Calculate Manhattan from 8-Puzzle games in Python

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

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

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 am trying to write a simple A* solver in Python for a simple 8-Puzzle game.
I used this way to represent The goal of the game:

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 algorithm for my goal. I know it should be defined as a general state and my goal state. The sum of the distances between them. I think I should write similar code:

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 question is I didn’t clearly indicate the coordinates of the various parts in the goal state, so I don’t know how to define’x_goal’ and’y_goal’ for the “value” part of the chessboard. I tried to use division and module operations to accomplish it, but it was difficult. /p>

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

Thank you

You can find most pythonic implementations.

If you say,

0 1 2

3 4 5

6 7 8

is the target Country…
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]< br />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 to explain this. It just works. Please enjoy! : D