Puzzle Solving with A* Search
Learn how to solve the 3x3 grid 8-puzzle using A* search.
The 8-puzzle, also known as the sliding puzzle, was invented in the 1870s by Noyes Palmer Chapman and became widely popular after being marketed by Sam Loyd, who falsely claimed its invention. Initially seen as a simple yet challenging game, it later gained significance in the field of computer science and artificial intelligence as a classic problem for exploring search algorithms like A*.
Objective
Let's implement the A* search algorithm to solve a classic puzzle: the 8-puzzle. This exercise will help you understand how A* can be applied to solve problems where the goal is to arrange tiles in a specific order.
Puzzle Overview
The 8-puzzle consists of a 3x3 grid with 8 numbered tiles and one empty space. The goal is to move the tiles around until they are in a specific order. The puzzle starts in a scrambled state, and you need to move tiles to reach the goal state.
Steps to solve the puzzle
Here's a detailed guide to understanding and solving the 8-puzzle problem using the provided code. We'll break it down into logical steps and then explore how each part fits together programmatically.
Defining the puzzle states
The puzzle is represented as a state in which the tiles and the empty space (represented by 0) are arranged in a 3x3 grid. We will use a nested list where each sublist represents a row in the grid, here is the initial configuration of a puzzle:
start_state = [[1, 2, 3],[4, 0, 5],[7, 8, 6]]
Movement of the empty space
In the 8-puzzle, the empty space (represented by 0) can be moved up, down, left, or right within the grid. Each move changes the position of the 0 and swaps it with an adjacent tile. The valid moves depend on the current position of the empty space. Here's how to calculate possible moves for the empty space:
Determine position:
Convert the flat list index of the empty space to a 2D grid position (row, column) using
divmod.
Generate possible Moves:
Move up: If the empty space is not in the top row (row > 0), it can move up.
Move down: If the empty space is not in the bottom row (row < 2), it can move down.
Move left: If the empty space is not in the leftmost column (col > 0), it can move left.
Move right: If the empty space is not in the rightmost column (col < 2), it can move right.
def get_possible_moves(zero_index):"""Get possible moves for the empty space (0) in the 8-puzzle."""moves = []row, col = divmod(zero_index, 3)if row > 0: # Move upmoves.append(zero_index - 3)if row < 2: # Move downmoves.append(zero_index + 3)if col > 0: # Move leftmoves.append(zero_index - 1)if col < 2: # Move rightmoves.append(zero_index + 1)return moves
The ...