Question

I am making a 3D maze in c++. I am having trouble with a recursive method to find a valid path between the two endpoints (starting point is m[0][0][0]; endpoint is m[7][7][7];). It checks positions in the array. If its contents are a 1, then it is a valid part of the path; if 0, it is not a valid part of the path. Here is my method:

bool Maze::findPath(int row, int column, int level,string path){
cout << "findPath " << row << ", " << column << ", " << level << " value " << m[row][column][level] << endl;
if(row < 0 || row > 7 || column < 0 || column > 7 || level < 0 || level > 7 ){
    cout << "Out of bounds" << endl;
    //system("PAUSE");
    return false;
}
else if(m[row][column][level] == 0){
    cout << "spot is zero" << endl;
    //system("PAUSE");
    return false;
}
else if(visited[row][column][level] == 1){
    cout << "visited" << endl;
    return false;
}
else if(row == 7 && column == 7 && level == 7 && m[row][column][level] == 1){
    cout << "Found!" << endl;
    //system("PAUSE");
    return true;
}
else{
    visited[row][column][level] = 1;
    //cout << "searching..." << endl;
    if(row < 7 && findPath(row + 1,column,level,path))
        return true;
    if(column < 7 && findPath(row,column + 1,level,path))
        return true;
    if(level < 7 && findPath(row,column,level + 1,path))
        return true;
    if(row > 7 && findPath(row - 1,column,level,path))
        return true;
    if(column > 7 && findPath(row,column - 1,level,path))
        return true;
    if(level > 7 && findPath(row,column,level - 1,path))
        return true;
}
return false;

}

So the method checks for “Out of bounds”, an invalid spot on the path (zero), a visited location. I’m not sure what exactly I’m missing, but the method returns true to mazes that are unsolvable. Can anybody see some blatant mistake that I may be missing with my recursive call? Thanks

EDIT: Fixed a few code mistakes, but it still seems to be “solving” unsolvable mazes.

Here’s an example of a solvable maze that it is saying is not possible to solve:

1 0 0 0 0 0 0 1 
0 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 1 
0 0 0 1 0 0 0 0 
1 0 0 1 0 1 0 0 
0 0 0 1 0 0 0 0 
1 0 0 1 0 0 0 1 

1 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 
1 1 1 1 0 0 0 0 
0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 
1 0 0 0 0 0 0 0 
0 1 1 0 0 0 0 0 
0 0 0 1 0 1 1 1 

0 0 0 0 0 0 0 1 
0 0 0 0 0 0 0 0 
0 0 0 1 0 0 0 1 
0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 
0 1 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 
0 0 0 1 0 0 0 0 

0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 
0 0 0 1 0 0 0 0 
0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 
1 0 0 0 0 1 0 0 
0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 1 

1 1 1 1 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 1 0 0 0 1 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 
1 0 0 0 0 1 0 0 
0 1 0 0 0 0 0 0 
1 0 0 0 0 0 0 1 

1 0 0 0 0 0 0 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 
0 0 0 0 0 0 1 0 
1 1 1 1 0 0 0 0 
0 0 0 1 0 0 0 0 
0 0 0 1 0 0 0 0 
1 1 1 1 0 0 0 1 

1 1 1 1 1 1 1 1 
0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 
0 0 0 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 1 0 0 0 0 0 
0 0 1 0 0 0 0 0 

0 0 1 0 0 0 0 1 
0 0 1 0 0 0 0 1 
0 0 1 0 0 0 0 1 
0 0 1 0 0 0 0 1 
0 0 1 1 0 0 0 1 
0 0 0 1 0 0 0 1 
0 0 0 1 0 0 0 1 
0 0 0 1 1 1 0 1 

Answer 1

There’s a problem in the findPath(++row,column,level,path) (and similar recursive calls): you don’t want the variable increments to carry over to the other recursive calls. (For example, the variable row in findPath(row,++column,level,path) would be affected by the first recursive call.)

Use findPath(row + 1,column,level,path) (and similar) instead.

Also, in the last three recursive calls, you’re not making the right tests:

//instead of level < 7
if(level < 7 && findPath(--row,column,level,path)) //should be row > 0
    return true;
if(level < 7 && findPath(row,--column,level,path)) //should be column > 0
    return true;
if(level < 7 && findPath(row,column,--level,path)) //should be level > 0
    return true;

EDIT

However, you don’t actually need these tests since you filter out out of bounds errors at the top of your recursive function. Therefore, these calls can be simplified to:

return  findPath(row + 1,column,level,path) || findPath(row,column + 1,level,path)
          || findPath(row,column,level + 1,path) || findPath(row - 1,column,level,path)
          || findPath(row,column - 1,level,path) || findPath(row,column,level - 1,path);

Additionally, the test && m[row][column][level] == 1 is redundant since the else if(m[row][column][level] == 0) takes care of that. (I’d check m[7][7][7] before even calling this function the first time, by the way.)