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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