Toggle navigation
Ask Questions
Ask
Answer Questions
Answer
Users
FAQ
Login
Register
Preview 50% of the Answer Below
Due to formatting, images, tables, or paragraphs may be out of place or not shown. Rest assured that they will be included and formatted correctly in your purchased answer.
Details
Question Title:
computer science
Go Back to the Question
Answer Preview
<span class="katex-mathml">n = 1</span><span class="katex-html" aria-hidden="true"><span class="base"><span class="strut"></span><i>n</i><span class="mspace"></span><span class="mrel">=</span><span class="mspace"></span></span><span class="base"><span class="strut"></span><span class="mord">1</span></span></span></span>,<span XXXXX="katex"><span class="katex-mathml">T(n) = XXX</span><span XXXXX="XXXXX-html" aria-hidden="true"><span XXXXX="XXXX"><span XXXXX="strut"></span><i>T</i><span XXXXX="XXXXX">(</span><i>n</i><span class="mclose">)</span><span XXXXX="mspace"></span><span class="XXXX">=</span><span XXXXX="XXXXXX"></span></span><span XXXXX="XXXX"><span XXXXX="XXXXX"></span><span XXXXX="XXXX"><i>c</i><span XXXXX="XXXXXXX"><span class="XXXXX-t vlist-XX"><span class="XXXXX-r"><span class="XXXXX"><span XXXXX="XXXXXX"></span><span class="sizing reset-size6 size3 XXXXXX"><span class="XXXX mtight">X</span></span></span><span XXXXX="vlist-s"></span></span><span XXXXX="vlist-r"><span XXXXX="vlist"><span></span></span></span></span></span></span></span></span></span>, XXXXX<span class="XXXXX"><span class="katex-mathml">c_1</span><span XXXXX="katex-XXXX" XXXX-hidden="XXXX"><span XXXXX="base"><span class="strut"></span><span XXXXX="mord"><i>c</i><span class="msupsub"><span XXXXX="vlist-t XXXXX-XX"><span class="vlist-r"><span XXXXX="XXXXX"><span class="pstrut"></span><span XXXXX="XXXXXX reset-XXXXX XXXXX XXXXXX"><span class="XXXX mtight">1</span></span></span><span class="XXXXX-s"></span></span><span class="vlist-r"><span XXXXX="vlist"><span></span></span></span></span></span></span></span></span></span>XX some XXXXXXXX. XXX on XXXXXXX XXX<span class="XXXXX"><span class="katex-XXXXXX">n > X</span><span class="katex-html" XXXX-XXXXXX="true"><span class="base"><span class="XXXXX"></span><i>n</i><span class="mspace"></span><span XXXXX="mrel">&XX;</span><span XXXXX="mspace"></span></span><span XXXXX="XXXX"><span class="XXXXX"></span><span XXXXX="mord">1</span></span></span></span>, inserting an XXXXXXX in XXX proper position in a sorted array requires XXXXXXXX half XX the elements, i.e.<span class="XXXXX"><span class="XXXXX-XXXXXX">XXXX/2 + XXX</span><span class="katex-XXXX" aria-hidden="XXXX"><span XXXXX="XXXX"><span class="XXXXX"></span><span XXXXX="mord"><i>c</i><span class="msupsub"><span XXXXX="XXXXX-t vlist-t2"><span XXXXX="vlist-r"><span XXXXX="vlist"><span class="pstrut"></span><span class="sizing XXXXX-size6 size3 mtight"><span class="XXXX mtight">2</span></span></span><span XXXXX="XXXXX-s"></span></span><span XXXXX="vlist-r"><span XXXXX="vlist"><span></span></span></span></span></span></span><i>n</i><span class="mord">/</span><span XXXXX="mord">X</span><span XXXXX="mspace"></span><span XXXXX="XXXX">+</span><span class="mspace"></span></span><span class="base"><span class="strut"></span><span XXXXX="mord"><i>c</i><span class="XXXXXXX"><span XXXXX="vlist-t XXXXX-XX"><span XXXXX="XXXXX-r"><span XXXXX="vlist"><span XXXXX="pstrut"></span><span XXXXX="XXXXXX XXXXX-XXXXX XXXXX XXXXXX"><span class="mord mtight">3</span></span></span><span XXXXX="vlist-s"></span></span><span XXXXX="vlist-r"><span XXXXX="XXXXX"><span></span></span></span></span></span></span></span></span></span>time (<span XXXXX="katex"><span XXXXX="katex-mathml">c_2n/X</span><span class="katex-html" aria-hidden="XXXX"><span class="base"><span class="XXXXX"></span><span XXXXX="mord"><i>c</i><span XXXXX="XXXXXXX"><span class="vlist-t vlist-XX"><span class="vlist-r"><span XXXXX="XXXXX"><span class="pstrut"></span><span XXXXX="XXXXXX reset-size6 XXXXX XXXXXX"><span class="XXXX mtight">X</span></span></span><span class="vlist-s"></span></span><span XXXXX="vlist-r"><span XXXXX="vlist"><span></span></span></span></span></span></span><i>n</i><span XXXXX="mord">/</span><span class="mord">X</span></span></span></span>for shifting the XXXXXXXX and<span class="katex"><span class="katex-mathml">c_3</span><span class="katex-XXXX" aria-hidden="XXXX"><span class="base"><span class="XXXXX"></span><span class="XXXX"><i>c</i><span XXXXX="XXXXXXX"><span class="XXXXX-t vlist-XX"><span XXXXX="vlist-r"><span XXXXX="XXXXX"><span class="XXXXXX"></span><span XXXXX="XXXXXX XXXXX-XXXXX size3 XXXXXX"><span XXXXX="mord mtight">X</span></span></span><span class="XXXXX-s"></span></span><span class="XXXXX-r"><span class="XXXXX"><span></span></span></span></span></span></span></span></span></span>for inserting XXX element).</p><p>$ T(n) & = X(n - X) + c_2(n - 1)/X + XXX \\ & = T(n - 2) + XXX(n - 2)/2 + c_3 + \{XXX(n - X)/X + XXX\} \\ & = T(X) + \XXXX \cdot \XXXX + \{XXX(n - 2)/X + XXX\} + \{c_2(n - X)/X + XXX\} \\ & = c_1 + \frac {c_2} 2 \{1 + X + \XXXX \XXXX \XXXX + (n - X)\} + c_3(n - X) \\ & = XXX + \frac {XXX} 2 \cdot \XXXX {n(n - X)} X + c_3(n - X) \\ & = \Theta(n^X)$</p><p><br></p>">
Attachment #1 Preview
