Algorithm EC 9. In the desert there is a jail. After rebellionthe single guard has been immobilized. Hewatched helplessly how prisoners left one by onewith different speed in different directions. Laterhe free himself and took a motobike with extraseat. Now he can follow footprints and pick upone prisoner at a time and bring them back to jail.Each prisoner moves with constant individualspeed v_i and left the jail at time t_i. In whichorder the guard should bring the prisoners backin order to minimize the time?

Answered: EC 9. In the desert there is a jail.…

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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Algorithm

EC 9. In the desert there is a jail. After rebellion
the single guard has been immobilized. He
watched helplessly how prisoners left one by one
with different speed in different directions. Later
he free himself and took a motobike with extra
seat. Now he can follow footprints and pick up
one prisoner at a time and bring them back to jail.
Each prisoner moves with constant individual
speed v_i and left the jail at time t_i. In which
order the guard should bring the prisoners back
in order to minimize the time?

Expert Solution

Step 1

Solution:

We will solve this with greedy algorithm. At any given time instant 't' measure the value d_i_t = v_i * (t - t_i) for each of the prisoners. Choose the maximum value amongst these and go and catch that prisoner. For prisoners having the same value for d_i_t , go for the prisoner who has higher speed, else he will move more distance and the guard will take more time in catching that prisoner.

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