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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 DepthFirst 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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This note was uploaded on 10/18/2009 for the course COMP 271 taught by Professor Arya during the Spring '07 term at HKUST.
 Spring '07
 ARYA
 Algorithms

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