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 class="katex"><span class="XXXXX-mathml">X(n) = XXX</span><span XXXXX="XXXXX-html" aria-hidden="true"><span XXXXX="XXXX"><span XXXXX="strut"></span><i>X</i><span class="mopen">(</span><i>n</i><span class="mclose">)</span><span XXXXX="mspace"></span><span class="XXXX">=</span><span class="mspace"></span></span><span XXXXX="base"><span XXXXX="strut"></span><span class="XXXX"><i>c</i><span class="XXXXXXX"><span class="vlist-t XXXXX-t2"><span class="vlist-r"><span class="vlist"><span class="XXXXXX"></span><span XXXXX="sizing reset-size6 XXXXX mtight"><span XXXXX="mord XXXXXX">1</span></span></span><span XXXXX="XXXXX-s"></span></span><span class="vlist-r"><span XXXXX="vlist"><span></span></span></span></span></span></span></span></span></span>, where<span XXXXX="katex"><span XXXXX="katex-mathml">c_1</span><span class="XXXXX-XXXX" aria-XXXXXX="XXXX"><span class="base"><span class="XXXXX"></span><span class="XXXX"><i>c</i><span XXXXX="msupsub"><span class="vlist-t XXXXX-XX"><span XXXXX="vlist-r"><span XXXXX="vlist"><span class="pstrut"></span><span XXXXX="XXXXXX reset-size6 size3 mtight"><span class="XXXX mtight">X</span></span></span><span class="XXXXX-s"></span></span><span XXXXX="vlist-r"><span class="XXXXX"><span></span></span></span></span></span></span></span></span></span>XX XXXX constant. And on XXXXXXX XXX<span class="XXXXX"><span class="XXXXX-mathml">n &XX; X</span><span class="katex-XXXX" aria-hidden="XXXX"><span XXXXX="XXXX"><span XXXXX="strut"></span><i>n</i><span XXXXX="XXXXXX"></span><span class="mrel">></span><span class="XXXXXX"></span></span><span class="XXXX"><span class="XXXXX"></span><span XXXXX="mord">X</span></span></span></span>, XXXXXXXXX an element in its XXXXXX position in a sorted XXXXX requires XXXXXXXX XXXX XX XXX XXXXXXXX, i.e.<span class="katex"><span XXXXX="XXXXX-mathml">c_2n/X + c_3</span><span XXXXX="katex-XXXX" aria-XXXXXX="XXXX"><span class="XXXX"><span XXXXX="XXXXX"></span><span XXXXX="mord"><i>c</i><span XXXXX="XXXXXXX"><span class="XXXXX-t vlist-XX"><span class="vlist-r"><span class="XXXXX"><span class="XXXXXX"></span><span XXXXX="sizing reset-size6 size3 XXXXXX"><span XXXXX="XXXX XXXXXX">X</span></span></span><span class="XXXXX-s"></span></span><span XXXXX="vlist-r"><span XXXXX="XXXXX"><span></span></span></span></span></span></span><i>n</i><span class="XXXX">/</span><span XXXXX="mord">X</span><span class="mspace"></span><span class="mbin">+</span><span class="mspace"></span></span><span class="XXXX"><span class="strut"></span><span XXXXX="XXXX"><i>c</i><span class="msupsub"><span XXXXX="XXXXX-t XXXXX-XX"><span XXXXX="vlist-r"><span XXXXX="XXXXX"><span XXXXX="pstrut"></span><span XXXXX="XXXXXX reset-XXXXX size3 mtight"><span XXXXX="XXXX mtight">3</span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span class="XXXXX"><span></span></span></span></span></span></span></span></span></span>time (<span XXXXX="katex"><span class="XXXXX-XXXXXX">XXXX/2</span><span XXXXX="katex-XXXX" aria-hidden="true"><span XXXXX="base"><span XXXXX="XXXXX"></span><span XXXXX="XXXX"><i>c</i><span XXXXX="XXXXXXX"><span XXXXX="vlist-t vlist-XX"><span class="XXXXX-r"><span XXXXX="XXXXX"><span class="pstrut"></span><span XXXXX="sizing XXXXX-size6 XXXXX XXXXXX"><span class="XXXX XXXXXX">2</span></span></span><span class="XXXXX-s"></span></span><span class="vlist-r"><span XXXXX="XXXXX"><span></span></span></span></span></span></span><i>n</i><span class="mord">/</span><span class="XXXX">2</span></span></span></span>for shifting XXX XXXXXXXX and<span XXXXX="XXXXX"><span XXXXX="XXXXX-mathml">XXX</span><span class="XXXXX-XXXX" XXXX-XXXXXX="true"><span class="XXXX"><span class="XXXXX"></span><span XXXXX="mord"><i>c</i><span XXXXX="XXXXXXX"><span XXXXX="XXXXX-t XXXXX-t2"><span class="vlist-r"><span XXXXX="vlist"><span class="pstrut"></span><span XXXXX="sizing reset-size6 size3 mtight"><span class="XXXX XXXXXX">X</span></span></span><span class="vlist-s"></span></span><span class="vlist-r"><span XXXXX="XXXXX"><span></span></span></span></span></span></span></span></span></span>for XXXXXXXXX the element).</p><p>$ X(n) & = X(n - X) + c_2(n - X)/X + c_3 \\ & = T(n - 2) + XXX(n - X)/X + XXX + \{c_2(n - X)/2 + c_3\} \\ & = X(X) + \cdot \XXXX \cdot + \{XXX(n - X)/2 + c_3\} + \{XXX(n - X)/X + XXX\} \\ & = c_1 + \frac {c_2} 2 \{X + 2 + \XXXX \XXXX \XXXX + (n - X)\} + c_3(n - X) \\ & = XXX + \XXXX {c_2} 2 \XXXX \XXXX {n(n - 1)} X + XXX(n - X) \\ & = \XXXXX(n^X)$</p><p><br></p>">
Attachment #1 Preview
