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11 replies to this topic

### #1 psychic_mind

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Posted 15 August 2010 - 01:47 PM

There doesn't appear to be many algorithm puzzles on this forum, so I thought I would start some and see how they are received.

You are given an n x m matrix/array of 1s and 0s. You are given starting co-ordinates (A,B) and destination co-ordinates (X,Y). Your goal is to find the quickest path to get from start to finish moving 1 square at a time (no diagonals). However, you cannot move onto a square with a 1 in it. Effectively you have to solve a maze. The output should give directions and be something of the form:

`UUDDLRLUUD`

You can use this as a test case:

```m=10
n=10
A=0
B=0
X=9
Y=9

Maze {
0,1,0,0,0,1,0,0,0,0,
0,0,0,1,0,0,0,1,1,0,
0,1,1,1,1,1,1,1,0,0,
0,1,0,0,0,0,0,1,0,1,
0,1,0,1,1,1,0,1,0,1,
0,1,0,0,0,1,0,1,0,0,
0,1,1,1,0,1,0,1,1,0,
0,1,0,0,0,1,0,1,0,0,
0,1,0,1,1,1,0,1,0,1,
0,0,0,0,0,0,0,1,0,0
}
```
The most time efficient algorithm will be the winner (credit may also be given to the most memory efficient solution). Good Luck.

Edited by psychic_mind, 15 August 2010 - 01:48 PM.

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### #2 qwe qwe

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Posted 15 August 2010 - 02:10 PM

Spoiler for suggestion, not solution

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### #3 krityx

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Posted 15 August 2010 - 04:28 PM

sorry double post.

Edited by krityx, 15 August 2010 - 04:30 PM.

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### #4 krityx

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Posted 15 August 2010 - 04:30 PM

Spoiler for idea

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### #5 qwe qwe

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Posted 15 August 2010 - 08:47 PM

Spoiler for idea

Ingenious, I like that idea...
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### #6 K4D

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Posted 15 August 2010 - 10:03 PM

Spoiler for

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### #7 fedorocker

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Posted 16 August 2010 - 05:45 AM

Spoiler for idea

I was thinking that a little variation of this algorithm should work better. We could apply the algo. with two start points : the starting point(with every successive no. on the +ve scale i.e. 2,3,4,...) and the destination point(with every successive path unit getting a no. on the negative scale -2,-3,-4,...). This will first of all ensure that there exists an entry into the destination. The algo. will then stop as soon as a positive no. (obviously >1) is found besides a negative one. Also in case of multiple such paths, it is highly likely that we always get the shortest path.
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### #8 DeeGee

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Posted 16 August 2010 - 10:13 AM

Spoiler for I think

Spoiler for Just realised

Edited by DeeGee, 16 August 2010 - 10:17 AM.

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### #9 psychic_mind

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Posted 16 August 2010 - 10:32 AM

I think the correct solution has been found by krityx and implemented K4D. The algorithm should only have linear time complexity for a maze with N squares. Now I need to see if I something else for Algorithm 2!
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### #10 qwe qwe

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Posted 16 August 2010 - 02:29 PM

I think the correct solution has been found by krityx and implemented K4D. The algorithm should only have linear time complexity for a maze with N squares. Now I need to see if I something else for Algorithm 2!

In case you didn't get the VM I sent you, go check out the "Other Mind Boggling Stuff on the Web" forum...
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