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Консультация № 186351
11.06.2012, 15:29
94.84 руб.
0
4
1
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
Построить Эйлеров путь в графе, заданном своей матрицей смежности
Построить Эйлеров путь в графе, заданном своей матрицей смежности
Обсуждение
11.06.2012, 15:47
общий
Что Вы хотите получить?
1) какой-нибудь один Эйфелев путь;
2) алгоритм их нахожденияж
3) может, программу, которая их ищет;
4) что-то другое.
1) какой-нибудь один Эйфелев путь;
2) алгоритм их нахожденияж
3) может, программу, которая их ищет;
4) что-то другое.
Об авторе:
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
"Если вы заметили, что вы на стороне большинства, —
это верный признак того, что пора меняться." Марк Твен
11.06.2012, 23:01
общий
это ответ
Здравствуйте, Андрей!
Полученный неориентированный граф – связный. Эйлеров путь существует тогда и только тогда, когда граф связный и в нём ровно две вершины нечётной степени. В данном графе все вершины четной степени, значит, можем построить эйлеров цикл.
Эйлеров цикл существует тогда и только тогда, когда граф связный и в нём отсутствуют вершины нечётной степени.
Начиная со стартовой вершины v строим путь, добавляя на каждом шаге не пройденное еще ребро, смежное с текущей вершиной. Вершины пути накапливаются в стеке S. Когда наступает такой момент, что для текущей вершины w все инцидентные ей ребра уже пройдены, записываем вершины из S в ответ, пока не встретим вершину, которой инцидентны не пройденные еще ребра. Далее продолжаем обход по не посещенным ребрам.
Начнем с вершины 1
1-2-3-5-1-4-2-5-4-6-5-7-6-1
Полученный неориентированный граф – связный. Эйлеров путь существует тогда и только тогда, когда граф связный и в нём ровно две вершины нечётной степени. В данном графе все вершины четной степени, значит, можем построить эйлеров цикл.
Эйлеров цикл существует тогда и только тогда, когда граф связный и в нём отсутствуют вершины нечётной степени.
Начиная со стартовой вершины v строим путь, добавляя на каждом шаге не пройденное еще ребро, смежное с текущей вершиной. Вершины пути накапливаются в стеке S. Когда наступает такой момент, что для текущей вершины w все инцидентные ей ребра уже пройдены, записываем вершины из S в ответ, пока не встретим вершину, которой инцидентны не пройденные еще ребра. Далее продолжаем обход по не посещенным ребрам.
Начнем с вершины 1
1-2-3-5-1-4-2-5-4-6-5-7-6-1
А, ну да 
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