Anyone knows an algorithm for finding “shapes” in 2d arrays?

Question

Let\'s take this map, where \'#\' illustrates a taken square and \'.\' illustrates a free square:

1 . # # # . .
2 . # . . # .
3 # . . . . #
4 . # # # . .
5 . . . . .          


        

Answer 1

If you can convert your problem to a graph, what you are looking for is to identify connected components. And if a connected component does not contain an edge that is the boundary edge, then you have found the region that needs to be filled.

If I define the graph like this:

G = (V, E)
V = {r1, r2, r3, r4, r5, r6, c1, c2, c3, c4, c5, c6}
E = {(u, v) | u, v are elements of V && the cell(u, v) is not taken}

Now run DFS to find all disconnected trees. Algorithm:

for each u in V:
    color[u] = white

for each u in V:
    if color[u] == white:
        contains_boundary_edge = False
        DFS-visit( u, contains_boundary_edge )

        if not contains_boundary_edge:
            Flood-fill( u )

DFS-visit( u, contains_boundary_edge ):
    color[u] = gray
    for each v in adjacent( u ):
        if color[v] == white:
            if edge(u, v) is a boundary edge: // Can be easily identified if one of u, v is start or end row/col.
                contains_boundary_edge = True

            DFS-visit( v, contains_boundary_edge )

    color[u] = black