https://github.com/primaryobjects/eightpuzzle
Eight Puzzle Solver using A*
https://github.com/primaryobjects/eightpuzzle
Last synced: 10 months ago
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Eight Puzzle Solver using A*
- Host: GitHub
- URL: https://github.com/primaryobjects/eightpuzzle
- Owner: primaryobjects
- Created: 2015-01-19T01:01:27.000Z (about 11 years ago)
- Default Branch: master
- Last Pushed: 2015-01-21T02:34:33.000Z (about 11 years ago)
- Last Synced: 2025-02-09T17:47:47.276Z (12 months ago)
- Language: JavaScript
- Homepage:
- Size: 152 KB
- Stars: 2
- Watchers: 3
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: readme.md
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README
Eight Puzzle Solver
=========
Solves the eight-puzzle (sliding block puzzle) by using the A* algorithm.
A* Algorithm Details
---
The program works by taking the starting state and evaluating the next possible moves, applying a cost value to each next state.
The cost (h) of a state is calculated by adding up the manhatten distance of each block from their goal state. For example, if a particular block is 3 moves left and 2 moves down from its goal state, then this adds 5 to the cost. You repeat this for the other blocks.
A cost (g) is also applied to each state, which cooresponds to the depth to reach this part of the path. This provides a penalty to re-visiting an already-visited state.
The final A* cost of a state is: f(n) = h(n) + g(n)
The A* algorithm then selects the next unvisited state with the lowest cost. The selected state may even be a parent state, higher up in the path. Each child state records it's parent, so that once a solution is found, you can walk backwards up the parent path to return the solution.
Compare the results of this program to online versions, using A* and manhatten distance:
https://n-puzzle-solver.appspot.com/
http://himanshug.info/8puzzle/8puzzle.html
Examples
---
```
start: [4, 7, 6,
3, 2, 8,
0, 5, 1],
end: [1, 2, 3,
4, 5, 6,
7, 8, 0],
```
A solution is found in 22 steps.
LLDRDRULURDLDRULLDRUUL
```
start: [2, 1, 5,
4, 0, 7,
6, 8, 3],
end: [1, 2, 3,
4, 5, 6,
7, 8, 0],
```
A solution is found in 22 steps.
LURDDLUURRDLULDRDRUULL
```
start: [6, 4, 8,
1, 5, 7,
0, 3, 2],
end: [1, 2, 3,
4, 5, 6,
7, 8, 0],
```
A solution is found in 26 steps.
LDDRUULDRULLDDRUULDDRURULL
Running It
---
```
node app
```
Fun Fact
----
The number of possible eight-puzzle configurations at each step from the goal can be calculated by running a breadth-first search from the goal. Then evaluate backwards down all paths. Doing this shows all possible board configurations from the goal, as shown below.
License
----
MIT
Author
----
Kory Becker
http://www.primaryobjects.com/kory-becker