# 8 puzzle problem using depth first search in python

• 8 puzzle Problem using Branch And Bound
• Using Uninformed & Informed Search Algorithms to Solve 8-Puzzle (n-Puzzle) in Python / Java
• What is BFS? (Breadth-first Search)
• ## 8 puzzle Problem using Branch And Bound

In most scenarios, there will be additional constraints that will need to be fulfilled such as the time taken to reach the desired state, memory availability, maximum number of moves. The blank is used to slide other tiles that are horizontally or vertically adjacent into that position in an attempt to reach the goal state.

The objective is to rearrange the tiles from some random configuration to a specified goal configuration. The number of possible solvable states for the 8-puzzle is 9! However for the puzzle with 16! All that is required to execute a brute-force search is some legal operators, an initial state and an acknowledged goal state. Uninformed search generates the search tree without using any domain-specific knowledge.

Completeness and optimality Often in search, the input may be an implicit representation of an infinite graph. Given these conditions, a search algorithm is characterised as being complete if it is guaranteed to find a goal state provided one exists.

Breadth-first search is complete and when applied to infinite graphs it will eventually find the solution. Depth-first search is not complete and may get lost in parts of the graph that do not contain a goal state.

Breadth-First Search Breadth-first search is one of the simplest algorithms for searching a graph, it expands the nodes in a tree in the order of their given distance from the root, so it expands all the neighbouring nodes before going to the next level of the tree. The space requirement of breadth-first search is its largest deficiency.

The 8-tile has a search space of 9! In terms of practicality, with larger problem states such as the tile puzzle, a breadth-first search will exhaust the available memory rather quickly with its 16! Which also scales: The algorithm The algorithm is really simple, each state is just an array, so the goal state is [0, 1, 2, 3, 4, 5, 6, 7, 8].

To begin with each state gets added to a queue and a seen array. Only having to expand states. The number of states expanded rose sharply to You can see how this could get out of hand very quickly. Informed search attempts to minimise this by producing intelligent choices for each selected state.

This implies the use of a heuristic function which evaluates the likelihood that a given node is on the solution path. A heuristic is a function that ranks possible moves at each branching step to decide which branch to follow. The goal of a heuristic is to produce a fast estimation of the cost from the current state to the desired state, the closer the estimation is to the actual cost the more accurate the heuristic function.

In the context of the sliding-tile puzzle, to find best move from a set configuration the heuristic function is executed on each of the child states, the child state with the smallest heuristic value is chosen.

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Outputs The following figures and animations show how the 8-puzzle was solved starting from different initial states with different algorithms. Also, the figures display the search paths from starting state to the goal node the states with red text denote the path chosen. As can be seen, with this simple example all the algorithms find the same path to the goal node from the initial state. The problem. The 8-puzzle problem is a puzzle invented and popularized by Noyes Palmer Chapman in the s.

It is played on a 3-by-3 grid with 8 square blocks labeled 1 through 8 and a blank square. Your goal is to rearrange the blocks so that they are in order.

You are permitted to slide blocks horizontally or vertically into the blank square. The following shows a sequence of legal moves from an initial board position left to the goal position right.

Best-first search. We define a state of the game to be the board position, the number of moves made to reach the board position, and the previous state. First, insert the initial state the initial board, 0 moves, and a null previous state into a priority queue. Then, delete from the priority queue the state with the minimum priority, and insert onto the priority queue all neighboring states those that can be reached in one move. Repeat this procedure until the state dequeued is the goal state.

The success of this approach hinges on the choice of priority function for a state. We consider two priority functions: Hamming priority function. The number of blocks in the wrong position, plus the number of moves made so far to get to the state. Intutively, a state with a small number of blocks in the wrong position is close to the goal state, and we prefer a state that have been reached using a small number of moves. Manhattan priority function. The sum of the distances sum of the vertical and horizontal distance from the blocks to their goal positions, plus the number of moves made so far to get to the state.

For example, the Hamming and Manhattan priorities of the initial state below are 5 and 10, respectively.

In most scenarios, there will be additional constraints that will need to be fulfilled such as the time taken to reach the desired state, memory availability, maximum number of moves. The blank is used to slide other tiles that are horizontally or vertically adjacent into that position in an attempt to reach the goal state. The objective is to rearrange the tiles from some random configuration to a specified goal configuration.

The number of possible solvable states for the 8-puzzle is 9! However for the puzzle with 16! All that is required to execute a brute-force search is some legal operators, an initial state and an acknowledged goal state. Uninformed search generates the search tree without using any domain-specific knowledge. Completeness and optimality Often in search, the input may be an implicit representation of an infinite graph. Given these conditions, a search algorithm is characterised as being complete if it is guaranteed to find a goal state provided one exists.

### Using Uninformed & Informed Search Algorithms to Solve 8-Puzzle (n-Puzzle) in Python / Java

Breadth-first search is complete and when applied to infinite graphs it will eventually find the solution. Depth-first search is not complete and may get lost in parts of the graph that do not contain a goal state. Breadth-First Search Breadth-first search is one of the simplest algorithms for searching a graph, it expands the nodes in a tree in the order of their given distance from the root, so it expands all the neighbouring nodes before going to the next level of the tree.

The space requirement of breadth-first search is its largest deficiency. The 8-tile has a search space of 9! Outputs The following figures and animations show how the 8-puzzle was solved starting from different initial states with different algorithms.

Also, the figures display the search paths from starting state to the goal node the states with red text denote the path chosen. As can be seen, with this simple example all the algorithms find the same path to the goal node from the initial state.

The problem.

## What is BFS? (Breadth-first Search)

The 8-puzzle problem is a puzzle invented and popularized by Noyes Palmer Chapman in the s. It is played on a 3-by-3 grid with 8 square blocks labeled 1 through 8 and a blank square. Your goal is to rearrange the blocks so that they are in order. You are permitted to slide blocks horizontally or vertically into the blank square. The following shows a sequence of legal moves from an initial board position left to the goal position right.

Best-first search.

## thoughts on “8 puzzle problem using depth first search in python”

1. Faulrajas says:

And I have faced it. We can communicate on this theme.