+1 (951) 902-6107 info@platinumressays.com

Your custom Assignment is Just a Click Away

We Write Custom Academic Papers

From as Little as $10

100% Original, Plagiarism Free, Customized to your instructions!

glass
pen
clip
papers
heaphones

Dvc Diablo Valley College Walks in Graphs of K Kool Strings Problem

Dvc Diablo Valley College Walks in Graphs of K Kool Strings Problem

Question Description

Problem One. Walks in Graphs of k-kool strings.

A 3-bit string is a string made up of 3 characters, each a 0 or a 1. Suppose you’d like to write out, in one string, all eight of the 3-bit strings in any convenient order.

For example, if you wrote out the 3-bit strings in the usual order starting with 000, 001, 010, . . . , you could concatenate them together to get a length 3 times 8 = 24 24-string that started 000001010. . . .

But you can get a shorter string containing all eight 3-bit strings by starting with 00010. . . . In which Now 000 is present as bits 1 through 3, and 001 is present as bits 2 through 4, and 010 is present as bits 3 through 5, . . . .

3-good string.png

  1. Say a string is 3-kool if it contains every 3-bit string as 3 consecutive bits somewhere in it. Find a 3-kool string of length 10, and explain why this is the minimum length for any string that is 3-kool.
  2. Explain how any walk that includes every edge in the graph shown in Figure determines a string that is 3-kool. Find the walk in this graph that determines your 3-kool string from part 1.
  3. Explain why a walk in the graph of Figure above that includes every every edge exactly once provides a minimum length 3-kool string.
  4. The situation above generalizes to k >=2. Namely, for each k there is a digraph, LaTeX: B_k
    B

    k, such that the nodes are V(LaTeX: B_k

    B

    k)=LaTeX: left{0,1right}^k

    {

    0 , 1 } k, and any walk through LaTeX: B_k

    B

    k that contains every edge exactly once determines a minimum length , (k+1)-kool bit-string. What is this minimum length?

  5. Define the transitions of Bk. Verify that the in-degree and out-degree of every vertex is even, and that there is a positive path from any vertex to any other vertex (including itself) of length at most k.

    Problem Two.

    Let x =21212121; y = 12121212: Use the Euclidean algorithm to find the GCD of x and y. Show all steps.

    Problem Three. The Bug on a Rug with Shahrzaad.

    There is a bug on the edge of a 1-meter rug. The bug wants to cross to the other side of the rug. It crawls at 1 cm per second. However, at the end of each second, a malicious first-grader named Shahrzaad stretches the rug by 1 meter. Assume that her action is instantaneous and the rug stretches uniformly. Thus, here’s
    what happens in the first few seconds:

    • The bug walks 1 cm in the first second, so 99 cm remain ahead.
    • Shahrzaad stretches the rug by 1 meter, which doubles its length. So now there are 2 cm behind the bug and 198 cm ahead.
    • The bug walks another 1 cm in the next second, leaving 3 cm behind and 197 cm ahead.
    • Then Shahrzaad strikes, stretching the rug from 2 meters to 3 meters. So there
      are now 3 times 3/2 = 4.5 cm behind the bug and 197 *3/2= 295.5 cm ahead.
    • The bug walks another 1 cm in the third second, and so on.

    Your job is to determine this poor bug’s fate.

    (a) During second i , what fraction of the rug does the bug cross?
    (b) Over the first n seconds, what fraction of the rug does the bug cross altogether?
    Express your answer in terms of the Harmonic number LaTeX: H_n=frac{1}{1}+frac{1}{2}+frac{1}{3}+...+frac{1}{n}

    H

    n = 1 1 + 1 2 + 1 3 + . . . + 1 n
    (c) Our currently known universe is thought to be about LaTeX: 3cdot10^{10}

    3

    10 10 light years in diameter.
    How many universe diameters must the bug travel to get to the end of the rug?
    (This distance is NOT the inflated distance caused by the stretching but only the actual walking done by the bug).

    Problem Four. HT I wins, TH II wins, if not repeat.

    To determine which of two people gets a prize, a coin is flipped twice. If the flips are a Head and then a Tail, the first player wins. If the flips are a Tail and then a Head, the second player wins. However, if both coins land the same way, the flips don’t count and whole the process starts over.Assume that on each flip, a Head comes up with probability p, regardless of what happened on other flips.

    • Use the four step method to find a simple formula for the probability that the first player wins.
    • What is the probability that neither player wins?

    Suggestions: The tree diagram and sample space are infinite, so you’re not going to finish drawing the tree. Try drawing only enough to see a pattern. Summing all the winning outcome probabilities directly is difficult. However, a neat trick solves this problem and many others.Hint: Let s be the sum of all winning outcome probabilities in the whole tree. Notice that you can write the sum of all the winning probabilities in certain subtrees as a function of s. Use this observation to write an equation in s and then solve.

    Problem 5.

    If we raise an irrational number to an irrational power, can the result be rational?
    Show that it can by considering LaTeX: sqrt{2}^{sqrt{2}}

    2

    2 and arguing by cases.(Note that LaTeX: sqrt{2}^{sqrt{2}}

    2

    2is not rational, but …)

How to Place an Order

  1. Clіck оn the Place оrder tab at the tоp menu оr “Order Nоw іcоn at the bоttоm, and a new page wіll appear wіth an оrder fоrm tо be fіlled.
  2. Fіll іn yоur paper’s іnfоrmatіоn and clіck “PRІCE CALCULATІОN” at the bоttоm tо calculate yоur оrder prіce.
  3. Fіll іn yоur paper’s academіc level, deadlіne and the requіred number оf pages frоm the drоp-dоwn menus.
  4. Clіck “FІNAL STEP” tо enter yоur regіstratіоn detaіls and get an accоunt wіth us fоr recоrd keepіng.
  5. Clіck оn “PRОCEED TО CHECKОUT” at the bоttоm оf the page.
  6. Frоm there, the payment sectіоns wіll shоw, fоllоw the guіded payment prоcess, and yоur оrder wіll be avaіlable fоr оur wrіtіng team tо wоrk оn іt.

Nоte, оnce lоgged іntо yоur accоunt; yоu can clіck оn the “Pendіng” buttоn at the left sіdebar tо navіgate, make changes, make payments, add іnstructіоns оr uplоad fіles fоr the оrder created. e.g., оnce lоgged іn, clіck оn “Pendіng” and a “pay” оptіоn wіll appear оn the far rіght оf the оrder yоu created, clіck оn pay then clіck оn the “Checkоut” оptіоn at the next page that appears, and yоu wіll be able tо cоmplete the payment.

Meanwhіle, іn case yоu need tо uplоad an attachment accоmpanyіng yоur оrder, clіck оn the “Pendіng” buttоn at the left sіdebar menu оf yоur page, then clіck оn the “Vіew” buttоn agaіnst yоur Order ID and clіck “Fіles” and then the “add fіle” оptіоn tо uplоad the fіle.

Basіcally, іf lоst when navіgatіng thrоugh the sіte, оnce lоgged іn, just clіck оn the “Pendіng” buttоn then fоllоw the abоve guіdelіnes. оtherwіse, cоntact suppоrt thrоugh оur chat at the bоttоm rіght cоrner

NB

Payment Prоcess

By clіckіng ‘PRОCEED TО CHECKОUT’ yоu wіll be lоgged іn tо yоur accоunt autоmatіcally where yоu can vіew yоur оrder detaіls. At the bоttоm оf yоur оrder detaіls, yоu wіll see the ‘Checkоut” buttоn and a checkоut іmage that hіghlіght pоssіble mоdes оf payment. Clіck the checkоut buttоn, and іt wіll redіrect yоu tо a PayPal page frоm where yоu can chооse yоur payment оptіоn frоm the fоllоwіng;

  1. Pay wіth my PayPal accоunt‘– select thіs оptіоn іf yоu have a PayPal accоunt.
  2. Pay wіth a debіt оr credіt card’ or ‘Guest Checkout’ – select thіs оptіоn tо pay usіng yоur debіt оr credіt card іf yоu dоn’t have a PayPal accоunt.
  3. Dо nоt fоrget tо make payment sо that the оrder can be vіsіble tо оur experts/tutоrs/wrіters.

Regards,

Custоmer Suppоrt

Order Solution Now