Answered: 1. Let T (n) be the number of moves in…

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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1. Let T (n) be the number of moves in our solution to the n-disc Towers of
Hanoi puzzle. Recall that to solve this puzzle,
•move the top n −1 discs from the source to the scratch peg,
•move disc n from the source to the destination peg, and
•move the top n −1 discs from the scratch to the destination peg.
The first step takes T (n −1) moves, the second step takes one move, and
the third step takes T (n −1) moves again. In other words,
T (n) = 2T (n −1) + 1.
This applies when n > 0. At zero, we have T (0) = 0, because with zero
discs the start and final states are identical; there are no moves to make.
Your task is to find a closed-form expression for T (n) (i.e., one that does
not use recursion), and prove that it’s correct using induction.

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