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

See similar textbooks

Similar questions

Use the Quine McCluskey algorithm to simplify the function:F(w, x, y, z) = Σ(2, 6, 9, 10, 11, 13, 14, 15)Show all work – no credit will be given for an answer without accompanying work
To expand (a + b)n, we can use the Theorem. Using this theorem, we find the expansion (a + b)4 = a4 + a3b + a2b2 + ab3 + b
To draw a line between (5,12) and (15,20) by using Bresenham algorithm In step (6) The Pk+1 4 6. 7 -2 -5 O -7 O 14 Other:
Given the following recurrence, find the growth rate of T(n):T(n) = 4T(n/2) + 6n3 with T(1) = Θ(1)
Plot a graph for the following polynomials each with x=-100 to +100 with a change in x as 0.2 a) f(x)= x(x-2) (x-1)(x+1) b) f(x) = -(x-2) (x-1)(x+1) ) f(x) = -x(x-1)(x+1)(x-2) d) f(x) = (1-x)(x+1) (x-2) Write c++ code that will output all the values of f(x) given values of x. Do it for a, b, c and d above.
For each set of cubes in terms of variables (a, b, c, d] obtain the minimized version for boolean fuction f(a, b, c, d) (00X1, 0XX1, 1000, 1100, 1010, 1110} {1XX0, 10XX, 11XX, 00XX} ✓ {00XX, 01XX, 0XXX, 01X1} (0100, 1010, 1XX1, XXXX, 0001} {0001, 0011, 0101, 0111, 1101, 1111, 1001, 1011} ✓ {000X, 010X, 1X00, 1X01} A f(a, b, c, d) = 1 B. f(a, b, c, d) = d C. f(a, b, c, d) = ē D. f(a, b, c, d) = a + a b Ef(a, b, c, d) = a F. f(a, b, c, d) = a d
If you know that: F1(X, Y, Z) = E(1, 4, 6) F2(X, Y, Z) = 7(0, 2, 4, 5, 7) Find F3 as Sum of Products if you know that F3 = (F1'.F2')' Select one: F3 = N(3, 4) F3 = E(1,3, 4, 6) F3 = E(1, 6) None of the answers F3 = E(3) %3D F3 = 1(1, 6, 7) F3 = E(0, 1, 2, 3, 5, 6, 7)
Diffie-Hellman Key exchange is based on the difficulty of solving the Discrete Logarithm Problem. For instance, Alice and Bob agree on a prime number p=7 and a number (base) g=4. This is the public aspect of the system. Using this algorithm, find the kprivate.
Prove or disprove each of the following: [10] 1. (n+a) = 0(nb), for any real constants, where b > 0. 2. 3an = 0(3")
Find f(1), f(2), f(3), f(4), and f(5) if f(n) is defined re-cursively by f(0) = 3 and for n = 0, 1, 2, ... a) f(n + 1) = −2f(n).b) f(n + 1) = 3f(n) + 7.
Express the following functions as sum of minterms and product of maxterms: (a) F(A, B, C, D) = BD+ AD+ BD (b) F(x, y, z) = (xy +z)(xz + y) %3D
6. Prove that if m and n are integers and mn is even, then m is even or n is even.