Question

I am solving an NxN puzzle in java 2D array. I can move to the empty tile in say four directions : LEFT, RIGHT, DOWN or UP. My question is if i get the indices(row en column values) of the empty tiles(node), how can i know if i must move LEFT, RIGHT, DOWN or UP to generate its successor(neighbour) nodes.

For instance if it is a 1Dimensional array of 9 elements then i can do something like: index is the index of the empty tile

if(index == 0){
            tempSuccessorNodes.add(new Node(swap(0,1,arrayPosition),curNode));
            tempSuccessorNodes.add(new Node(swap(0,3,arrayPosition),curNode));
        }
        else if(index == 1){
            tempSuccessorNodes.add(new Node(swap(0,1,arrayPosition),curNode));
            tempSuccessorNodes.add(new Node(swap(1, 4, arrayPosition),curNode));
            tempSuccessorNodes.add(new Node(swap(1, 2, arrayPosition),curNode));
        }

        ....

         if(index == 8){
            tempSuccessorNodes.add(new Node(swap(8, 7, arrayPosition),curNode));
            tempSuccessorNodes.add(new Node(swap(8, 5, arrayPosition),curNode));
        }

to generate the successors of the current node. But here am dealing with NxN(which 3×3 is an instance). How do i know if i must move LEFT, RIGHT, DOWN or UP after knowing the indices of the empty cell/tile/node?

I have a question here i posted earlier which relates to the same task am handling

Thanks

Answer 1

You’ll have to take two things into account, to determine in which direction you can move:

1. Whether you have already visited one of the neighboring tiles (otherwise, you risk entering an infinite loop). For that, each time you want to visit a tile you must check first if that tile has already been visited; if not add it to a set and visit it, otherwise ignore it. Notice that checking is easy, simply ask if the tile is already in the set.
2. For determining the neighbors of each tile, you must check four possible edge cases, in all other cases it’s safe to visit the tiles:
   • if the tile is in the first row, don’t go visiting the previous row
   • if the tile is in the last row, don’t go visiting the next row
   • if the tile is in the first column, don’t go visiting the previous column
   • if the tile is in the last column, don’t go visiting the next column