QUESTION 5 The Towers of Hanoi game starts with a pile of disks with different sizes on one of three pegs. The other two pegs start empty. The disks are initially piled in order of size with largest on the bottom. The aim of the game is to transfer all of the disks to a destination peg by moving one disk at a time, never placing a disk on top of a smaller one. The spare peg may be used for intermediate moves. One solution to the problem recursively moves all but the largest disk to the spare peg, moves the largest disk to the destination peg, and then recursively moves all the other disks from the spare peg to the destination peg. This process is described by the following pseudocode: Hanoi( n, start, destination, spare ) I/ n is the number of disks and start, destination and spare are peg numbers if n>0 Hanoi( n-1, start, spare, destination) moveTopDisk( start, destination) I/ move top disk on start peg to destination peg Hanoi( n-1, spare, destination, start) Which of the following most accurately gives a recurrence relation for the number of moves required by this algorithm and its asymptotic complexity? T(n) = 2T(n-1) + 1 with asymptotic complexity O(2"). T(n) = 2T(n-1) +1 with asymptotic complexity O(n-). O T(n) = T(n-1) +1 with asymptotic complexity O(n). T(n) = 2T(n/2) + 1 with asymptotic complexity O(n). O None of the above.
QUESTION 5 The Towers of Hanoi game starts with a pile of disks with different sizes on one of three pegs. The other two pegs start empty. The disks are initially piled in order of size with largest on the bottom. The aim of the game is to transfer all of the disks to a destination peg by moving one disk at a time, never placing a disk on top of a smaller one. The spare peg may be used for intermediate moves. One solution to the problem recursively moves all but the largest disk to the spare peg, moves the largest disk to the destination peg, and then recursively moves all the other disks from the spare peg to the destination peg. This process is described by the following pseudocode: Hanoi( n, start, destination, spare ) I/ n is the number of disks and start, destination and spare are peg numbers if n>0 Hanoi( n-1, start, spare, destination) moveTopDisk( start, destination) I/ move top disk on start peg to destination peg Hanoi( n-1, spare, destination, start) Which of the following most accurately gives a recurrence relation for the number of moves required by this algorithm and its asymptotic complexity? T(n) = 2T(n-1) + 1 with asymptotic complexity O(2"). T(n) = 2T(n-1) +1 with asymptotic complexity O(n-). O T(n) = T(n-1) +1 with asymptotic complexity O(n). T(n) = 2T(n/2) + 1 with asymptotic complexity O(n). O None of the above.
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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Transcribed Image Text:QUESTION 5
The Towers of Hanoi game starts with a pile of disks with different sizes on one of three pegs. The other two pegs start empty. The disks are initially piled in order of size
with largest on the bottom. The aim of the game is to transfer all of the disks to a destination peg by moving one disk at a time, never placing a disk on top of a smaller
one. The spare peg may be used for intermediate moves.
One solution to the problem recursively moves all but the largest disk to the spare peg, moves the largest disk to the destination peg, and then recursively moves all the
other disks from the spare peg to the destination peg. This process is described by the following pseudocode:
Hanoi( n, start, destination, spare )
// n is the number of disks and start, destination and spare are peg numbers
if n>0
Hanoi( n-1, start, spare, destination)
moveTopDisk( start, destination) // move top disk on start peg to destination peg
Hanoi( n-1, spare, destination, start)
Which of the following most accurately gives a recurrence relation for the number of moves required by this algorithm and its asymptotic complexity?
T(n) = 2T(n-1) + 1 with asymptotic complexity O(2").
T(n) = 2T(n-1) +1 with asymptotic complexity O(n2).
O T(n) = T(n-1) + 1 with asymptotic complexity O(n).
T(n) = 2T(n/2) + 1 with asymptotic complexity O(n).
O None of the above.
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