https://algorist.com/algowiki_v2/index.php?action=history&feed=atom&title=TADM2E_3.5 2026-05-01T09:09:39Z Revision history for this page on the wiki MediaWiki 1.28.0 https://algorist.com/algowiki_v2/index.php?title=TADM2E_3.5&diff=480&oldid=prev 2016-12-29T05:06:59Z

<p>Prettyprint using math extension</p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 05:06, 29 December 2016</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>1: Each node is identical, so the ratio of data over total should be: &lt;br&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>1: Each node is identical, so the ratio of data over total should be: &lt;br&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>4 <del class="diffchange diffchange-inline">/ (</del>4 + 3*4<del class="diffchange diffchange-inline">) </del>= 1/<del class="diffchange diffchange-inline">4</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">\frac{Data}{Data + 3*Pointers} = \frac{</ins>4<ins class="diffchange diffchange-inline">}{</ins>4 + 3*4<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\frac{</ins>1<ins class="diffchange diffchange-inline">}{4}</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;</ins>/<ins class="diffchange diffchange-inline">math&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: &lt;br&gt;</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: &lt;br&gt;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>4*n <del class="diffchange diffchange-inline">/ (</del>4*n + 4*(n-1)<del class="diffchange diffchange-inline">) </del>= <del class="diffchange diffchange-inline">4*n / 4 * (n + </del>n -1<del class="diffchange diffchange-inline">) </del>= <del class="diffchange diffchange-inline">n / </del>2<del class="diffchange diffchange-inline">*</del>n <del class="diffchange diffchange-inline">- 1, this approaches 1</del>/<del class="diffchange diffchange-inline">2 as n gets large</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">\frac{\text{Size of Leafs}}{\text{Size of Leaf} + \text{Size of Internal Nodes}} = \frac{</ins>4 * n<ins class="diffchange diffchange-inline">}{</ins>4*n + 4*(n-1)<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\frac{</ins>n<ins class="diffchange diffchange-inline">}{2n</ins>-1<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline"> \frac{1}{</ins>2<ins class="diffchange diffchange-inline">} (</ins>n<ins class="diffchange diffchange-inline">\to\infty)</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;</ins>/<ins class="diffchange diffchange-inline">math&gt;</ins></div></td></tr> </table>

Joky https://algorist.com/algowiki_v2/index.php?title=TADM2E_3.5&diff=479&oldid=prev 2016-12-29T04:55:54Z

<p>Undo revision 457 by <a href="/algowiki_v2/index.php/Special:Contributions/Letientai299" title="Special:Contributions/Letientai299">Letientai299</a> (<a href="/algowiki_v2/index.php?title=User_talk:Letientai299&amp;action=edit&amp;redlink=1" class="new" title="User talk:Letientai299 (page does not exist)">talk</a>), the hypothesis is that all node is identical, so the child pointers in the leaf node count as overhead even if not connected</p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 04:55, 29 December 2016</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>1: <del class="diffchange diffchange-inline">A tree with &lt;math&gt;n&lt;/math&gt; nodes would have &lt;math&gt;n-1&lt;/math&gt; edges, because our internal nodes have both parent and child pointers, we can say that the number of pointers </del>is <del class="diffchange diffchange-inline">equal to the double of edges. So</del>, the ratio of data over total should be: &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>1: <ins class="diffchange diffchange-inline">Each node </ins>is <ins class="diffchange diffchange-inline">identical</ins>, <ins class="diffchange diffchange-inline">so </ins>the ratio of data over total should be: <ins class="diffchange diffchange-inline">&lt;br&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&lt;math&gt;</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>4 <ins class="diffchange diffchange-inline">/ </ins>(4 <ins class="diffchange diffchange-inline">+ 3*</ins>4<ins class="diffchange diffchange-inline">) </ins>= 1/<ins class="diffchange diffchange-inline">4</ins></div></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">\frac{4n}{4n + </del>4<del class="diffchange diffchange-inline">*2*</del>(<del class="diffchange diffchange-inline">n-1)} = \frac{</del>4<del class="diffchange diffchange-inline">}{</del>4 <del class="diffchange diffchange-inline">+ 8} </del>= <del class="diffchange diffchange-inline">\frac{</del>1<del class="diffchange diffchange-inline">}{3} (n\to\infty)</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&lt;</del>/<del class="diffchange diffchange-inline">math&gt;</del></div></td><td colspan="2">&#160;</td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: &#160;</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: <ins class="diffchange diffchange-inline">&lt;br&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del class="diffchange diffchange-inline">&lt;math&gt; \frac{</del>4*n<del class="diffchange diffchange-inline">}{</del>(4*n + 4*(n-1))<del class="diffchange diffchange-inline">} </del>= <del class="diffchange diffchange-inline">\frac{</del>4*n<del class="diffchange diffchange-inline">}{</del>4 * (n + n -1)<del class="diffchange diffchange-inline">} </del>= <del class="diffchange diffchange-inline">\frac{</del>n<del class="diffchange diffchange-inline">}{</del>2*n - 1<del class="diffchange diffchange-inline">}&lt;/math&gt;</del>, this approaches <del class="diffchange diffchange-inline">&lt;math&gt;\frac{</del>1<del class="diffchange diffchange-inline">}{</del>2<del class="diffchange diffchange-inline">}&lt;/math&gt; </del>as n gets large</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>4*n <ins class="diffchange diffchange-inline">/ </ins>(4*n + 4*(n-1)) = 4*n <ins class="diffchange diffchange-inline">/ </ins>4 * (n + n -1) = n <ins class="diffchange diffchange-inline">/ </ins>2*n - 1, this approaches 1<ins class="diffchange diffchange-inline">/</ins>2 as n gets large</div></td></tr> </table>

Joky https://algorist.com/algowiki_v2/index.php?title=TADM2E_3.5&diff=457&oldid=prev 2016-10-19T09:59:56Z

<p></p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 09:59, 19 October 2016</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>1: <del class="diffchange diffchange-inline">Each node </del>is <del class="diffchange diffchange-inline">identical</del>, <del class="diffchange diffchange-inline">so </del>the ratio of data over total should be: <del class="diffchange diffchange-inline">&lt;br&gt;</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>1: <ins class="diffchange diffchange-inline">A tree with &lt;math&gt;n&lt;/math&gt; nodes would have &lt;math&gt;n-1&lt;/math&gt; edges, because our internal nodes have both parent and child pointers, we can say that the number of pointers </ins>is <ins class="diffchange diffchange-inline">equal to the double of edges. So</ins>, the ratio of data over total should be: &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>4 <del class="diffchange diffchange-inline">/ </del>(4 + 3<del class="diffchange diffchange-inline">*4</del>) <del class="diffchange diffchange-inline">= 1</del>/<del class="diffchange diffchange-inline">4</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;math&gt;</ins></div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">\frac{4n}{4n + </ins>4<ins class="diffchange diffchange-inline">*2*</ins>(<ins class="diffchange diffchange-inline">n-1)} = \frac{4}{</ins>4 + <ins class="diffchange diffchange-inline">8} = \frac{1}{</ins>3<ins class="diffchange diffchange-inline">} (n\to\infty</ins>)</div></td></tr> <tr><td colspan="2">&#160;</td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;</ins>/<ins class="diffchange diffchange-inline">math&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: <del class="diffchange diffchange-inline">&lt;br&gt;</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: &#160;</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>4*n <del class="diffchange diffchange-inline">/ </del>(4*n + 4*(n-1)) = 4*n <del class="diffchange diffchange-inline">/ </del>4 * (n + n -1) = n <del class="diffchange diffchange-inline">/ </del>2*n - 1, this approaches 1/<del class="diffchange diffchange-inline">2 </del>as n gets large</div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins class="diffchange diffchange-inline">&lt;math&gt; \frac{</ins>4*n<ins class="diffchange diffchange-inline">}{</ins>(4*n + 4*(n-1))<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\frac{</ins>4*n<ins class="diffchange diffchange-inline">}{</ins>4 * (n + n -1)<ins class="diffchange diffchange-inline">} </ins>= <ins class="diffchange diffchange-inline">\frac{</ins>n<ins class="diffchange diffchange-inline">}{</ins>2*n - 1<ins class="diffchange diffchange-inline">}&lt;/math&gt;</ins>, this approaches <ins class="diffchange diffchange-inline">&lt;math&gt;\frac{</ins>1<ins class="diffchange diffchange-inline">}{2}&lt;</ins>/<ins class="diffchange diffchange-inline">math&gt; </ins>as n gets large</div></td></tr> </table>

Letientai299 https://algorist.com/algowiki_v2/index.php?title=TADM2E_3.5&diff=118&oldid=prev 2014-09-11T18:22:24Z

<p>Recovering wiki</p> <table class="diff diff-contentalign-left" data-mw="interface"> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='en'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Older revision</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Revision as of 18:22, 11 September 2014</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Line 1:</td> <td colspan="2" class="diff-lineno">Line 1:</td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>1: Each node is identical, so the ratio of data over total should be: <del class="diffchange diffchange-inline">&amp;lt;</del>br<del class="diffchange diffchange-inline">&amp;gt;</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>1: Each node is identical, so the ratio of data over total should be: <ins class="diffchange diffchange-inline">&lt;</ins>br<ins class="diffchange diffchange-inline">&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>4 / (4 + 3*4) = 1/4</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>4 / (4 + 3*4) = 1/4</div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>−</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: <del class="diffchange diffchange-inline">&amp;lt;</del>br<del class="diffchange diffchange-inline">&amp;gt;</del></div></td><td class='diff-marker'>+</td><td style="color:black; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: <ins class="diffchange diffchange-inline">&lt;</ins>br<ins class="diffchange diffchange-inline">&gt;</ins></div></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"></td></tr> <tr><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>4*n / (4*n + 4*(n-1)) = 4*n / 4 * (n + n -1) = n / 2*n - 1, this approaches 1/2 as n gets large</div></td><td class='diff-marker'>&#160;</td><td style="background-color: #f9f9f9; color: #333333; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #e6e6e6; vertical-align: top; white-space: pre-wrap;"><div>4*n / (4*n + 4*(n-1)) = 4*n / 4 * (n + n -1) = n / 2*n - 1, this approaches 1/2 as n gets large</div></td></tr> </table>

Algowikiadmin https://algorist.com/algowiki_v2/index.php?title=TADM2E_3.5&diff=13&oldid=prev 2014-09-11T18:13:06Z

<p>Recovering wiki</p> <p><b>New page</b></p><div>1: Each node is identical, so the ratio of data over total should be: &amp;lt;br&amp;gt;<br /> <br /> 4 / (4 + 3*4) = 1/4<br /> <br /> 2: In a full tree, given n leaf nodes, there are n-1 internal nodes. Both leaf and internal nodes are worth 4 bytes: &amp;lt;br&amp;gt;<br /> <br /> 4*n / (4*n + 4*(n-1)) = 4*n / 4 * (n + n -1) = n / 2*n - 1, this approaches 1/2 as n gets large</div>

Algowikiadmin