The document discusses the 8-puzzle problem and the A* algorithm. The 8-puzzle problem involves a 3x3 grid with 8 numbered tiles and 1 blank space that can be moved. The A* algorithm maintains a tree of paths from the initial to final state, extending the paths one step at a time until the final state is reached. It is complete and optimal but depends on the accuracy of the heuristic used to estimate costs.

1. Welcome to our
Presentation

2. 2
8 puzzle problem
 What is 8 puzzle Problem?
The 8-puzzle problem is a puzzle invented and popularized by
Noyes Palmer Chapman in the 1870s. It is played on a 3-by-3
grid with 8 square blocks labeled 1 through 8 and a blank
square.

3. Rules for solving the puzzle
Down
Left
Up
Right

4. Before we talk about the A* algorithm, we need to discussHeuristic Search
A Heuristic is a technique to
solve a problem faster than
classic methods, or to find an
approximate solution when
classic methods cannot. This is
a kind of a shortcut as we
often trade one of optimality,
completeness, accuracy, or
precision for speed.

5. How it works?
1. A* Algorithm maintains a tree of
paths originating at the initial state.
2. It extends those paths one edge at a
time.
3. It continues until final state is
reached.

6. Example

7. Example

8. Example

9. Example

10. Example

11. Pros
&
Cons
Pros:
 It is complete and optimal.
 It is the best one from other techniques. It is used to solve very complex problems.
 It is optimally efficient, i.e. there is no other optimal algorithm guaranteed to expand fewer nodes than A*.
Cons:
 This algorithm is complete if the branching factor is finite and every action has fixed cost.
 The speed execution of A* search is highly dependent on the accuracy of the heuristic algorithm that is used to compute h (n).
 It has complexity problems.

12. Important Note
A* Algorithm
is one of the
best path
finding
algorithms.
.
But it does
not
produce the
shortest
path
always.
This is
because it
heavily
depends on
heuristics.

13. Thank You