Calculating Manhattan Distance in Python in an 8-Puzzle game

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I am trying to code a simple A* solver in Python for a simple 8-Puzzle game. I have represented the goal of my game in this way:

goal = [[1, 2, 3],
        [8, 0, 4], 
        [7, 6, 5]]

My problem is that I don't know how to write a simple Manhattan Distance heuristic for my goal. I know it should be defined as the sum of the distances between a generic state and my goal state. I think I should code something like:

def manhattan_distance(state):
    distance = 0
    for x in xrange(3):
        for y in xrange(3):
            value = state[x][y]
            x_value = x
            y_value = y
            x_goal = ...?
            y_goal = ...?
            distance += abs(x_value - x_goal) + abs(y_value - y_goal)
    return distance

My problem is that I don't have an explicit representation of the coordinates of the pieces in the goal state, so I don't know how to define 'x_goal' and 'y_goal' for the 'value' piece of the board. I am trying to do it using division and module operations, but it's difficult.

Can you give me some hints to define my 'x_goal' and 'y_goal' variables?

Thank you

Most pythonic implementation you can find.

assuming that,

0 1 2

3 4 5

6 7 8

is the goal state... AND,

1 5 3

4 2 6

7 8 9

is the final state.

initial_state = [1,5,3,4,2,6,7,8,0]
goal_state = [0,1,2,3,4,5,6,7,8]
def calculateManhattan(initial_state):
    initial_config = initial_state
    manDict = 0
    for i,item in enumerate(initial_config):
        prev_row,prev_col = int(i/ 3) , i % 3
        goal_row,goal_col = int(item /3),item % 3
        manDict += abs(prev_row-goal_row) + abs(prev_col - goal_col)
    return manDict

I don't know how else to explain this. It just works. Enjoy ! :D

I am trying to code a simple A* solver in Python for a simple 8-Puzzle game. I have represented the goal of my game in. Manhattan distance is the taxi distance in road similar to those in Manhattan. You are right with your formula. distance += abs(x_value - x_goal) + abs(y_value - y_goal) where x_value, y_valueis where you are and x_goal, y_goalis where you want to go.

Manhattan distance is the taxi distance in road similar to those in Manhattan. You are right with your formula

distance += abs(x_value - x_goal) + abs(y_value - y_goal)

where x_value, y_value is where you are and x_goal, y_goal is where you want to go.

This implementation using mhd uses this heuristic: the mhd between the point defined by the indices of each of '12346578' in current position and the point defined by the indices of each of '12346578' in goal

def h(self, node):
    """Heuristic for 8 puzzle: returns sum for each tile of manhattan
    distance between it's position in node's state and goal"""
    sum = 0
    for c in '12345678':
        sum =+ mhd(node.state.index(c), self.goal.index(c))
    return sum

Didnt try yet. Maybe link is of some help.

Don't import things you don't use. You can safely remove dt and sys . Don't overwrite builtins. all is already a function, and your implementation is more  The manhattan distance is the distance defined as the increase in the distance when moving pieces diagonally. If the movable tile is in the upper right hand corner, to move the piece to the bottom left hand corner, you can't move it directly along the diagonal. You have to make sequential left then down move. The increase is the manhattan distance.

I had the exact same question that you had, and I solved it by writing a different function that takes the representation you have and translates it into the representation you settled on (dictionary of value/coordinate pairs).

def make_dict(state):
    coordinate_dict = {}
    for x, row in enumerate(state):
        for y, value in enumerate(row):
            coordinate_dict[value] = (x, y)
    return coordinate_dict

That way, you get the best of both worlds. Whenever you want to treat the grid as a grid, you can use the original list-of-lists form, but if all you need is a quick lookup of where the value is for the Manhattan distance function, you can use the new dictionary you've created.

This is a python based 3x3 puzzle solver which solves the problem by using list Calculating Hamming Distance,. * Calculating Manhattan Distance (BONUS),. Python script for solving the classic "8-puzzle" game game python puzzle solver a-star heuristic 8-puzzle misplaced-tiles manhatten-distance 8-puzzle-solver Updated Jun 23, 2015

you may be able to use it

def manhatan_dist(board,goal_stat):
    #Manhattan priority function. The sum of the Manhattan 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 search node.
    import math
    b = board
    g = goal_stat

    manh_dist = 0
    for i in range (0,3,1):
        for j in range (0,3,1):
            bij = b[i][j]
            i_b = i
            j_b = j

            i_g, j_g = value_index(g,bij) 

            manh_dist += (math.fabs(i_g - i_b) + math.fabs(j_g - j_b))

    return manh_dist

This course teaches you how to calculate distance metrics, form and identify clusters A java program that solves the Eight Puzzle problem using five different search This python file solves 8 Puzzle using A* Search with Manhattan Distance. I have actually find this code somewhere it only use Manhattan as a heuristic function but i also want to use linear conflict and x-y heuristic so that the puzzle can be solved more efficiently.

The slide puzzle consists of a three by three board with eight numbered tiles furthermore, the best known algorithm for solving the eight puzzle optimally is A*. a program that uses BFS search and A* search to solve the Eight Puzzle game. The Manhattan distance heuristic is used for its simplicity and also because it is​  An eight-puzzle solver in python. GitHub Gist: instantly share code, notes, and snippets.

admissible heuristics is to relax one or more of the problem constraints, as we Manhattan distance computes for each tile how many moves it must make to The difficulty of finding a solution is a given domain depends, among other The program below solves the 8 puzzle using the A* algorithm with the Manhattan  Notice that each distance from x j to some x k, where x k < x j equals the distance from x i to x k plus the distance between x j and x i. If there are A points smaller than x j and S is the sum of distances from x i to smaller points, then the sum of distances from x j to smaller points equals S + ( x j – x i ) * A .

The 8-puzzle problem is a puzzle invented and popularized by Noyes Palmer a general artificial intelligence methodology known as the A* search algorithm. of the Manhattan distances (sum of the vertical and horizontal distance) from the count the blank square when computing the Hamming or Manhattan priorities. Manhattan distance. The distance between two points measured along axes at right angles.The Manhattan distance between two vectors (or points) a and b is defined as ∑i|ai−bi| over the dimensions of the vectors. Manhattan distance. all paths from the bottom left to top right of this idealized city have the same distance. Manhattan Distance

Comments
  • You're right to use divison and modulo operators. Try working out the formula on paper before writing any code.
  • I have seen other implementations using division and modulo operations, but they define the goal state in a different way. My problem is that I can't find anything in common between the elements in the second and third rows of my goal state...
  • How about: Relabel the pieces so the goal is 012345678 (easier to think about). Solve (textbook). Restore the original labels.
  • I have changed the representation of the goal state to a dictionary of labels with their coordinates. I don't know if there is a better solution, but now it works. Thank you anyway!
  • I know it would work, but a method like this would have a greater complexity than the method I was trying to code...
  • What is value_index?