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Ch4 圖論演算法
第 46 題／共 111 題
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46. Transitive Closure、Topological Order、BFS
#AL-04-046
中
Transitive Closure
Topological Order
BFS
📝
☆
[10%] For the given directed graph (the numbers inside the vertices are the vertex indices), answer the following questions:
A
(a) [2%] Give the count of "1" elements in the transitive closure of this graph.
B
(b) [2%] Give a topological order of the vertices in the graph. (The answer is not unique; you only need to give a valid one.)
C
(c) [2%] Assume now that the direction of edge
2
→
5
2\to5
2
→
5
is flipped to
5
→
2
5\to2
5
→
2
. What happens to the topological order? If there still exists a topological order, give one. If no topological order exists now, explain why.
D
(d) [2%] Starting from the original graph, if one more edge
1
→
3
1\to3
1
→
3
is added, what happens to the topological order? If there still exists a topological order, give one. If no topological order exists now, explain why.
E
(e) [2%] Consider the following statement: "If a suitable starting vertex is selected, one can obtain the topological order of a directed graph using breadth-first search (BFS) if one exists." Indicate whether the statement is TRUE of FALSE. If your answer is TRUE, indicate how you will select the suitable starting vertex. If you answer if FALSE, describe one condition that makes BFS fail this task.
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