1. Consider the following program that uses a data structure P: Program1 (A, n) /* A is an array of n elements 1 P.Initialize(); 2 for i 1 to n do 3 4 5 6 end 7 while P.Size() # 0 do 8 xP.ExtractMax (); Print x; for j1 to [²/³] do | P.Insert (A[i] * A[j]); end 9 10 end P.Initialize () initializes the data structure P. P.Insert (x) inserts elements x in P. P.ExtractMax () returns the maximum element of P and deletes it from P. P.Size() returns the number of elements in P. Analyze carefully the running time of Program1 assuming that the data structure P is implemented as a Max-Heap. (Analyze the total time for both the P.Insert () and P.Extract Max () operations. Note that the time for P.Insert () and P.Extract Max () is dependent on the number of elements in P which changes over the running time of the algorithm. Operations P.Initialize() and P.Size() take constant time.) Show your work.
1. Consider the following program that uses a data structure P: Program1 (A, n) /* A is an array of n elements 1 P.Initialize(); 2 for i 1 to n do 3 4 5 6 end 7 while P.Size() # 0 do 8 xP.ExtractMax (); Print x; for j1 to [²/³] do | P.Insert (A[i] * A[j]); end 9 10 end P.Initialize () initializes the data structure P. P.Insert (x) inserts elements x in P. P.ExtractMax () returns the maximum element of P and deletes it from P. P.Size() returns the number of elements in P. Analyze carefully the running time of Program1 assuming that the data structure P is implemented as a Max-Heap. (Analyze the total time for both the P.Insert () and P.Extract Max () operations. Note that the time for P.Insert () and P.Extract Max () is dependent on the number of elements in P which changes over the running time of the algorithm. Operations P.Initialize() and P.Size() take constant time.) Show your work.
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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Please show steps clearly
![1. Consider the following program that uses a data structure P:
Program1 (A, n)
/* A is an array of n elements
1 P.Initialize();
2 for i 1 to n do
3
for j1 to [n²/³] do
P.Insert (A[i] * A[j]);
4
5
6 end
7 while P.Size() # 0 do
8
x← P.ExtractMax();
9
Print x;
10 end
end
*/
P.Initialize() initializes the data structure P.
P.Insert (x) inserts elements x in P.
P.ExtractMax () returns the maximum element of P and deletes it from P.
P.Size() returns the number of elements in P.
Analyze carefully the running time of Program1 assuming that the data structure P is implemented as
a Max-Heap.
(Analyze the total time for both the P.Insert () and P.Extract Max () operations. Note that the time
for P.Insert() and P.ExtractMax () is dependent on the number of elements in P which changes over
the running time of the algorithm. Operations P.Initialize() and P.Size() take constant time.)
Show your work.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbf24fe0a-0da7-4e45-9e5d-fa69e5b3ec9c%2F063ac87d-5819-4b45-9579-e5bcef7d13ab%2Fq7jkwyv_processed.png&w=3840&q=75)
Transcribed Image Text:1. Consider the following program that uses a data structure P:
Program1 (A, n)
/* A is an array of n elements
1 P.Initialize();
2 for i 1 to n do
3
for j1 to [n²/³] do
P.Insert (A[i] * A[j]);
4
5
6 end
7 while P.Size() # 0 do
8
x← P.ExtractMax();
9
Print x;
10 end
end
*/
P.Initialize() initializes the data structure P.
P.Insert (x) inserts elements x in P.
P.ExtractMax () returns the maximum element of P and deletes it from P.
P.Size() returns the number of elements in P.
Analyze carefully the running time of Program1 assuming that the data structure P is implemented as
a Max-Heap.
(Analyze the total time for both the P.Insert () and P.Extract Max () operations. Note that the time
for P.Insert() and P.ExtractMax () is dependent on the number of elements in P which changes over
the running time of the algorithm. Operations P.Initialize() and P.Size() take constant time.)
Show your work.
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