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Здравствуйте Уважаемые эксперты! Требуется ваша помощь
6. Теория графов
Найти кратчайшее расстояние от вершины B до вершин A, C, D, E, F, G.
A B C D E F G A ∞ 46 85 23 75 81 68 B 46 ∞ 68 15 64 57 20 C 85 68 ∞ 19 67 51 27 D 23 15 19 ∞ 46 51 23 E 75 64 67 46 ∞ 24 29 F 81 57 51 51 24 ∞ 52 G 68 20 27 23 29 52 ∞
Обсуждение
Неизвестный
05.01.2010, 17:07
общий
kot31: Здравствуйте.
Как у Вас обстоят дела с С? Могу представить процедуры которые ищут кратчайший путь по Алгоритму Дейкстры и Беллмана-Форда с занесением всех шагов в массив. Вам надо будет организовать заполнение входных данных и отображение выходных.
Неизвестный
05.01.2010, 17:27
общий
что такое С?
Неизвестный
05.01.2010, 17:53
общий
kot31: Язык программировния С.
Неизвестный
05.01.2010, 18:21
общий
Язык программировния С я незнаю. В институте нам препод сам объяснял,но на заочке большой матерьял,всё усвоить сложно. . .
Можно поступить следующим образом, если в Вашем распоряжении нет программы, реализующей какой-либо алгоритм решения поставленной задачи. Рассмотрим пути от вершины B до вершины A. Имеем: 1) путь, соединяющий вершины B и A непосредственно, длиной |BA| = 46. Все остальные пути не содержат это ребро; 2) путь, соединяющий вершины B и A через вершину D, включающий ребро |BD| = 15. Все остальные пути не содержат это ребро; 3) путь, соединяющий вершины B и A через вершину G, включающий ребро |BG| = 20. Все остальные пути не содержат это ребро. Пути, проходящие от вершины B к вершине A через вершины C, E, F, не рассматриваем, поскольку их длины будут заведомо больше длины |BA|.
Кандидатом в кратчайшие пути является путь |BA| = 46. Рассматриваем теперь пути, соединяющие вершины D и A. Имеем: 1) |DA| = 23; |BA| = |BD| + |DA| = 15 + 23 = 38; 2) |DC| = 19.
Кандидатом в кратчайшие пути теперь является путь |BA| = |BD| + |DA| = 38. Рассматриваем теперь пути, соединяющие вершины C и A. Имеем 1) |CA| = 85; |BA| = |BD| + |DC| + |CA| = 15 + 19 + 85 = 119 > 38; 2) |CG| = 27; |BD| + |DC| + |CG| = 15 + 19 + 27 = 61, хотя вершина A еще не достигнута.
Пути, соединяющие вершины G и A, при аналогичном рассмотрении имеют длины, большие 38.
Следовательно, кратчайшим путем, соединяющим вершины B и A, является путь, проходящий по ребрам BD и DA. Его длина равна 38.
Кратчайшие пути, соединяющие вершину B с другими вершинами, находятся аналогично. Здесь Вам придется потрудиться…
С уважением.
5
Об авторе:
Facta loquuntur.
Неизвестный
06.01.2010, 12:58
общий
Гордиенко Андрей Владимирович: спасибо большое,я понял как нужно решать ,если вас незатруднит(так как у вас глаз больше намётан), могли бы вы просто написать короткие пути остальных вершин без подробного объяснения, для самопроверки,хочу сделать без ошибок задание
Неизвестный
06.01.2010, 13:16
общий
Гордиенко Андрей Владимирович: у меня получилось: 1)B[$8594$]D[$8594$]A=38 2)B[$8594$]D[$8594$]C=34 3)B[$8594$]D=15 4)B[$8594$]D[$8594$]E=61 5)B[$8594$]F=57 6)B[$8594$]G=20
Гордиенко Андрей Владимирович: А расскажите, пожалуйста, как именно получается решение? Ручным перебором (суммированием) элементов матрицы? Я мало изучал теорию графов. Но мне казалось, что решения задач здесь получаются некоторыми матрично-векторными операциями.
В принципе можно решать и при помощи операций над матрицами. Но поскольку в условии задачи не был оговорен метод ее решения, то был применен перебор. Из матрицы брались только длины путей.
Хочется знать, как это делается. Думал: решит кто-нибудь задачу -- поучусь.
Конечно, книги надо читать, но так ведь было бы проще. Кстати, знаете что-нибудь попонятнее по теме?
Неизвестный
01.02.2010, 15:01
общий
Гордиенко Андрей Владимирович: могли бы вы ещё разок глянуть на задание, теперь мне нужно Найти кратчайшее расстояние от вершины D до вершин A, B, C, E, F, G. , у меня получилось:
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