https://lib.custis.ru/index.php?action=history&feed=atom&title=%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D1%80%D1%8E%D0%BA%D0%B7%D0%B0%D0%BA%D0%B5 2026-05-14T17:16:44Z История изменений этой страницы в вики MediaWiki 1.26.4 https://lib.custis.ru/index.php?title=%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D1%80%D1%8E%D0%BA%D0%B7%D0%B0%D0%BA%D0%B5&diff=27235&oldid=prev 2011-06-13T17:24:53Z

<p>Содержимое страницы заменено на «#REDIRECT [[discopal:{{PAGENAME}}]]»</p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='ru'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Предыдущая</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Версия 17:24, 13 июня 2011</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Строка 1:</td> <td colspan="2" class="diff-lineno">Строка 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><del class="diffchange diffchange-inline">Задача о рюкзаке (</del>[[<del class="diffchange diffchange-inline">Knapsack problem]]) содержательно </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">#REDIRECT </ins>[[<ins class="diffchange diffchange-inline">discopal:</ins>{{<ins class="diffchange diffchange-inline">PAGENAME</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">означает выбор предметов с наибольшей суммарной</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></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">стоимостью, умещающихся в рюкзак заданного размера.</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></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">Эта задача часто возникает при выборе оптимального управления</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></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">в различных экономико-финансовых областях (распределение</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></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">бюджета отдела по проектам и т. п.).</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></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>&#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></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">Задача имеет несколько более формальных постановок, представленных ниже.</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></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>&#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></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">== 0-1 Рюкзак ==</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></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>&#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></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">Даны натуральные числа &lt;m&gt;a_1,\ldots,a_n&lt;/m&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></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">(называемые «размерами» или «весами» предметов), </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></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">&lt;m&gt;c_1, \ldots, c_n&lt;/m&gt; («стоимости» предметов) </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></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">и ''B'' («размер» рюкзака).</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></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>&#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></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">Найти максимальное значение &lt;m&gt;f^*&lt;/m&gt; целевой функции</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></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">&lt;m&gt;&#160; f \equiv \sum_</del>{<del class="diffchange diffchange-inline">i=1}^n c_i x_i \to \max &lt;/m&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></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>&#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></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">с ограничением на размер «рюкзака»</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></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">&lt;m&gt;&#160; \sum_</del>{<del class="diffchange diffchange-inline">i=1</del>}<del class="diffchange diffchange-inline">^n a_i x_i \leq B, \ \ \ x_i \in \{0,1\</del>}<del class="diffchange diffchange-inline">.&lt;/m&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></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>&#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></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>&#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></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">==Алгоритмы==</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></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">* [[Задача о рюкзаке:жадный алгоритм</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></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">* [[Задача о рюкзаке:динамическое программирование]]</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></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">* [[Задача о рюкзаке:PTAS]]</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></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>&#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></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">[[Category:Задачи]]</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></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">{{replicate-from-custiswiki-to-lib}}</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></div></td></tr> </table>

StasFomin https://lib.custis.ru/index.php?title=%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D1%80%D1%8E%D0%BA%D0%B7%D0%B0%D0%BA%D0%B5&diff=9981&oldid=prev 2008-10-23T16:48:02Z

<p>1 версия</p> <table class='diff diff-contentalign-left'> <tr style='vertical-align: top;' lang='ru'> <td colspan='1' style="background-color: white; color:black; text-align: center;">← Предыдущая</td> <td colspan='1' style="background-color: white; color:black; text-align: center;">Версия 16:48, 23 октября 2008</td> </tr><tr><td colspan='2' style='text-align: center;' lang='ru'><div class="mw-diff-empty">(нет различий)</div> </td></tr></table>

WikiSysop https://lib.custis.ru/index.php?title=%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D1%80%D1%8E%D0%BA%D0%B7%D0%B0%D0%BA%D0%B5&diff=9980&oldid=prev 2008-10-22T15:40:43Z

<p>обновление данных</p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='ru'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Предыдущая</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Версия 15:40, 22 октября 2008</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l10" >Строка 10:</td> <td colspan="2" class="diff-lineno">Строка 10:</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>== 0-1 Рюкзак ==</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>== 0-1 Рюкзак ==</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>Даны натуральные числа &lt;<del class="diffchange diffchange-inline">math</del>&gt;a_1,\ldots,a_n&lt;/<del class="diffchange diffchange-inline">math</del>&gt; &#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>Даны натуральные числа &lt;<ins class="diffchange diffchange-inline">m</ins>&gt;a_1,\ldots,a_n&lt;/<ins class="diffchange diffchange-inline">m</ins>&gt; &#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;"><div>(называемые «размерами» или «весами» предметов), &#160;</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>(называемые «размерами» или «весами» предметов), &#160;</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>&lt;<del class="diffchange diffchange-inline">math</del>&gt;c_1, \ldots, c_n&lt;/<del class="diffchange diffchange-inline">math</del>&gt; («стоимости» предметов) &#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>&lt;<ins class="diffchange diffchange-inline">m</ins>&gt;c_1, \ldots, c_n&lt;/<ins class="diffchange diffchange-inline">m</ins>&gt; («стоимости» предметов) &#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;"><div>и ''B'' («размер» рюкзака).</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>и ''B'' («размер» рюкзака).</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>Найти максимальное значение &lt;<del class="diffchange diffchange-inline">math</del>&gt;f^*&lt;/<del class="diffchange diffchange-inline">math</del>&gt; целевой функции</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>Найти максимальное значение &lt;<ins class="diffchange diffchange-inline">m</ins>&gt;f^*&lt;/<ins class="diffchange diffchange-inline">m</ins>&gt; целевой функции</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>&lt;<del class="diffchange diffchange-inline">math</del>&gt;&#160; f \equiv \sum_{i=1}^n c_i x_i \to \max &lt;/<del class="diffchange diffchange-inline">math</del>&gt;</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>&lt;<ins class="diffchange diffchange-inline">m</ins>&gt;&#160; f \equiv \sum_{i=1}^n c_i x_i \to \max &lt;/<ins class="diffchange diffchange-inline">m</ins>&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'>&#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>с ограничением на размер «рюкзака»</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>с ограничением на размер «рюкзака»</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>&lt;<del class="diffchange diffchange-inline">math</del>&gt;&#160; \sum_{i=1}^n a_i x_i \leq B, \ \ \ x_i \in \{0,1\}.&lt;/<del class="diffchange diffchange-inline">math</del>&gt;</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>&lt;<ins class="diffchange diffchange-inline">m</ins>&gt;&#160; \sum_{i=1}^n a_i x_i \leq B, \ \ \ x_i \in \{0,1\}.&lt;/<ins class="diffchange diffchange-inline">m</ins>&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'>&#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> </table>

StasFomin https://lib.custis.ru/index.php?title=%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D1%80%D1%8E%D0%BA%D0%B7%D0%B0%D0%BA%D0%B5&diff=9809&oldid=prev 2008-08-04T09:55:52Z

<p>1 версия</p> <table class='diff diff-contentalign-left'> <tr style='vertical-align: top;' lang='ru'> <td colspan='1' style="background-color: white; color:black; text-align: center;">← Предыдущая</td> <td colspan='1' style="background-color: white; color:black; text-align: center;">Версия 09:55, 4 августа 2008</td> </tr><tr><td colspan='2' style='text-align: center;' class='diff-multi' lang='ru'>(не показана 1 промежуточная версия 1 участника)</td></tr><tr><td colspan='2' style='text-align: center;' lang='ru'><div class="mw-diff-empty">(нет различий)</div> </td></tr></table>

WikiSysop https://lib.custis.ru/index.php?title=%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D1%80%D1%8E%D0%BA%D0%B7%D0%B0%D0%BA%D0%B5&diff=2809&oldid=prev 2006-04-20T19:07:48Z

<p>реплицировано из внутренней CustisWiki</p> <p><b>Новая страница</b></p><div>Задача о рюкзаке ([[Knapsack problem]]) содержательно <br /> означает выбор предметов с наибольшей суммарной<br /> стоимостью, умещающихся в рюкзак заданного размера.<br /> Эта задача часто возникает при выборе оптимального управления<br /> в различных экономико-финансовых областях (распределение<br /> бюджета отдела по проектам и т. п.).<br /> <br /> Задача имеет несколько более формальных постановок, представленных ниже.<br /> <br /> == 0-1 Рюкзак ==<br /> <br /> Даны натуральные числа &lt;math&gt;a_1,\ldots,a_n&lt;/math&gt; <br /> (называемые «размерами» или «весами» предметов), <br /> &lt;math&gt;c_1, \ldots, c_n&lt;/math&gt; («стоимости» предметов) <br /> и ''B'' («размер» рюкзака).<br /> <br /> Найти максимальное значение &lt;math&gt;f^*&lt;/math&gt; целевой функции<br /> &lt;math&gt; f \equiv \sum_{i=1}^n c_i x_i \to \max &lt;/math&gt;<br /> <br /> с ограничением на размер «рюкзака»<br /> &lt;math&gt; \sum_{i=1}^n a_i x_i \leq B, \ \ \ x_i \in \{0,1\}.&lt;/math&gt;<br /> <br /> <br /> ==Алгоритмы==<br /> * [[Задача о рюкзаке:жадный алгоритм]]<br /> * [[Задача о рюкзаке:динамическое программирование]]<br /> * [[Задача о рюкзаке:PTAS]]<br /> <br /> [[Category:Задачи]]<br /> {{replicate-from-custiswiki-to-lib}}</div>

BenderBot https://lib.custis.ru/index.php?title=%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D1%80%D1%8E%D0%BA%D0%B7%D0%B0%D0%BA%D0%B5&diff=9808&oldid=prev 2006-04-19T16:23:52Z

<p></p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='ru'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Предыдущая</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Версия 16:23, 19 апреля 2006</td> </tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Строка 1:</td> <td colspan="2" class="diff-lineno">Строка 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>Задача о рюкзаке (Knapsack problem) содержательно &#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>Задача о рюкзаке (<ins class="diffchange diffchange-inline">[[</ins>Knapsack problem<ins class="diffchange diffchange-inline">]]</ins>) содержательно &#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;"><div>означает выбор предметов с наибольшей суммарной</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>означает выбор предметов с наибольшей суммарной</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;"><div>стоимостью, умещающихся в рюкзак заданного размера.</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>стоимостью, умещающихся в рюкзак заданного размера.</div></td></tr> </table>

StasFomin https://lib.custis.ru/index.php?title=%D0%97%D0%B0%D0%B4%D0%B0%D1%87%D0%B0_%D0%BE_%D1%80%D1%8E%D0%BA%D0%B7%D0%B0%D0%BA%D0%B5&diff=8812&oldid=prev 2006-04-19T10:47:39Z

<p>реплицировано из внутренней CustisWiki</p> <table class='diff diff-contentalign-left'> <col class='diff-marker' /> <col class='diff-content' /> <col class='diff-marker' /> <col class='diff-content' /> <tr style='vertical-align: top;' lang='ru'> <td colspan='2' style="background-color: white; color:black; text-align: center;">← Предыдущая</td> <td colspan='2' style="background-color: white; color:black; text-align: center;">Версия 10:47, 19 апреля 2006</td> </tr><tr><td colspan='4' style='text-align: center;' class='diff-multi' lang='ru'>(не показана 1 промежуточная версия 1 участника)</td></tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l1" >Строка 1:</td> <td colspan="2" class="diff-lineno">Строка 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>Задача о рюкзаке (<del class="diffchange diffchange-inline">[[</del>Knapsack problem<del class="diffchange diffchange-inline">]]</del>) содержательно &#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>Задача о рюкзаке (Knapsack problem) содержательно &#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;"><div>означает выбор предметов с наибольшей суммарной</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>означает выбор предметов с наибольшей суммарной</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;"><div>стоимостью, умещающихся в рюкзак заданного размера.</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>стоимостью, умещающихся в рюкзак заданного размера.</div></td></tr> </table>

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