https://wiki.algo.informatik.tu-darmstadt.de/index.php?action=history&feed=atom&title=Big_O_notation
Big O notation - Revision history
2026-10-31T14:41:57Z
Revision history for this page on the wiki
MediaWiki 1.46.2
https://wiki.algo.informatik.tu-darmstadt.de/index.php?title=Big_O_notation&diff=1276&oldid=prev
Luedecke: Luedecke moved page Asymptotic notation to Big O notation
2014-10-18T16:04:44Z
<p>Luedecke moved page <a href="/Asymptotic_notation" class="mw-redirect" title="Asymptotic notation">Asymptotic notation</a> to <a href="/Big_O_notation" title="Big O notation">Big O notation</a></p>
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<td colspan="1" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:04, 18 October 2014</td>
</tr><tr><td colspan="2" class="diff-notice" lang="en"><div class="mw-diff-empty">(No difference)</div>
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Luedecke
https://wiki.algo.informatik.tu-darmstadt.de/index.php?title=Big_O_notation&diff=1275&oldid=prev
Luedecke at 16:03, 18 October 2014
2014-10-18T16:03:56Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 16:03, 18 October 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1">Line 1:</td>
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<tr><td class="diff-marker"></td><td style="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;"><br></td><td class="diff-marker"></td><td style="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;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div>:<math>\Theta(g(n)) = {f(n) : there exist positive constants <del style="font-weight: bold; text-decoration: none;">c1</del>,<del style="font-weight: bold; text-decoration: none;">c2 </del>and <del style="font-weight: bold; text-decoration: none;">n0 such that 0</del><<del style="font-weight: bold; text-decoration: none;">=''c''</del><<del style="font-weight: bold; text-decoration: none;">sub</del>><del style="font-weight: bold; text-decoration: none;">1</del><<del style="font-weight: bold; text-decoration: none;">/sub</del>><del style="font-weight: bold; text-decoration: none;">*g</del>(n) <del style="font-weight: bold; text-decoration: none;"><= </del>f(n) <del style="font-weight: bold; text-decoration: none;"><= c2*g</del>(n) for all ><del style="font-weight: bold; text-decoration: none;">= n0 </del>}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div>:<math>\Theta(g(n)) = <ins style="font-weight: bold; text-decoration: none;">\</ins>{f(n) :<ins style="font-weight: bold; text-decoration: none;"></math> </ins>there exist positive constants <ins style="font-weight: bold; text-decoration: none;"><math>c_1</math></ins>,<ins style="font-weight: bold; text-decoration: none;"><math>c_2</math> </ins>and <<ins style="font-weight: bold; text-decoration: none;">math>n_0</ins><<ins style="font-weight: bold; text-decoration: none;">/math</ins>> <ins style="font-weight: bold; text-decoration: none;">such that </ins><<ins style="font-weight: bold; text-decoration: none;">math</ins>><ins style="font-weight: bold; text-decoration: none;">0\le \;c_1g</ins>(n) <ins style="font-weight: bold; text-decoration: none;">\le \; </ins>f(n) <ins style="font-weight: bold; text-decoration: none;">\le \; c_2g</ins>(n)<ins style="font-weight: bold; text-decoration: none;"></math> </ins>for all <ins style="font-weight: bold; text-decoration: none;"><math</ins>><ins style="font-weight: bold; text-decoration: none;">n \ge \; n_0 \</ins>}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br></td><td class="diff-marker"></td><td style="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;"><br></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:<math>O(g(n)) = \{f(n) :</math> there exist positive constants <math>c</math> and <math>n_0</math> such that <math>0\le \; f(n) \le \; cg(n)</math> for all <math>n \ge \; n_0 \}</math></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br></td><td class="diff-marker"></td><td style="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;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div>:<math><del style="font-weight: bold; text-decoration: none;">O</del>(g(n)) = {f(n) : there exist positive constants <del style="font-weight: bold; text-decoration: none;">c1,c2 and n0 such that 0</del><<del style="font-weight: bold; text-decoration: none;">=''</del>c<del style="font-weight: bold; text-decoration: none;">''</del><<del style="font-weight: bold; text-decoration: none;">sub</del>><del style="font-weight: bold; text-decoration: none;">1</del></<del style="font-weight: bold; text-decoration: none;">sub</del>><del style="font-weight: bold; text-decoration: none;">*g</del>(n) <del style="font-weight: bold; text-decoration: none;"><= </del>f(n) <<del style="font-weight: bold; text-decoration: none;">= c2*g(n) </del>for all ><del style="font-weight: bold; text-decoration: none;">= n0 </del>}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div>:<math><ins style="font-weight: bold; text-decoration: none;">\Omega</ins>(g(n)) = <ins style="font-weight: bold; text-decoration: none;">\</ins>{f(n) :<ins style="font-weight: bold; text-decoration: none;"></math> </ins>there exist positive constants <<ins style="font-weight: bold; text-decoration: none;">math></ins>c<<ins style="font-weight: bold; text-decoration: none;">/math> and <math</ins>><ins style="font-weight: bold; text-decoration: none;">n_0</ins></<ins style="font-weight: bold; text-decoration: none;">math</ins>> <ins style="font-weight: bold; text-decoration: none;">such that <math>0 \le \; cg</ins>(n)<ins style="font-weight: bold; text-decoration: none;">\le \; </ins>f(n)<<ins style="font-weight: bold; text-decoration: none;">/math> </ins>for all <ins style="font-weight: bold; text-decoration: none;"><math</ins>><ins style="font-weight: bold; text-decoration: none;">n \ge \; n_0 \</ins>}</math></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br></td><td class="diff-marker"></td><td style="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;"><br></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:<math>o(g(n)) = \{f(n) :</math> for any positive constant <math>c > 0</math>, there exists ac constant <math>n_0 > 0</math> such that <math>0 \le \; f(n) < cg(n)</math> for all <math>n \ge \; n_0 \}</math></ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><br></td><td class="diff-marker"></td><td style="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;"><br></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div><del style="font-weight: bold; text-decoration: none;">:<math>\Omega(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div><del style="font-weight: bold; text-decoration: none;"></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div><del style="font-weight: bold; text-decoration: none;">:<math>o(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>[[File:anots.png]]</div></td><td class="diff-marker"></td><td style="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;"><div>[[File:anots.png]]</div></td></tr>
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Luedecke
https://wiki.algo.informatik.tu-darmstadt.de/index.php?title=Big_O_notation&diff=46&oldid=prev
Luedecke at 00:50, 10 September 2014
2014-09-10T00:50:44Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:50, 10 September 2014</td>
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<tr><td class="diff-marker"></td><td style="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;"><br></td><td class="diff-marker"></td><td style="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;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>:<math>o(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></div></td><td class="diff-marker"></td><td style="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;"><div>:<math>o(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div>[[File:anots.<del style="font-weight: bold; text-decoration: none;">jpg</del>]]</div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div>[[File:anots.<ins style="font-weight: bold; text-decoration: none;">png</ins>]]</div></td></tr>
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Luedecke
https://wiki.algo.informatik.tu-darmstadt.de/index.php?title=Big_O_notation&diff=45&oldid=prev
Luedecke at 00:50, 10 September 2014
2014-09-10T00:50:15Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:50, 10 September 2014</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10">Line 10:</td>
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<tr><td class="diff-marker"></td><td style="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;"><br></td><td class="diff-marker"></td><td style="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;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="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;"><div>:<math>o(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></div></td><td class="diff-marker"></td><td style="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;"><div>:<math>o(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></div></td></tr>
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Luedecke
https://wiki.algo.informatik.tu-darmstadt.de/index.php?title=Big_O_notation&diff=41&oldid=prev
Luedecke at 00:36, 10 September 2014
2014-09-10T00:36:17Z
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:36, 10 September 2014</td>
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<tr><td class="diff-marker" data-marker="−"></td><td style="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;"><div><math><del style="font-weight: bold; text-decoration: none;">x^</del>{<del style="font-weight: bold; text-decoration: none;">a+b</del>}</math></div></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:</ins><math><ins style="font-weight: bold; text-decoration: none;">\Theta(g(n)) = </ins>{<ins style="font-weight: bold; text-decoration: none;">f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:<math>O(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></ins></div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:<math>\Omega(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 }</math></ins></div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div> </div></td></tr>
<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="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;"><div><ins style="font-weight: bold; text-decoration: none;">:<math>o(g(n)) = {f(n) : there exist positive constants c1,c2 and n0 such that 0<=''c''<sub>1</sub>*g(n) <= f(n) <= c2*g(n) for all >= n0 </ins>}</math></div></td></tr>
</table>
Luedecke
https://wiki.algo.informatik.tu-darmstadt.de/index.php?title=Big_O_notation&diff=40&oldid=prev
Luedecke: Created page with "<math>x^{a+b}</math>"
2014-09-09T23:53:29Z
<p>Created page with "<math>x^{a+b}</math>"</p>
<p><b>New page</b></p><div><math>x^{a+b}</math></div>
Luedecke