There are n bacteria and one virus in a Petri dish. Within the first minute, the virus kills one bacterium and produces another copy of itself, and all of the remaining bacteria reproduce, making 2 viruses and 2(n-1) bacteria. In the second minute, each of the viruses kills a bacterium and produces a new copy of itself, resulting in 4 viruses and 2(2(n − 1)2)) = 4n - 8 bacteria. Again, the remaining bacteria reproduce. This process continues every minute. Will the viruses eventually kill all the bacteria? If so, give an algorithm that computes how many steps it will take. How does the running time of your algorithm depend on n?

There are n bacteria and one virus in a Petri dish. Within the first minute, the virus kills one bacterium and produces another copy of itself, and all of the remaining bacteria reproduce, making 2 viruses and 2(n-1) bacteria. In the second minute, each of the viruses kills a bacterium and produces a new copy of itself, resulting in 4 viruses and 2(2(n − 1)2)) = 4n - 8 bacteria. Again, the remaining bacteria reproduce. This process continues every minute. Will the viruses eventually kill all the bacteria? If so, give an algorithm that computes how many steps it will take. How does the running time of your algorithm depend on n?

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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