CLEANRBT - Cleaning Robot


Here, we want to solve path planning for a mobile robot cleaning a rectangular room floor with furniture.

Consider the room floor paved with square tiles whose size fits the cleaning robot (1 × 1). There are 'clean tiles' and 'dirty tiles', and the robot can change a 'dirty tile' to a 'clean tile' by visiting the tile. Also there may be some obstacles (furniture) whose size fits a tile in the room. If there is an obstacle on a tile, the robot cannot visit it. The robot moves to an adjacent tile with one move. The tile onto which the robot moves must be one of four tiles (i.e., east, west, north or south) adjacent to the tile where the robot is present. The robot may visit a tile twice or more.

Your task is to write a program which computes the minimum number of moves for the robot to change all 'dirty tiles' to 'clean tiles', if ever possible.

Input

IThe input consists of multiple maps, each representing the size and arrangement of the room. A map is given in the following format.

w h
c11 c12 c13 ... c1w
c21 c22 c23 ... c2w
...
ch1 ch2 ch3 ... chw

The integers w and h are the lengths of the two sides of the floor of the room in terms of widths of floor tiles. w and h are less than or equal to 20. The character cyx represents what is initially on the tile with coordinates (x, y) as follows.

'.' : a clean tile
'*' : a dirty tile
'x' : a piece of furniture (obstacle)
'o' : the robot (initial position)

In the map the number of 'dirty tiles' does not exceed 10. There is only one 'robot'.

The end of the input is indicated by a line containing two zeros.

Output

For each map, your program should output a line containing the minimum number of moves. If the map includes 'dirty tiles' which the robot cannot reach, your program should output -1.

Example

Input:
7 5
.......
.o...*.
.......
.*...*.
.......
15 13
.......x.......
...o...x....*..
.......x.......
.......x.......
.......x.......
...............
xxxxx.....xxxxx
...............
.......x.......
.......x.......
.......x.......
..*....x....*..
.......x.......
10 10
..........
..o.......
..........
..........
..........
.....xxxxx
.....x....
.....x.*..
.....x....
.....x....
0 0

Output:
8
49
-1

hide comments
yousef hadder: 2014-03-16 07:48:07

i changed my 'vist' array from global int into local bool and my time differed by two seconds :\

BLANKRK: 2013-07-14 14:01:32

got AC but surly one of my non-regular type code .... :P

Mukesh Yadav: 2012-12-08 22:25:57

oh , got it Finally , thnx @ :D

Ahmed Abo El Kheir: 2012-09-22 19:19:12

what DP? Please tell me how you can solve a problem like this by DP because all what i can think about is BFS

:D: 2012-09-15 10:24:53

By looking at it per permutation your code is being very redundant. There is other, much more efficient DP approach. Maybe try looking at permutations sequences and try to think what can be limited. I will not straight out say how to do it.

Mukesh Yadav: 2012-09-15 10:19:27

Hey , How Did u get time so close to zero , i did it by finding all pairs shortest path and then checking all the permutations ...... Any Hints to improve this time limit pls ???


Added by:Camilo Andrés Varela León
Date:2007-07-26
Time limit:0.609s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: ERL JS-RHINO NODEJS PERL6 VB.NET
Resource:Japan Domestic, 2005