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	<id>https://eoa.aitzazimtiaz.xyz/index.php?action=history&amp;feed=atom&amp;title=Sorting_Problem</id>
	<title>Sorting Problem - Revision history</title>
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	<updated>2026-08-05T19:21:11Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
	<generator>MediaWiki 1.46.0</generator>
	<entry>
		<id>https://eoa.aitzazimtiaz.xyz/index.php?title=Sorting_Problem&amp;diff=22&amp;oldid=prev</id>
		<title>Aitzaz at 22:44, 3 August 2026</title>
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		<updated>2026-08-03T22:44:05Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw-interface=&quot;&quot;&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 18:44, 3 August 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot;&gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Input:&amp;#039;&amp;#039;&amp;#039;  A sequence of $n$ numbers $&amp;lt;a_1,a_2,a_3 \cdots a_n&amp;gt;$&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Input:&amp;#039;&amp;#039;&amp;#039;  A sequence of $n$ numbers $&amp;lt;a_1,a_2,a_3 \cdots a_n&amp;gt;$&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Output:&#039;&#039;&#039; A permutated reordering $&amp;lt;a_1^`, a_2^`,a_3^` \cdots a_n^`&amp;gt;$ so that  $&amp;lt;a_1^` \geq a_2^` \geq a_3^` \cdots   \geq a_n^`&amp;gt;$ or $&amp;lt;a_1^` \leq a_2^` \leq a_3^` \cdots  \leq a_n^`&amp;gt;$&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Output:&#039;&#039;&#039; A permutated reordering $&amp;lt;a_1^`, a_2^`,a_3^` \cdots a_n^`&amp;gt;$ so that  $&amp;lt;a_1^` \geq a_2^` \geq a_3^` \cdots   \geq a_n^`&amp;gt;$ or $&amp;lt;a_1^` \leq a_2^` \leq a_3^` \cdots  \leq a_n^`&amp;gt;$ &lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;ref&amp;gt;Cormen, Thomas H.; Leiserson, Charles E.; Rivest, Ronald L.; Stein, Clifford (2009). Introduction to Algorithms (3rd ed.). Cambridge, MA: The MIT Press. ISBN 978-0-262-03384-8.&amp;lt;/ref&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;&quot;&gt;&lt;div&gt; &lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;== References ==&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-side-deleted&quot;&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;&quot;&gt;&lt;div&gt;&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;&amp;lt;references /&amp;gt;&lt;/ins&gt;&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Aitzaz</name></author>
	</entry>
	<entry>
		<id>https://eoa.aitzazimtiaz.xyz/index.php?title=Sorting_Problem&amp;diff=21&amp;oldid=prev</id>
		<title>Aitzaz at 22:40, 3 August 2026</title>
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		<updated>2026-08-03T22:40:30Z</updated>

		<summary type="html">&lt;p&gt;&lt;/p&gt;
&lt;table style=&quot;background-color: #fff; color: #202122;&quot; data-mw-interface=&quot;&quot;&gt;
				&lt;col class=&quot;diff-marker&quot; /&gt;
				&lt;col class=&quot;diff-content&quot; /&gt;
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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 18:40, 3 August 2026&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l3&quot;&gt;Line 3:&lt;/td&gt;
&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot;&gt;Line 3:&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Input:&amp;#039;&amp;#039;&amp;#039;  A sequence of $n$ numbers $&amp;lt;a_1,a_2,a_3 \cdots a_n&amp;gt;$&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;&amp;#039;&amp;#039;&amp;#039;Input:&amp;#039;&amp;#039;&amp;#039;  A sequence of $n$ numbers $&amp;lt;a_1,a_2,a_3 \cdots a_n&amp;gt;$&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;br&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;tr&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;−&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Output:&#039;&#039;&#039; A permutated reordering $&amp;lt;a_1^`, a_2^`,a_3^` \cdots a_n^`&amp;gt;$ so that  $&amp;lt;a_1^` \geq a_2^` \&lt;del style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;geqa_3&lt;/del&gt;^` \cdots   \geq a_n^`&amp;gt;$ or $&amp;lt;a_1^` \leq a_2^` \leq a_3^` \cdots  \leq a_n^`&amp;gt;$&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot; data-marker=&quot;+&quot;&gt;&lt;/td&gt;&lt;td style=&quot;color: #202122; 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;&quot;&gt;&lt;div&gt;&#039;&#039;&#039;Output:&#039;&#039;&#039; A permutated reordering $&amp;lt;a_1^`, a_2^`,a_3^` \cdots a_n^`&amp;gt;$ so that  $&amp;lt;a_1^` \geq a_2^` \&lt;ins style=&quot;font-weight: bold; text-decoration: none;&quot;&gt;geq a_3&lt;/ins&gt;^` \cdots   \geq a_n^`&amp;gt;$ or $&amp;lt;a_1^` \leq a_2^` \leq a_3^` \cdots  \leq a_n^`&amp;gt;$&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
&lt;/table&gt;</summary>
		<author><name>Aitzaz</name></author>
	</entry>
	<entry>
		<id>https://eoa.aitzazimtiaz.xyz/index.php?title=Sorting_Problem&amp;diff=20&amp;oldid=prev</id>
		<title>Aitzaz: Initial text on sorting problem.</title>
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		<updated>2026-08-03T22:39:56Z</updated>

		<summary type="html">&lt;p&gt;Initial text on sorting problem.&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Stub}}The &amp;#039;&amp;#039;&amp;#039;sorting problem&amp;#039;&amp;#039;&amp;#039; is aimed at taking a numerically unordered list of sequence, and reordering this sequence into an ascended or descended sequence of order.&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Input:&amp;#039;&amp;#039;&amp;#039;  A sequence of $n$ numbers $&amp;lt;a_1,a_2,a_3 \cdots a_n&amp;gt;$&lt;br /&gt;
&lt;br /&gt;
&amp;#039;&amp;#039;&amp;#039;Output:&amp;#039;&amp;#039;&amp;#039; A permutated reordering $&amp;lt;a_1^`, a_2^`,a_3^` \cdots a_n^`&amp;gt;$ so that  $&amp;lt;a_1^` \geq a_2^` \geqa_3^` \cdots   \geq a_n^`&amp;gt;$ or $&amp;lt;a_1^` \leq a_2^` \leq a_3^` \cdots  \leq a_n^`&amp;gt;$&lt;/div&gt;</summary>
		<author><name>Aitzaz</name></author>
	</entry>
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