There are the some examples of Iterative deepening search & Bidirectional Search with some definitions and some theory related to the both searches. If you have any query please ask in comment or mail i will be happy to help you

1. EXAMPLE OF ITERATIVE DEEPENING
SEARCH & BIDIRECTIONAL SEARCH
Presented by-
Abhijeet Agarwal
M.Tech 1st Year
Roll no- 1704301

2. CONTENT
 Search Strategies
 Iterative Deepening Search Technique
 Iterative deepening search l =0,1,2,3
 Properties of Iterative Deeping Search
 Examples of Iterative Deeping Search
 Bidirectional Search
 Search
 Factor Affect the Search
 Examples

3. SEARCH STRATEGIES
• A search strategy is defined by picking the order of
node expansion
• Strategies are evaluated along the following
dimensions:
– completeness: does it always find a solution if one
exists?
– time complexity: number of nodes generated
– space complexity: maximum number of nodes in
memory
– optimality: does it always find a least-cost solution?
• Time and space complexity are measured in terms of
– b: maximum branching factor of the search tree
– d: depth of the least-cost solution
– m: maximum depth of the state space (may be ∞)

4. ITERATIVE DEEPENING DEPTH
SEARCH TECHNIQUE
COMBINATION OF DEPTH FIRST
SEARCH AND BREADTH FIRST
SEARCH.

5. ITERATIVE DEEPENING SEARCH
– The problem with depth limited search on a
suitable depth parameter.
• This search tries all possible depth limits first 0,
then 1, then 2 etc un till a solution found.
• For large search space where is the depth of
solution is not known then it is normally
preferred.

6. ITERATIVE DEEPENING SEARCH L =0

7. ITERATIVE DEEPENING SEARCH L
=1

8. ITERATIVE DEEPENING SEARCH L
=2

9. ITERATIVE DEEPENING SEARCH L
=3

10. PROPERTIES OF ITERATIVE
DEEPENING SEARCH
• Complete- Yes
• Time- (b d)
• Space- (b d)
• Optimal- Yes, if step cost = 1

11. EXAMPLE 1:- SEARCH TREE FOR THE
8 PUZZLE PROBLEM

12. EXAMPLE 2:- 8-QUEENS PROBLEM
-any arrangement of n<=8 queens
-or arrangements of n<=8
queens in leftmost n
columns, 1 per column, such
that no queen
attacks any other.
initial state -no queens on the board
actions -add queen to any empty square
-or add queen to leftmost empty
square such that it is not attacked by other
queens.
goal test 8 queens on the board, none
attacked.
path cost-1 per move

13. BIDIRECTIONAL SEARCH WITH
EXAMPLES
• It is combination of feature of Breadth first, Best first, A*
search.
• Breadth first : Adds nodes to a list every time it checks
for the goal node using a tree structure until it is reached
• Best-first: Will choose which node should be next using
the node's score (often an f-value) which takes into
account its cost and length.
• A*: similar to best-first but will take into account the cost
of the path from the start to the specified node as well as
the cost from that node to the goal.
• The most effective map search would be bidirectional
combined with A*

14. BIDIRECTIONAL SEARCH
• Expand nodes from the start and goal state
simultaneously. Check at each stage if the nodes of one
have been generated by the other. If so, the path
concatenation is the solution
• The operators must be reversible
• single start, single goal
• Efficient check for identical states
• Type of search that happens in each half

15. SEARCH
• Optimality: yes
• Time complexity: O(b^d/2)
• Completeness: yes
• Space complexity: O(b^d/2)
Initial State
Final State
d
d /
2

16. FACTORS THAT AFFECT SEARCH EFFICIENCY
1- Branching factor: move in the direction with the
lower branching factor
I
G I
G

17. More start or goal states. Move towards the larger
set
I
G
G
G
I
G
I
I

18. EXAMPLE-1
 Suppose b = 10, d = 6.
 Suppose each direction runs BFS
 In the worst case, two searches meet when each
search has generated all of the nodes at depth 3.
 Breadth first search will examine 11, 11, 111
nodes.
 Bidirectional search will examine 2,220 nodes.

19. Example of Bi Directional Problem
Find the Shortest Root