's description. [Note: your answer must show the steps that lead to your final answer] (5 marks each) The algorithm solves the problem of 2) size n by recursively solving sub- problems of size n – 1, and then combining the solutions in constant time. 1) The algorithm solves the problem by breaking it into 16 sub- problems of 1/4 the scale, recursively solving each sub- maze, and then combining the solutions in linear time 3) The algorithm solves the problem of size n by dividing it problems of size n/2, recursively solving each sub-problem, and then combining the solutions in O(n5) time 32 sub Page 4 of 5 고ㄷ미어미식미어 ACAFE wAE O ME uw UDD ---- --- L
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