Depth-First Search (DFS) Properties
•
•
•
•
Non-optimal solution path
Incomplete unless there is a depth bound
Exponential time
Linear space
BFS
Comments on Iterative Deepening
Search
•
Complexity
– Space complexity = O(bd)
– Time Complexity
• = O(bd)
(i.e., asymptotically the same as BFS or DFS in the the worst case)
• The overhead in repeated searching of the same subtrees is small relative to the
overall time
– e.g., for b=10, only takes about 11% more time than DFS
•
A useful practical method
– combines
• guarantee of finding an optimal solution if one exists (as in BFS)
• space efficiency, O(bd) of DFS
• But still has problems with loops like DFS
Time requirements for depth-first
iterative deepening on binary tree
Nodes at
each level
Nodes searched
by DFS
Nodes searched
by iterative DFS
1
1
1
2
+2
=
3
+3
=
4
4
+4
=
7
+7
=
11
8
+8
= 15
+15
=
26
16
+16
= 31
+31
=
57
32
+32
= 63
+63
= 120
64
+64
= 127
+127 = 247
+128 = 255
+255 = 502
128
12
Homework
Example