How to find all possible paths in a mxn matrix starting from the top left to reach the bottom right

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I'm trying to find all possible paths in a MxN matrix starting from the top left to reach the bottom right.
Four moves are allowed (up, down, right, left).

Example 1:
Input: 
[[1,2,3],[4,5,6]]

Output:
1 2 3 6
1 2 5 6
1 4 5 6
1 4 5 2 3 6

Example 2:
Input:
[[1,2,3],
[4,5,6],
[7,8,9]]

Output:
1 2 3 6 9
1 2 3 6 5 8 9
1 2 3 6 5 4 7 8 9
1 2 5 6 9
1 2 5 8 9
1 2 5 4 7 8 9
1 4 5 6 9
1 4 5 8 9
1 4 5 2 3 6 9
1 4 7 8 9
1 4 7 5 6 9
1 4 7 8 5 2 3 6 9

I got the following error
[1] [1, 2] [1, 2, 3] Traceback (most recent call last):
  File "/home/me/test.py", line 47, in <module>
    printAllPath(mat,0,0,[])
  File "/home/me/test.py", line 31, in printAllPath
    printAllPath(matrix, i, j+1, result) 
  File "/home/me/test.py.py", line 31, in printAllPath
    printAllPath(matrix, i, j+1, result) 
  File "/home/me/test.py", line 31, in printAllPath
    printAllPath(matrix, i, j+1, result) 
  [Previous line repeated 995 more times]
  File "/home/me/test.py", line 4, in printAllPath
    rows = len(matrix)
RecursionError: maximum recursion depth exceeded while calling a Python object

What I have tried:

Python

  1  def printAllPath(matrix, i, j, result):
  2  
  3      # get rows and columns
  4      rows = len(matrix)
  5      columns = len(matrix[0])
  6  
  7      # Track visited cell
  8      visited = [[False]*columns for k in range(rows)]
  9  
 10      # Define a queue
 11      q = []
 12      q.append((i,j))
 13      # result.append(matrix[i][j])
 14      # visited[i][j] = True
 15  
 16      while q:
 17          x, y = q.pop()
 18  
 19          # Destination reached
 20          if x == rows-1 and y == columns-1:
 21              print(result.append(matrix[x][y]))
 22  
 23  		# Condition
 24          if (x >= 0 and y >= 0 and x < rows  and y < columns and not visited[x][y]):
 25              q.append((x,y))
 26              result.append(matrix[x][y])
 27              visited[x][y] = True
 28              print(result, end=' ')
 29  
 30          # go to the right
 31          printAllPath(matrix, i, j+1, result) 
 32  
 33          # go to the down
 34          printAllPath(matrix, i+1, j, result)
 35  
 36          # go to the left
 37          printAllPath(matrix, i, j-1, result)
 38  
 39          # go to the up
 40          printAllPath(matrix, i-1, j, result)
 41  
 42  
 43  # Example
 44  mat = [[1,2,3],
 45          [4,5,6]]
 46  
 47  printAllPath(mat,0,0,[])

Posted 21-Feb-23 21:21pm

Maminiaina Rakotovao

Updated 22-Feb-23 0:15am

Richard MacCutchan

v6

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Comments

Richard MacCutchan 22-Feb-23 3:55am

Which line causes the error, and what is the value of the index in question?

Maminiaina Rakotovao 22-Feb-23 6:01am

Please check the update for the errors

Richard MacCutchan 22-Feb-23 6:19am

The error details are telling you that you have called printAllPath(matrix, i, j+1, result) 998 times, which seems excessive. So you need to check your logic to find out why it keeps repeating the same thing.

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OriginalGriff · Answer 1 · 2023-02-21T22:54:00

Getting your code to run does not mean it is right! :laugh:
Think of the development process as writing an email: compiling successfully means that you wrote the email in the right language - English, rather than German for example - not that the email contained the message you wanted to send.

So now you enter the second stage of development (in reality it's the fourth or fifth, but you'll come to the earlier stages later): Testing and Debugging.

Start by looking at what it does do, and how that differs from what you wanted. This is important, because it give you information as to why it's doing it. For example, if a program is intended to let the user enter a number and it doubles it and prints the answer, then if the input / output was like this:

Input   Expected output    Actual output
  1            2                 1
  2            4                 4
  3            6                 9
  4            8                16

Then it's fairly obvious that the problem is with the bit which doubles it - it's not adding itself to itself, or multiplying it by 2, it's multiplying it by itself and returning the square of the input.
So with that, you can look at the code and it's obvious that it's somewhere here:

C#

int Double(int value)
   {
   return value * value;
   }

Once you have an idea what might be going wrong, start using the debugger to find out why. Put a breakpoint on the first line of the method, and run your app. When it reaches the breakpoint, the debugger will stop, and hand control over to you. You can now run your code line-by-line (called "single stepping") and look at (or even change) variable contents as necessary (heck, you can even change the code and try again if you need to).
If you don't know how to use a debugger, then start here: pdb — The Python Debugger — Python 3.11.2 documentation[^]
Think about what each line in the code should do before you execute it, and compare that to what it actually did when you use the "Step over" button to execute each line in turn. Did it do what you expect? If so, move on to the next line.
If not, why not? How does it differ?
Hopefully, that should help you locate which part of that code has a problem, and what the problem is.
This is a skill, and it's one which is well worth developing as it helps you in the real world as well as in development. And like all skills, it only improves by use!