Question

Say I have two maps, each represented as a 2D array. Each map contains several distinct features (rocks, grass, plants, trees, etc.). I know the two maps are of the same general region but I would like to find out: 1.) if they overlap and 2.) if so, where does this overlap occur. Does anyone know of any algorithms which would help me do this?

[EDIT]
Each feature is contained entirely inside an array index. Although it is possibly to discern (for example) a rock from a patch of grass, it is not possible to discern one rock from another (or one patch of grass from another).

Answer 1

When doing this in 1D, I would for each index in the first collection (a string, really), try find the largest match in the second collection. If the match goes to the end, I have an overlap (like in action and ionbeam).

match( A on B ):
    for each i in length(A):
        see if A[i..] matches B[0..]
    if no match found: do the same for B on A.

For 2D, you do the same thing, basically: find an ‘edge’ of A that overlaps with the opposite edge of B. Only the edges aren’t 1D, but 2D:

for each point xa,ya in A:
    find a row yb in B that has a match( A[ya] on B[yb] )
        see if A[ya..] matches B[yb..]

You need to do this for the 2 diagonals, in each sense.