A safe is locked by a combination of of four binary digits (that is, 0 or 1), but theowner has forgotten the combination. The safe is designed in such a way that nomatter how many digits have been pressed, if the correct combination of three digitsis pressed at any point, then the safe automatically opens (there is no ”enter” key).Our goal is to find the minimum number of digits that one needs to key in in order toguarantee that the safe opens. In other words, we wish to find the smallest possiblelength of a binary sequence containing every four-digit sequence in it.(a) Create a digraph whose vertex set consists of three-digit binary sequences. Fromeach vertex labelled xyz, there is one outgoing edge (labelled 0) leading to vertexyz0, and another outgoing edge (labelled 1) leading to vertex yz1.(b) Explain why every edge represents a four digit sequence and why an Euleriantour of this graph represents the desired sequence of keystrokes.(c) Find the minimum number of digits that one needs to key in to guarantee thatthe safe opens. 3. A safe is locked by a combination of of four binary digits (that is, 0 or 1), but theowner has forgotten the combination. The safe is designed in such a way that nomatter how many digits have been pressed, if the correct combination of three digitsis pressed at any point, then the safe automatically opens (there is no "enter" key).Our goal is to find the minimum number of digits that one needs to key in in order toguarantee that the safe opens. In other words, we wish to find the smallest possiblelength of a binary sequence containing every four-digit sequence in it.(a) Create a digraph whose vertex set consists of three-digit binary sequences. Fromeach vertex labelled ryz, there is one outgoing edge (labelled 0) leading to vertexyz0, and another outgoing edge (labelled 1) leading to vertex yz1l.(b) Explain why every edge represents a four digit sequence and why an Euleriantour of this graph represents the desired sequence of keystrokes.(c) Find the minimum number of digits that one needs to key in to guarantee thatthe safe opens.

Answered: (a) Create a digraph whose vertex set…

Computer Networking: A Top-Down Approach (7th Edition)

7th Edition

ISBN:9780133594140

Author:James Kurose, Keith Ross

Publisher:James Kurose, Keith Ross

Chapter1: Computer Networks And The Internet

Section: Chapter Questions

Problem R1RQ: What is the difference between a host and an end system? List several different types of end...

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Question

A safe is locked by a combination of of four binary digits (that is, 0 or 1), but the
owner has forgotten the combination. The safe is designed in such a way that no
matter how many digits have been pressed, if the correct combination of three digits
is pressed at any point, then the safe automatically opens (there is no ”enter” key).
Our goal is to find the minimum number of digits that one needs to key in in order to
guarantee that the safe opens. In other words, we wish to find the smallest possible
length of a binary sequence containing every four-digit sequence in it.
(a) Create a digraph whose vertex set consists of three-digit binary sequences. From
each vertex labelled xyz, there is one outgoing edge (labelled 0) leading to vertex
yz0, and another outgoing edge (labelled 1) leading to vertex yz1.
(b) Explain why every edge represents a four digit sequence and why an Eulerian
tour of this graph represents the desired sequence of keystrokes.
(c) Find the minimum number of digits that one needs to key in to guarantee that
the safe opens.