Graphs Trees

1
Chapter 15
Graphs Trees Networks
2
(No Transcript)
3
Example
X Y
Z

T 5 VERTICES 6 EDGES
S
4

Collection List

Set   ArrayList LinkedList
SortedSet  
HashSet
TreeSet
5
(No Transcript)
6
(No Transcript)
7
(No Transcript)
8

X Y
Z

T X, Y, T, Z, S has length 4. Shortest path from
X to S ?
S In general, how can the smallest
path between 2 vertices be determined?
9
(No Transcript)
10

X Y
Z

T X, Y, T, Z, X is a cycle. Y, T, S, Z, T, Y is
not a cycle.
S Is Y, Z, T, S, Z, X, Y
a cycle?
11

Collection List

Set   ArrayList LinkedList
SortedSet  
HashSet
TreeSet This undirected graph is
acyclic.
12
(No Transcript)
13
(No Transcript)
14
(No Transcript)
15
(No Transcript)
16
(No Transcript)
17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21

Collection List

Set   ArrayList LinkedList
SortedSet  
HashSet
TreeSet
22
(No Transcript)
23
(No Transcript)
24
(No Transcript)
25
(No Transcript)
26
(No Transcript)
27
(No Transcript)
28
(No Transcript)
29
(No Transcript)
30
(No Transcript)
31

x v
Y
Z
T
S Assume the
vertices are entered in alphabetical
order. Perform a breadth-first iteration from S.
32
(No Transcript)
33
(No Transcript)
34
(No Transcript)
35
(No Transcript)
36
(No Transcript)
37
(No Transcript)
38
(No Transcript)
39

X V
Y
Z
T
S
40
Assume the edges are inserted into the graph as
follows S, T (Same as T, S) S, Z T, Y T,
Z V, Y V, Z X, Y X, Z Perform a breadth-first
iteration from S.
41
queue Vertex returned by next( ) S
T, Z S Z, Y T Y, V, X Z V,
X Y X V
X
42
Note For a breadth-first iteration of a directed
graph, the algorithm is the same, but neighbor
takes into account the direction of the
arrow.
A
B C
D For a breadth-first iteration starting
at A, the neighbors of A are B and C, but not D.
43
(No Transcript)
44

Collection List

Set   ArrayList LinkedList
SortedSet  
HashSet
TreeSet
45
(No Transcript)
46
A Stack!
47
(No Transcript)
48
(No Transcript)
49

X V
Y
Z
T
S
50
Assume the edges are inserted into the graph as
follows S, T // Same as T, S S, Z T, Y T,
Z V, Y V, Z X, Y X, Z Perform a depth-first
iteration from S.
51
Stack Vertex returned by next( ) S
Z, T S X, V, T Z Y, V, T X V,
T Y T
V T Top of stack is leftmost.
52
(No Transcript)
53
(No Transcript)
54
(No Transcript)
55
(No Transcript)
56
(No Transcript)
57
(No Transcript)
58
(No Transcript)
59
(No Transcript)
60
(No Transcript)
61
(No Transcript)
62
(No Transcript)
63
(No Transcript)
64
(No Transcript)
65
(No Transcript)
66
(No Transcript)
67
(No Transcript)
68
(No Transcript)
69
(No Transcript)
70
(No Transcript)
71
(No Transcript)
72
(No Transcript)
73
(No Transcript)
74
(No Transcript)
75
(No Transcript)
76
(No Transcript)
77
(No Transcript)
78
(No Transcript)
79
(No Transcript)
80
(No Transcript)
81
(No Transcript)
82
(No Transcript)
83
(No Transcript)
84
(No Transcript)
85
(No Transcript)
86
(No Transcript)
87
(No Transcript)
88
(No Transcript)
89
(No Transcript)
90
(No Transcript)
91
(No Transcript)
92
(No Transcript)
93
(No Transcript)
94
(No Transcript)
95
(No Transcript)
96
(No Transcript)
97
(No Transcript)
98
(No Transcript)
99
(No Transcript)
100
(No Transcript)
101
(No Transcript)
102
(No Transcript)
103
(No Transcript)
104
(No Transcript)
105
(No Transcript)
106
(No Transcript)
107
(No Transcript)
108
A collection in which order is unimportant A
linked list
109
(No Transcript)
110
(No Transcript)
111
(No Transcript)
112
(No Transcript)
113
(No Transcript)
114
(No Transcript)
115
(No Transcript)
116
(No Transcript)
117
(No Transcript)
118
(No Transcript)
119
(No Transcript)
120
(No Transcript)
121
(No Transcript)
122
(No Transcript)
123
(No Transcript)
124
(No Transcript)
125
(No Transcript)
126
(No Transcript)
127
(No Transcript)
128
(No Transcript)
129
(No Transcript)
130
(No Transcript)
131
(No Transcript)
132
(No Transcript)
133
(No Transcript)
134
(No Transcript)
135
(No Transcript)
136
(No Transcript)
137
(No Transcript)
138
(No Transcript)
139
(No Transcript)
140
(No Transcript)
141
(No Transcript)
142
(No Transcript)
143
(No Transcript)
144
(No Transcript)