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03 - Depth First Search (Solution)

# 03 - Depth First Search (Solution) - The Hong Kong...

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Unformatted text preview: The Hong Kong University of Science & Technology COMP 271: Design and Analysis of Algorithms Fall 2007 Tutorial 3: Depth First Search (Solution) Below are the solution to the problems of the tutorial. Question 1 : (a) Show the tree produced by Depth-First Search (DFS) when it is run on the graph G (shown in the ﬁgure below), using vertex a as the source. Please also show the assigned time stamps (discovery and ﬁnishing time) for each vertex. Note: You must follow the order of vertices in the adjacency list shown in the table below. a: b: c: d: e: f: g: h: i: −→ −→ −→ −→ −→ −→ −→ −→ −→ b, c, d a, e, f a, d, g a, c, g, h b, f, i b, e, g c, d, f d e a b e i f c g Graph G d h Step 0: Step 1: (1, a b e i 1 a d g h e i b f c g d h c f Step 2: (1, Step 3: (1, a (2, (2, a d (3, b e i Step 4: c f g b h e i f c g d h (1, Step 5: (1, a (2, (2, a d (3, b (3, c f g b h e i f (4, c g (5, d h e i Step 6: (4, (1, Step 7: (1, a (2, (2, a (7, b (3, c (6, d (3, b h e i 2 c (6, d g (5, e i f (4, g (5, f (4, h Step 8: (1, Step 9: (1, a (2, (7, (2, a (7, b (3, c (6, d (3, b h (8, c (6, d g (5, e i Step 10: (2, f (4, g (5, e i f (4, h (8,9) (1, a (7,10) Step 11: (1, a (2, (7,10) b (3, c (6, d (3, b h (8,9) c (6,11) d g (5, e i Step 12: f (4, g (5, e i f (4, h (8,9) (1, Step 13: (1, a (2, (7,10) (2, a (7,10) b (3, c (6,11) d (3, b h (8,9) c (6,11) d g (5,12) e i f (4, g (5,12) e i 3 f (4,13) h (8,9) Step 14: (2, (1, a (7,10) Step 15: (2, (1, a (7,10) b (3, c (6,11) d (3, b h (8,9) c (6,11) d g (5,12) e i (14, f (4,13) g (5,12) e i f (4,13) (14,15) h (8,9) Step 16: (1, a (2, (7,10) Step 17: (2,17) (1, a (7,10) b (3,16) c (6,11) d (3,16) b h (8,9) c (6,11) d g (5,12) e i f (4,13) (14,15) (1,18) g (5,12) e i f (4,13) (14,15) (1,18) h (8,9) Step 18: (2,17) Result: (7,10) (2,17) a b (3,16) a (7,10) c (6,11) d (3,16) b h (8,9) c (6,11) d g (5,12) e i f (4,13) (14,15) g (5,12) e i 4 f (4,13) (14,15) h (8,9) (b) In the DFS tree of part(a), show the edges of the graph G which are not present in the DFS tree by dashed lines. DFS Tree: (1,18) a (2,17) (7,10) Tree edge d g (5,12) b (3,16) c (6,11) Back edge h (8,9) e i f (4,13) (14,15) 5 ...
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