diff --git a/ProninVV/aufgabe-1-data-structures/report/document.aux b/ProninVV/aufgabe-1-data-structures/report/document.aux index 391cf11..ce8bce9 100644 --- a/ProninVV/aufgabe-1-data-structures/report/document.aux +++ b/ProninVV/aufgabe-1-data-structures/report/document.aux @@ -10,5 +10,4 @@ \@writefile{toc}{\contentsline {subsection}{\numberline {2.3}Двоичное дерево поиска}{3}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {3}Методика эксперимента}{3}{}\protected@file@percent } \@writefile{toc}{\contentsline {section}{\numberline {4}Результаты и анализ}{3}{}\protected@file@percent } -\@writefile{toc}{\contentsline {section}{\numberline {5}Заключение}{3}{}\protected@file@percent } -\gdef \@abspage@last{4} +\gdef \@abspage@last{8} diff --git a/ProninVV/aufgabe-1-data-structures/report/document.pdf b/ProninVV/aufgabe-1-data-structures/report/document.pdf index 927339c..cbaed04 100644 Binary files a/ProninVV/aufgabe-1-data-structures/report/document.pdf and b/ProninVV/aufgabe-1-data-structures/report/document.pdf differ diff --git a/ProninVV/aufgabe-1-data-structures/report/document.synctex.gz b/ProninVV/aufgabe-1-data-structures/report/document.synctex.gz index 1d04987..c40314e 100644 Binary files a/ProninVV/aufgabe-1-data-structures/report/document.synctex.gz and b/ProninVV/aufgabe-1-data-structures/report/document.synctex.gz differ diff --git a/ProninVV/aufgabe-1-data-structures/report/document.tex b/ProninVV/aufgabe-1-data-structures/report/document.tex index d27b9b8..256db59 100644 --- a/ProninVV/aufgabe-1-data-structures/report/document.tex +++ b/ProninVV/aufgabe-1-data-structures/report/document.tex @@ -53,10 +53,54 @@ \section{Результаты и анализ} Было проведено 5 опытов. - \subsection{Связный список} + \subsection*{1. Бинарное дерево поиска (BST) и влияние порядка} + + \begin{figure}[H] + \includegraphics[scale=0.7]{plots/Tree.eps} + \end{figure} + + \begin{figure}[H] + \includegraphics[scale=0.7]{plots/Tre1.eps} + \end{figure} + + \begin{itemize} + \item \textbf{Деградация на отсортированных данных:} При вставке отсортированных данных время увеличилось с \textbf{0.12с} (1000 эл.) до \textbf{13.24с} (10000 эл.). Рост более чем в 100 раз при увеличении данных в 10 раз указывает на сложность $O(n^2)$ для заполнения. Дерево выродилось в список. + \item \textbf{Эффективность на перемешанных данных:} На \texttt{shuffled} данных вставка 10000 элементов заняла всего \textbf{0.03с}. Это подтверждает логарифмическую сложность $O(\log n)$ для сбалансированного дерева. + \end{itemize} + + \subsection*{2. Хеш-таблица: Стабильность и скорость} + + \begin{figure}[h] + \includegraphics[scale=0.7]{plots/hasht.eps} + \end{figure} + + \begin{itemize} + \item \textbf{Чувствительность к порядку:} Хеш-таблица показала идентичные результаты как на \texttt{shuffled}, так и на \texttt{sorted} данных (около \textbf{0.16с} для 10000 вставок). Это объясняется тем, что хеш-функция распределяет ключи по бакетам независимо от их исходного порядка. + \item \textbf{Превосходство:} На больших объемах хеш-таблица оказалась самой быстрой структурой для поиска и удаления ($\approx 0.001$с), что подтверждает среднюю сложность $O(1)$. + \item \textbf{Замечание} так как таблица содержит списки со вставкой в конец, при вставке наблюдается отклонение от линейной зависимости в сторону квадратичной + \end{itemize} + + \subsection*{3. Связный список: Стабильная медлительность} + + \begin{figure}[h] + \includegraphics[scale=0.7]{plots/llist.eps} + \end{figure} + + \begin{itemize} + \item \textbf{Поиск и удаление:} Связный список показал худшие результаты среди всех структур на случайных данных. Время поиска при 10000 элементах (\textbf{0.03с}) на два порядка медленнее, чем у хеш-таблицы. Это подтверждает линейную сложность $O(n)$. + \item \textbf{Вставка:} Вставка в конец без указателя на хвост дает $O(n^2)$ при заполнении (\textbf{3.04с} на 10000 эл.), что сопоставимо с выродившимся деревом. + \end{itemize} + + \subsection*{Вывод: выбор структуры данных} + \begin{enumerate} + \item \textbf{Хеш-таблица} — лучший выбор для реальных задач «ключ-значение». Она обеспечивает стабильное $O(1)$ и не зависит от порядка входящих данных. + \item \textbf{BST} — эффективен только при условии случайного распределения данных или использовании самобалансирующихся деревьев. В противном случае велик риск деградации до скорости списка. + \item \textbf{Связный список} — в данной реализации неэффективен для поиска и массовой вставки. Его стоит использовать только для специфических задач (стеки, очереди), где работа идет преимущественно с головой списка за $O(1)$. + \end{enumerate} - \section{Заключение} + + %\section{Заключение} % Ответ на вопрос о выборе структуры в реальной жизни \end{document} diff --git a/ProninVV/aufgabe-1-data-structures/report/document.toc b/ProninVV/aufgabe-1-data-structures/report/document.toc index ffb0d6e..c44e383 100644 --- a/ProninVV/aufgabe-1-data-structures/report/document.toc +++ b/ProninVV/aufgabe-1-data-structures/report/document.toc @@ -6,4 +6,3 @@ \contentsline {subsection}{\numberline {2.3}Двоичное дерево поиска}{3}{}% \contentsline {section}{\numberline {3}Методика эксперимента}{3}{}% \contentsline {section}{\numberline {4}Результаты и анализ}{3}{}% -\contentsline {section}{\numberline {5}Заключение}{3}{}% diff --git a/ProninVV/aufgabe-1-data-structures/report/plots/Tre1.eps b/ProninVV/aufgabe-1-data-structures/report/plots/Tre1.eps new file mode 100644 index 0000000..5249416 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